Breakthrough Drugs, Statistics, and Anecdotes: Three Things Every Individual Investor Needs to Know – Yield Curve Inversion and Recession – Part 3 of 3

02 Monday Dec 2019

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balanced probit model, BIS, bond yields, bonds, econometrics, economics, fixed income, forecast, forecasting, investing, math, mathematics, probabilities, probit, probit model, recession, spreads, statistics, yield curve, yield curve inversion

Here is the last article related to our discussion of observations by the financial media with only a handful of observations, statistics, and time series data. The goal here is to provide an actual example to see what some of the pitfalls are. Prior to starting that discussion, I wanted to provide links to the first and second articles:

The first article laid the groundwork for the idea that there are many misuses of statistics and related items which appear most everyday in the print and television financial media. Here is a link:

https://latticeworkwealth.com/2019/11/11/breakthrough-drugs-statistics-and-anecdotes-investing/

The second article focused more on time series data and using the normal distribution to make conclusions and predictions about the financial markets. As promised, I will be posting a more detailed mathematical article as a supplement. However, the point of this article is only to make you aware of what to look for in general. You do not need to feel the need to get very granular. The audience that really wants more information has contacted me offline and is very small. Here is a link:

https://latticeworkwealth.com/2019/11/20/breakthrough-drugs-statistics-and-anecdotes-time-series-statistics/

Now let’s begin our journey to sum up these two articles by using the specific example of a “yield curve inversion”. First, what exactly is the yield curve? Okay, we are going to keep this explanation simple. The point of this article is not to become an expert on bond yields. The yield curve is simply the interest rate (referred to as “coupon” in the financial jargon) of bonds at certain maturities. For U.S. Treasury issues, you normally look at the interest rate on one-month, three-month, and six-month U.S. Treasury Bills. Then you add in one-year, two-year, three-year, five-year, seven-year, and ten-year U.S. Treasury Notes. And finally, you have the thirty-year Treasury Bonds (otherwise referred to as the “long bond” in financial jargon). Why bills, notes, and bond? It is simply a naming convention for all U.S. Treasury debt less than twelve-months is a bill, between one-year and ten-years is a note, and anything greater than ten-years is a bond. Once you know all those interest rates, you draw a line that connects all of those interest rates from one-month U.S. Treasury Bills all the way to thirty-year U.S. Treasury Bonds.

Why do people focus on this? Well, first, you would expect that interest rates for one-month bills to be lower than thirty-year bonds. Think of it like this: if your friend borrowed $20 and was going to pay you back at the end of the week or in three years. What interest rate would you charge him/her? Now a totally altruistic person would say nothing. But let’s say you are trying to teach your kids the value of money. Most people would charge a greater amount of interest for three years compared to one week. The U.S. Treasury debt market works very similarly. People who loan the government money for one month normally demand a lower interest rate than those people who are going to have to wait thirty years to get their money back. When the economy is growing normally, the yield curve is called steep. It goes from lower interest rates and gradually moves higher. But that is not the only shape of the yield curve possible.

The other two are flat and inverted. A flat yield curve simply means that interest rates all along the various maturities are pretty much the same. Now, as our article will shift to, an inverted yield curve means that closer maturities actually have a higher interest rate than the very long-term maturities. Why does this happen? Well, most economists and financial professionals will tell you that the economy is slowing down and a recession is coming. Why? The last 7-8 recessions were preceded by a yield curve inversion. Let’s take a look at the yield curve over time by comparing two-year U.S. Treasury Notes with ten-year U.S. Treasury Notes. Keep in mind that we are taking a look at the difference between the two. A number that is positive means that interest rates are higher for ten-year bonds and a negative number means just the opposite.

Here is a daily comparison from June 1, 1976 through November 6, 2019:

Daily Spreads - All Data

Here is the same comparison but on a monthly basis:

Monthly Spreads - All Data

I used a graph of the month difference (“spread”) to smooth out some of the volatility. Now if you remember your economic history, you will notice that there are negative “spreads” that occur prior to a downturn in the U.S. economy. Let’s focus on the yield curve inversion prior to the Financial Crisis. As you can see, the yield curve was inverted at various times over the course of 2006 to 2008. It took approximately two years from the yield curve inversion before the Financial Crisis hit in full force in September 2008. Because this pattern has occurred before, economists and financial professionals appearing on television or writing articles have pointed to the yield curve inversion just recently.

But you should take a closer look at the latest inversion of the yield curve. It is only a small difference and only lasted for a short period of time. I will blow it up to investigate and will show November 1, 2018 through October 31, 2019:

Daily Spreads - 2018 to 2019

I had to use a one-year timeframe to even be able to get the difference in interest rates to show up. So, for a period during August 2019 and September 2019, there were a plethora of financial markets’ articles and television commentators who talked about how soon a recession would take place in the U.S. economy. In fact, there were days when over 25% of the day’s coverage of financial market news focused only on this yield curve inversion. Now, will the U.S. economy go into recession in the next 12-24 months? Well, that is still an open question. The main point is that the financial news media focus on things that have similar patterns for only a brief period of time. Even worse though, financial “experts” who know very little about the bond market and economics start making predictions. And, as I have said many times in the past, the financial news media rarely, if ever, invites guests back or has another article written about how wrong they were.

Lastly, you will sometimes here people say that there is a 30% chance that the U.S. economy will enter a recession in the next 12-24 months. Where does that percentage come from? Oftentimes, it is a “best guess”. Unless you hear that same financial professional talk about a probity econometric model that came up with that percentage of recession probability, you should take the comment with a “grain of salt”. Trust me though, most financial professionals are not running probit models when they tell you their opinion on this matter (related to an inverted yield curve or due to another topics/event). In the supplemental article that is forthcoming, I will actually discuss a panel probit model that the Bank of International Settlements (BIS) just ran to look at the phenomenon of yield curve inversion preceding a recession in an economy. It is not that the percentages derived are “correct” per se. The important point is that they are not “pulled out of a hat” by someone.

I hope that this series of articles has been helpful in covering this important topic. The main takeaway is that, whenever you hear or read about a financial market prediction, you should always look to see how many examples (observations) are being used. If it is less than 30, you should not take it very seriously at all. Additionally, any time series data that is trending upward or downward cannot be used to talk about the financial markets. Remember you need to first-difference the time series data or adjust it in some other manner. Why? Otherwise, there may be correlations between two or more time series that just are not really there because the trend dominates. (Please refer to the second article for more information in this regard). So, please be more aware and skeptical of what you hear or read. It is not that the information/prediction is totally wrong. The salient thing is that it should be based on sound statistics and mathematics.

Breakthrough Drugs, Statistics, and Anecdotes: Three Things Every Individual Investor Needs to Know – Statistics and Time Series Data – Part 2 of 3

20 Wednesday Nov 2019

Posted by wmosconi in asset allocation, correlation, correlation coefficient, finance theory, financial advice, Financial Media, Financial News, financial services industry, historical returns, Individual Investing, individual investors, investing, investing advice, investing tips, risks of stocks, standard deviation, stock market, Stock Market Returns, time series, time series data

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correlation, correlation coefficient, Financial Market History, financial markets, Financial Media, Financial News, invest, investing, investing tips, math, mathematics, noise, statistics, time series, time series data

The first article of this three-part series covered the broad strokes of this issues to be aware of in terms of all the “data” and “relationships” that get thrown around by the financial media (print and television). Most of the discussion uses data points that are not statistically significant to draw any sort of conclusion. In fact, time series data is notoriously hard to model and predict the future. Additionally, the specific time series data of stock market returns is even more difficult.

You can refer to the link below to examine the content of the first article:

https://latticeworkwealth.com/2019/11/11/breakthrough-drugs-statistics-and-anecdotes-investing/

The task at hand for the second article is to put some “meat on the bones” of the discussion. I realize that anything to do with math and statistics is not easy for everyone (or of interest either). Therefore, I will be writing a supplemental article that covers the mathematics and statistics in more detail. The goal here is to be able to identify some of the more common errors that you will encounter.

The first item to talk about is any sort of data that has a substantial trend component. In layman’s terms, there is a data series where the line graph goes up or down in more of a straight-line manner. You can think of the Gross Domestic Product (GDP) of the United States here. Every year the GDP figures will generally go up unless there is a recession. But, even after the recession passes, the trend for GDP will resume upward. So, where does the problem come in?

I am going to give a contrived example to illustrate why it is dangerous to compare two series that are trending. The example will consist of two different equations which are trends. Both have the same trend component and an error term (we will call that eta). The variables will be exactly the opposite. More specifically, the two equations we will use are the following:

Trend_1 = Time + 100 + 0.9 * x + eta

Trend_2 = Time +100 – 0.9 * x + eta

Now the x values and eta values were simply generated by selected variables at random between 0 and 1. The eta values were also selected at random between 0 and 1. You can think of eta as representing the general “noise” that occurs on a daily basis when observing stock prices in the financial markets. So, let’s graph the first 100 observations for these two equations:

Trend_Graph_Statistics_Revised

You will notice that the trend component dominates the line graphs. However, we know by construction that the two equations which produce trend_1 and trend_2 are fundamentally different. Now the correlation coefficient between those two equations is 0.9984. A correlation coefficient of 1 means that the two lines move in lockstep. Why is this important? Why is it very dangerous?

Well, financial pundits will talk about these types of graphs all the time. It looks like there is some relationship, but we know there is very little relationship between the two trends. In fact, we can look at these equations by subtracting the current value from the previous value to see what changes. Formally, this topic is called first differencing. It will allow us to see more clearly what we already know. Here is the graph:

First_Difference_Graph_Statistics_Revised

Now we have a totally different picture. We can see that at many times the two trend equations are moving in exactly the opposite direction. In fact, the correlation coefficient for the first-differenced equations is 0.2675. There is only a slight positive relationship between the two trends.

In the example above, we can see that looking at the two trends is very deceiving. Remember that I added the eta term to represent “noise” that is always present in financial market data. So, anytime someone talks to you about the comparison of two trends, you should be very skeptical. You always want to see first-differenced data or at least a comparison of changes in some manner. Otherwise, you will mistakenly assume that there is a strong positive or negative relationship between two time series.

The second example that I am going to use is stock market returns for the S&P 500 Index from 1966 through 2018. Why start at 1966? Well, the S&P 500 Index started with its current number of component stocks back in 1957, and I would like to show annual stock returns and also ten-year annualized returns. This particular topic can get messy quite quickly, so I am not going to cover it in a lot of depth with statistical and mathematical jargon. For those of you who are interested, I had mentioned that it will be contained in a forthcoming supplemental article.

A great many individuals in the financial markets talk about stock market returns in the same breath as the normal distribution. What is the normal distribution? It is the old bell curve that you are familiar with. The normal distribution is symmetrical and tails off at the end as more and more data points are gathered. Well, stock market returns are anything but strongly normal.

Let’s first take a look at one-year stock market returns for the S&P 500 Index.

One Year Returns - Histogram - Non Normal

A useful test to see if a particular distribution is normal is the Jarque-Bera test. Now it is not necessary to know exactly what is being calculated. However, you should refer to the bottom of the box that reads “Probability”. The value of 0.179 is called a p-value. A p-value less than or equal to 0.10 means that we can reject the hypothesis that the one-year distribution of stock returns is normal. At a value of 0.179, we would not reject the hypothesis of normality for this distribution. However, the p-value in our case is not large enough to be totally sure and confident. But what about looking at annualized stock market returns over ten-year periods?

We can look at a similar graph to check to see if stock market returns over longer timeframes are indeed akin to the normal distribution (i.e. the bell curve). Here is the graph:

Ten Year Returns - Histogram - Non Normal

Looking at the same “Probability” value, we have 0.489. Therefore, we cannot reject the hypothesis that these stock market returns follow a normal distribution. Looking at ten-year annualized stock market data tells us that we can use the normal distribution as an assumption for calculating statistics.

Now why does this matter? Well, you will here over and over again statistics that apply only to the normal distribution in relationship to actual, observed stock market returns. We have just seen that stock market returns over the short-term stock returns weakly follow the normal distribution. On the other hand, long-term stock returns are definitely normal. Now I will not get into the technicalities, but time series data is indeed asymptotically normal. What? Say again?

This is just a fancy way of saying that, as the number of data points (sample size) approaches infinitely, the time series will look like the normal distribution. Pretty much all financial market and economic data have very few data points. In fact, you usually need several hundred data points prior to making any assumptions and using the statistics related to the normal distribution (think standard deviation or correlation coefficients).

Thus, most of the banter in the financial media is just subjective notions of what is going on in the stock market and the economy. More often than not, an assertion by someone in the financial print or television media is more of an educated guess than based on a solid mathematical foundation. That fact explains why financial pundits hedge their statements. Like I say half-jokingly, “I see the stock market going up in the next several months, but of course it might not resume its uptrend or could even take a leg downward”.

Well yes, I guarantee you that every day stocks will go up, down, or remain unchanged. This type of daily commentary in the financial press about the short-term performance of stocks (or other financial assets) is just not helpful and can be downright distracting you from investing for your long-term financial goals.

I apologize for getting too detailed in certain parts of this article. What are the key takeaways? First, you should be extremely leery of drawing any conclusions from the comparison of two or more data series that are trending upward or downward. Second, you need to have several hundred observations prior to invoking any reference to the normal distribution. So, what is left after that? As you might imagine, there are not too many comparisons or studies that pass the muster to give you insights on investing or actionable information to make changes to your investment portfolio.

Don’t focus on the mathematics or statistics. All you need to remember are the two takeaways above. And, first and foremost, you should always be skeptical whenever you are presented with comparisons and statistics related to the financial market or the economy as a whole.

Breakthrough Drugs, Statistics, and Anecdotes: Three Things Every Individual Investor Needs to Know – Part 1 of 3

11 Monday Nov 2019

Posted by wmosconi in asset allocation, Education, financial advice, financial goals, financial markets, Financial Media, Financial News, financial planning, financial services industry, investing, investing advice, investing information, investing tips, investment advice, investments, math, personal finance, portfolio, S&P 500, S&P 500 Index, statistics, time series, time series data

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asset allocation, Financial Media, Financial News, financial planning, investing, investing advice, investing information, investing tips, noise, statistics, time series, time series data

Although the title might appear to be random at first glance, I promise that there is an underlying theme. This article is the first in a three-part series that will discuss how individual investors are bombarded with information about what happens in the financial market. Most of the time you might hear that, 5 out of the last 7 times “x” happened, the S&P 500 index went up by 10% or more. I will argue that most of these types of comments might be useful trivia for the television show, Jeopardy; however, they should not impact your long-term investment plan.

So, why did I use breakthrough drugs? Prior to any drug coming to the marketplace, the FDA does a very thorough review of the test results to ensure that the drug is safe and also its efficacy is not overstated. What if I told you that a pharmaceutical firm came up with a possible cure for lung cancer, and there were successful trials of 10 individuals. Does that sound like a group too small to draw any conclusions? Would you take a drug that the testing was only done on a handful of people? Now the FDA would never allow such a thing, and there are tons of protocols and blind or double-blind randomized testing of many individuals. It just sounds weird if only 10 people were tested, and there was also no control group (i.e. a separate group given a placebo).

While the drug example seems a bit outrageous and contrived, I bet you can think of similar examples in the daily financial press (e.g. financial television or print media). Whenever you hear a small number of events happening that “tend to” lead to certain financial market outcomes, you should be extremely wary. For instance, I just heard today that, after the Singles Day huge ecommerce sale by Alibaba, the stock (Ticker Symbol: BABA) is up 80% of the time over the course of the next two weeks. Well, when did Alibaba start Singles Day? The first Singles Day sale was in 2009. Therefore, we have 10 data points to work with (2009 to 2018). Given the information I referred to above, the comment made today simply says that the stock has been up after two weeks 8 out of the last 10 years. Now I will try to hold in my red flags and bit of ludicrous thoughts, this type of information is not informative at all. There are just too few observations to draw any sort of valid conclusion.

Here is the plan of attack for the next two articles. The second part of this discussion will focus on statistics. Yes, I know this topic is not too much fun and can get complicated very quickly. However, individual investors need to know a bit about statistics to recognize when a quantitative quote is totally useless. We will not get too granular though, I promise. Essentially most financial market data is time series data. Different rules apply in that case, and these rules are broken all the time by even the most sophisticated professional investors and commentators. The third part of this discussion will be an in-depth examination of an actual event that grounds my argument in recent events. I will examine what is called the inversion of the yield curve and how it normally portends a recession for the U.S. economy. Don’t worry; I am going to explain those terms when the third part of this series rolls around.

Please join me in a critical review of all the financial market and economic data you get bombarded with. So much of it is just “noise” or simply interesting trivia at best. Note that the interesting trivia cannot guide or inform your particular asset allocation of investments. As always, if you have questions along the way, please feel free to comment on this or any other article.

How to Become a Successful Long-Term Investor – Summary

30 Monday Sep 2019

Posted by wmosconi in asset allocation, behavioral finance, correlation, correlation coefficient, Dot Com Bubble, Emotional Intelligence, EQ, financial advice, Financial Advisor, financial goals, financial markets, financial planning, financial services industry, historical returns, Individual Investing, individual investors, investing, investing advice, investing information, investing tips, investment advice, investments, market timing, math, personal finance, portfolio, risk, risk tolerance, risks of stocks, S&P 500, S&P 500 historical returns, S&P 500 Index, standard deviation, statistics, Stock Market Returns, stock prices, stocks, volatility

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asset allocation, behavioral finance, education, finance, historical stock returns, investing, investments, math, mathematics, performance, performance monitoring, portfolio, portfolio management, S&P 500, S&P 500 historical returns, S&P 500 Index, statistics, stock returns, stocks, success, successful long term investing, trading, uncertainty

The discussion of how to become a successful long-term investor in my three-part series is now finished. However, the journey is an ongoing one that takes discipline, constant learning, and monitoring your emotional reactions to fluctuations in the financial markets. I discussed the history of stock market returns of the S&P 500 Index (dividends reinvested) from 1957-2018, the concept of risk, and also the futility of trying to engage in “market timing”. But you may be asking yourself, why didn’t you tell me what stocks, bonds, and other assets to buy to build my investment portfolio? That is a valid question, and there is an extremely important reason why that gets at the very heart of my overall discussion.

The best way to answer the question posed above is with an analogy. Now my international readers will have to indulge me with this example. My favorite sport is football which is the most popular sport in the world. Most people in the United States refer to it as soccer and only watch if the men’s or women’s teams are competing in the World Cup. I could tell you all about the reasons why football clubs rarely use a 4-4-2 formation. Or I could talk about how the 4-2-3-1 formation has evolved in the Bundesliga. We also could discuss why goalies now need to be good with their feet in order to pass from the backline. Finally, I might even be more specific and give my rationale for why Liverpool in the Premier League uses a 4-4-3 formation given their current squad for the 2019-2020 season.

My analogy above relates to long-term investing because I would argue that you should not invest a single dollar in the stock or bond markets without knowing about the history of returns, risks and volatility, and “market timing”. Most Financial Advisors (FAs), Certified Financial Planners (CFPs), and Registered Investment Advisors (RIAs) jump right into the discussion of how to build an investment portfolio taking into account your financial goals and risk tolerance. This conversation is directly related to the football analogy above. Without a firm understanding of investing at a high level (or the general way football is played first), you are likely to fail in your resolve to stick with a long-term focus while investing. For example, when you are asked if you can tolerate a 20% decline in the stock market, how should you answer? I would say that, if you do not have some grasp of historical returns and the level of risk, you cannot properly answer. Remember that we covered how often you will experience negative returns (including 20% declines) in the first article. You need to understand the “composition of the forest before deciding how to deal with the trees”.

Here are the links to the three articles to have an understanding of first prior to jumping into the mix of long-term investing strategy and building an actual portfolio of investments.

Part 1 – Understanding Historical Stock Market Returns:

https://latticeworkwealth.com/2019/09/23/successful-long-term-investing/

Part 2 – Understanding and Managing Risk:

https://latticeworkwealth.com/2019/09/25/successful-long-term-investor-risk/

Part 3 – Giving up on the Allure of “Market Timing”:

https://latticeworkwealth.com/2019/09/28/successful-long-term-investing-market-timing/

Once you have a firm grasp on these topics, you are ready to get your feet wet in the world of investing.

For those of you wanting a little bit of guidance because your intention is the manage your investments personally, I have written about this topic in the past. I wrote a two-part series on how to build an investment portfolio and monitor the performance returns of that investment portfolio. I have included the links below:

Part 1 – Building an Investment Portfolio:

https://latticeworkwealth.com/2013/07/16/how-to-create-an-investment-portfolio-and-properly-measure-your-performance-part-1-of-2/

Part 2 – Monitoring the Performance of an Investment Portfolio:

https://latticeworkwealth.com/2013/07/19/how-to-create-an-investment-portfolio-and-properly-measure-your-performance-part-2-of-2/

Those two articles above will provide you with some ways to go about creating your own investment portfolio without the assistance of a financial professional. While it does contain a lot of information and suggestions, individual investors who are complete novices may find it easier and less confusing to seek out someone to guide them with investment selection, measuring risk tolerance, and understanding the goals of their financial plan.

In summary, I appreciate you taking the time to read my thoughts in regard to successful long-term investing. As you can see successful investing has more to do with preparation, setting realistic expectations, and knowing how you personally respond to risk. These topics need to be studied prior to investing money yourself or before going to seek out investment advice from a financial professional. If you have any questions, comments, feedback, or disagreements, you can feel free to let me know.

How to Become a Successful Long-Term Investor – Part 3 of 3 – The Folly of Market Timing

28 Saturday Sep 2019

Posted by wmosconi in Alan Greenspan, asset allocation, Average Returns, behavioral finance, bubbles, correlation, correlation coefficient, Dot Com Bubble, finance, finance theory, financial goals, financial markets, Financial Media, Financial News, financial planning, Greenspan, historical returns, Individual Investing, individual investors, Internet Bubble, investing, investing advice, investing information, investing tips, investment advice, investments, Irrational Exuberance, market timing, math, personal finance, portfolio, risk tolerance, risks of stocks, S&P 500, S&P 500 historical returns, S&P 500 Index, statistics, stock market, Stock Market Returns, Stock Market Valuation, stock prices, stocks, Valuation, volatility

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This article is the third and final post in my three-part series on learning how to be a successful long-term investor. The general theme underlying all of the topics has been developing enough of an understanding of the stock market gyrations and sometimes wild ride to form reasonable expectations at the outset. Those expectations lead directly into to developing a long-term investment strategy and plan that you are much more likely to stick with through “thick and thin” because you know what is coming. Of course, you will not know the order in which the ups and downs may come, but you will have a ton of information helpful to be much less likely to lose your nerve or get overly excited.

The last topic will be about “market timing”. We will delve deeply into the concept and see how very difficult it has been in the past, and, I believe, will continue to be for the foreseeable future. Now the discussion to follow will be entirely self-contained; however, it might be helpful to take a look at the first two articles to have additional context. The opening topic was an overview of the history of stock market returns using the S&P 500 Index (dividends reinvested). Here is a link to that post:

https://latticeworkwealth.com/2019/09/23/successful-long-term-investing/

The second topic was a discussion about the concept of risk. We explored how it is normally defined, ways that you can gauge your tolerance for risk given the information from the first post, and explored some methods/mindsets to reduce risk in your investment portfolio. Here is a link to that post:

https://latticeworkwealth.com/2019/09/25/successful-long-term-investor-risk/

So now, we will turn to the topic for the last article. As mentioned above, we are going to take a look at “market timing”. In general, the idea of “market timing” is to develop ways to be able to buy stocks when they are very undervalued and also sell stocks right near the market peak to avoid a big downturn. There are certain variations where an investor is not necessarily trying to time the most opportune time but trade along with the momentum of the stock market and anticipating the next movement prior to other stock market participants.

“Market timing” is notoriously difficult to do. But you will see considerable time devoted every day to financial market television and periodicals advising individual investors what trades to make. I would submit that following things and pundits on a daily basis adds to “noise” and “information overload”. Additionally, for every guest that predicts a big leg up in the market, there will be another guest later in the day who tells you that we are in a bubble and stocks will drop dramatically soon.

Another lesser talked about item is the main guests that are invited to speak on television or are quoted in financial periodicals. Typically, the guest introduction will be prefaced by this man/woman predicted the last major move in the stock market and we are so lucky to have him/her back again. While these guests are great to hear from, there is a severe amount of “selection bias”. What do I mean by “selection bias”? You will rarely see a guest brought on to be lambasted for a prediction that never came to fruition or was just flat out wrong. The vast majority of guests on television or market experts in financial articles will be the ones who made a very prescient call on the direction of the stock market.

The promise of “market timing” is still so enticing. It normally relates to the fear of losing money or the greed of just not wanting to miss the next big bull market trend upward in the stock market. However, the ability to call the market tops or bottoms has proven to be pretty much a 50/50 flip of the coin (now I am being generous at that). One of the examples that I love to give is the coining of the term “irrational exuberance”. The former chair of the Federal Reserve, Alan Greenspan, used that new term to state that the stock market was in what he thought was a bubble. Little do people remember, but he first gave the speech in December 1996 to refer to what would become the Dot.Com bubble and bust. Greenspan was proven right but the top of that bubble occurred in March 2000. I use that example because irrational activity in the markets can persist for much, much longer than you might expect.

So, now I know that some people reading this post will be able to point to experts who made the great calls or even their own calls on the direction of the stock market. Well, I will start off the discussion by showing that “market timing” is indeed somewhat possible. But it takes much longer periods of time than you might think at first. Here is how we will proceed in the analysis. I discussed how the long-term historical average of the S&P 500 Index from 1957-2018 has been 9.8%. It would seem logical then that, if stock market returns were below that average or above that average for a certain length of time, you could just do the opposite figuring that stock market returns would eventually trend back to that average (in the jargon reversion to the mean).

The problem is, as I briefly mentioned in the last paragraph, that the time period needs to be so long that it is almost untenable for individual investors to practically implement. In fact, we have to use 15-year annualized returns to illustrate the theory. So, if the stock market has been below/above trend, we will buy/sell because an inflection point has to come. Let’s take a look at it graphically to drive the point home:

Fifteen Year Correlation

In the graph depicted above, we have exactly the returns we would like to see. The blue dots are the past 15 years of stock market returns, and the orange dots are the next 15 years of stock market returns. The dots are what we would term to have an inverse relationship. In fact, for all of you somewhat familiar with statistics, the correlation coefficient is -0.857. Therefore, there is a really strong relationship here that leads us to the promise of “market timing”. Should we give up on it so early?

The problem with “market timing” is that, for any length of time less than 15 years of annualized stock returns, there really is no relationship (at least no actionable trading of stocks for your investment portfolio). Let’s take a look at the same concept in the first graph with a look at one-year and three-year current and then future returns:

One Year Correlation

Three Year Correlation

Using the one-year and three-year current and then future stock market returns of the S&P 500 Index, our dots just kind of do not follow a discernable pattern. Again, for the statistically inclined folks out there, the correlation coefficients are -0.10 and -0.041, respectively. As always, we won’t get too waded down into the mathematical weeds but a correlation coefficient close to 0 means that there is essentially no correlation/relationship between the two. To make an analogy, you can think of what is the correlation between birds in your backyard and the number of jars of pickles for sale at your local grocery store? Well, there should be no relationship whatsoever. Even if there were, it would not make any sense. In our case here, there is at least some logic underlying our premise of the most recent return on the S&P 500 Index and the future returns over that same time period. As we see though, there is really nothing actionable to embark upon for individual investors to properly engage in “market timing”.

Before we totally give up on “market timing”, we can take a look at the same charts but extending the time periods to five years and ten years. Let’s take a look at those two graphs:

Five Year Correlation

Ten Year Correlation

The correlation coefficient for the five-year chart is 0.028, so we cannot really use that long of a time period either. I will admit that the ten-year chart looks a little more promising. We have a graph that looks somewhat more like the fifteen-year graph that I started off with. In fact, the correlation coefficient is -0.276. And a negative number is what we want to see in order to try “market timing”. Unfortunately, the number is really not strong enough to not get caught. By this I mean, we can see that “market timing” would have worked from 1975-1985 and also from 1990-2001 roughly. However, 1965-1975 has a grouping of returns that don’t work and 2002-2008 has mixed results as well. Note that there are less data points because there needs to be at least 10 years of future returns in order to compare the current record of 10-year annualized returns with what the next 10 years of stock returns will end up being.

Overall, we have seen that “market timing” in the short term (even as defined out to five years) does not really have much, if any, predictive power. Therefore, if you make decisions related to “market timing” based upon how the stock market has performed in any time period five years or less, it is clearly a “fool’s errand” or incredibly difficult to do. And by the latter, I mean that you can reliably do so over more than one major change in market direction. The majority of market pundits that you will see or read about have made one correct call which is not nearly enough to judge his/her investing acumen related to “market timing”.

I will close out the discussion of “market timing” by using the Financial Crisis and ensuing Great Recession. Many folks correctly called (or were proven right without the reason for the bubble matching their investment thesis) this major stock market inflection point. They correctly saw the unsustainable bubble in housing, the rise of financial stocks, and the buildup of toxic securities like subprime loans. However, many of those same individuals never changed their investment thesis and failed to tell individual investors to return to the stock market and buy. Essentially there are still folks that will tell you we are in a bubble. Now I am not bold and/or grandiose enough to weigh in on the current value of the stock market. But you need to know that most of the people who call a wicked crash in stocks or a massive bull market do not change their investment thesis prior to the next big turn.

For example, let’s say that you learned about stock investing 10 years or so ago and decided to invest $1,000.00 in the S&P 500 Index toward the end of October 2007. And yes, this was the absolute worst time to invest in stocks. Sadly, by March 2009, you would have lost 50% of your investment and have only $500.00 at that point in time. You might feel great if you listened to someone who called the top and told you that the fourth quarter of 2007 was the absolute worse time to buy stocks. But I am willing to bet that this same person would not have told you when it was “safe” to invest again. If you knew to expect bouts of extreme volatility in the stock market beforehand, you could have kept your money in the stock market. At the end of December 2018, you would have had $1,712.36 using our 13.1% 10-year annualized return over that time. If the original market predictor of catastrophe told you to just keep your $1,000.00 in the bank you would have $1,160.54 (assuming generously that you could earn 1.50% over the ten years in your bank saving account). Adjusting the hypothetical investor who simply kept his/her money in stocks back to inflation, he/she would have $1,404.73 (assuming 2.0% inflation over the last 10 years which is higher than was actually experienced). At the end of December 2018, you would have a bit more than 21% higher in inflation-adjusted dollars than the person who just never invested (or took his/her money out of stocks right at the end of October 2007 but never returned to stocks).

Now I will admit that my hypothetical scenario would have tried the “intestinal fortitude” of the most seasoned professional investors after seeing a 50% market drop over 1.5 years. My only point with the example is that, even if you could not have held your nerve to remain invested in stocks over the Financial Crisis, the investment pundit(s) who tells you the exact top with a brilliant prediction also needs to tell you when to invest or sell again in the future (i.e. “market timing”). Rarely will you see such a prognosticator that can totally change their investment thesis to get the next call right. You are much better off abstaining from “market timing” and sticking to your long-term investment strategy. Of course, that may indeed call for selling or buying a portion of stocks at certain given points to change your investment portfolio allocation to match your risk tolerance and financial goals. But trying to utilize “market timing” to be in and out to experience hardly any losses and capture all the gains is just not realistic, so you might as well discard the entire investment strategy of “market timing”.

How to Become a Successful Long-Term Investor – Part 2 of 3 – Understanding and Reducing Risk

25 Wednesday Sep 2019

Posted by wmosconi in asset allocation, behavioral finance, Consumer Finance, Education, finance, finance theory, financial advice, Financial Advisor, financial goals, financial markets, Financial Media, Financial News, financial planning, financial services industry, Geometric Returns, historical returns, Individual Investing, individual investors, investing, investing advice, investing tips, investment advice, investments, math, Modern Portfolio Theory, MPT, personal finance, portfolio, risk, risk tolerance, risks of stocks, S&P 500, S&P 500 historical returns, S&P 500 Index, standard deviation, statistics, stock market, Stock Market Returns, Stock Market Valuation, stock prices, stocks, volatility

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Another extremely important part of being a long-term investor is to understand the concept of risk. Financial professionals define risk in a number of different ways, and we will examine some of those definitions. The overarching goal is to look at risk from the standpoint of the volatility or dispersion of stock market returns. Diversification of various investments in your portfolio is normally the way that most financial professionals discuss ways to manage the inevitable fluctuations in one’s investment portfolio. However, there is another more intuitive way to reduce risk which will be the topic of this second part of this examination into becoming a successful long-term investor.

The first part of this series on long-term investing was a look back at the historical returns of the S&P 500 Index (including the reinvestment of dividends). The S&P 500 Index will again be the proxy used to view the concept of risk. If you have not had a chance to read the first part of the series, I would urge you to follow the link provided below. Note that it is not a prerequisite to follow along with the discussion to come, but it would be helpful to better understand the exploration of risk in this article.

The link to part one of becoming a successful long-term investor is:

https://latticeworkwealth.com/2019/09/23/successful-long-term-investing/

But now we will turn our attention to risk. Risk can be a kind of difficult or opaque concept that is discussed by financial professionals. Most individual investors have a tough time following along. Sometimes there is a lot of math and statistics included with the overview. Although this information is helpful, we need to build up to that aspect. However, there will be no detailed calculations utilized in this article that might muddy the waters further. I believe it helps to take a graphical approach and then build up to what some individual investors consider the harder aspects of grasping risk.

Risk related to investing in stocks can be defined differently, but the general idea is that stocks do not go up or down in a straight line. As discussed in depth in part one, the annual return of the S&P 500 Index jumps around by a large margin. Most individual investors are surprised at seeing the wide variation. Ultimately, the long-term historical average of the S&P 500 Index from 1957 to 2018 is 9.8%. But rarely does the average annual return end up being anywhere near that number.

The first way I would like to look at risk within the context of long-term investing is to go back to our use of “buckets” of returns. If you have not already read part one, I used “buckets” with ranges of 5% to see where stock returns fit in. As it relates to risk, we are only going to look at the “bucket” that includes the historical average 7% to 12% and then either side of that “bucket” (2% to 7% and 12% to 17%). Additionally, we will look at yearly stock returns and then annualized stock returns for three years, five years, and ten years. Here is our first graph:

Returns on Either Side of Historical Average

The main takeaway from viewing this graph is that, as the length of time increases, more stock market returns for the S&P 500 Index group around the historical average for the index of 9.8%. Remember that part one covered the useful information that, even though the historical average to be expected from investing in stocks is 9.8%, individual investors need to know that it can take long periods of time to see that historical average. In fact, if we look only at one-year increments, approximately 33.9% of stock returns will fall into the range of 2% to 17%. Or, if we use our yearly equivalent, stock market returns will only fall within that range 1 out of every 3 years. When individual investors see this graph for the first time, they are usually shocked and somewhat nervous about investing in stocks.

The important thing to keep in mind is that as the length of time examined increased many more stock returns fall into this range. The numbers are 65.0%, 67.1%, and 81.1%, for three years, five years, and ten years, respectively. Converting those numbers to yearly equivalents we have about 6-7 years out of ten for three years and five years. And, as one would intuitively suspect, the longest timeframe of ten years will have stock returns falling into the 2% to 17% range roughly 8 in every 10 years. Now that still means that 20% to 35% of long-term returns fall outside of that range when considering all those time periods. But I believe that it is certainly much more palatable for individual investors than looking at investing through the lens of only one-year increments.

Another aspect of risk is what would be termed downside protection. Most individual investors are considered to be risk averse. This term is just a fancy way of saying that the vast majority of investors need a lot more expected positive returns to compensate them for the prospect of losing large sums of money. Essentially an easier way to look at this term is that most individual investors have asymmetric risk tolerances. All that this means in general is that a 10% loss is much more painful than the pleasure of a 10% gain in the minds of most investors. Think about yourself in these terms. What would you consider the offset to be equal when it comes to losing and earning money in the stock market? Would you need the prospect of a 15% positive return (or 20%, 25% and so forth) to offset the possibility of losing 10% of your money in any one year? Let’s look at the breakdown of the number of years that investors will experience a loss. To be consistent with my first post, I am going to use the “bucket” of -3% to 2% and work down from there. Here is the graph:

Returns Less than 2%

There are 61 years of stock market returns from the S&P 500 Index for the period 1957 to 2018. If we look at the category of 1 year, stock market returns were 2% or less 38.7% of the time (17 years out of 61 years). However, if we move to five-year and ten-year annualized returns, there were no observations in the -3% to -8%, -8% to -13%, or less than -13% “buckets”. When looking at losing money by investing in the stock market, a long-term focus and investment strategy will balance out very negative return years and your portfolio is less likely to be worth significantly less after five or ten years. Of course, there are no guarantees and perfect foresight is something that we do not have. However, I believe that looking carefully at the historical data shows why it is important to not be so discouraged by years when the stock market goes down and even stays down for longer than just one year. Hopefully these figures do provide you with more fortitude to resist the instinct to sell stocks when the stock market takes a deep decline if your investment horizon and financial goals are many, many years out into the future.

The final concept I would like to cover is standard deviation. The term standard deviation comes up more often than not either in discussions with financial professionals during client meetings or is used a lot in the financial media. There are many times when even the professionals use the term and explain things incorrectly, but we will save that conversation for another post. Standard deviation is a statistical term that really is a measure of how far away stock market returns are from the mean (i.e. the average). It is a concept related to volatility or dispersion. So, the higher the number is, the more likely it is that stock market returns will have a wide range of returns in any given year. Let’s first take a look at a graph to put things into context. Here it is:

Standard Deviation

The chart is striking in terms of how much the standard deviation decreases as the time period increases. A couple things to note. First, I do not want to confuse you with a great deal of math or statistical jargon and calculations. My point is not to obscure the main idea. Second, the 25-year and 50-year numbers are just included only to cover the entire period of 1957 to 2018 for the S&P 500 Index. These periods of time are not of much use to individual investors to consider their tolerance for risk and the right investments to include in their portfolios. And, as one of the most famous economists of the 20^th century, John Maynard Keynes, quipped: “In the long run, we are all dead”. My only point is that discussion of how the stock market has performed over 25 years or longer is just not relevant to how most individuals think. It is nice to know but not very useful from a practical perspective.

The main item of interest from the graph above of standard deviation is that you can “lower” the risk of your portfolio just by lengthening your time horizon to make investment decisions on buying or selling stock. For example, the standard deviation goes down 46.9% (to 8.95% from 16.87%) between one-year returns and three-year annualized returns. Why do I use “lower”? Well, the risk of your portfolio will stay constant over time and focusing on longer periods of time will not decrease the volatility per se. However, most financial professionals tell their clients to not worry about day-to-day fluctuations in the stock market. Plus, most Financial Advisors tell their clients to not get too upset when reviewing quarterly brokerage statements. This advice is very good indeed. However, I urge you to lengthen the period of your concern about volatility in further out into time. My general guideline to the individuals that I assist in building financial portfolios, setting a unique risk tolerance, and planning for financial goals is to view even one year as short term akin to examining your quarterly brokerage statement.

Why? If you are in what is termed the “wealth accumulation” stage of life (e.g. saving for retirement), what occurs on a yearly basis is of no concern in the grand scheme of things. The better investment strategy is to consider three years as short term, five years as medium term, and ten years as the long term. I think that even retirees can benefit with this type of shift. Now please do not get me wrong. I am not advising that anyone make absolutely no changes to his/her investment portfolio for one-year increments. Rather, annual returns in the stock market vary so widely that it can lead you astray from building a long-term investing strategy that you can stick to when stock market returns inevitably decline (sometimes precipitously and by a large margin). Note that all the academic theories, especially Modern Portfolio Theory (MPT), were built using an assumption of a one-year holding period for stocks (also bonds, cash, and other investments). Most individual investors do not fall into the one-year holding period. Therefore, it does not make much sense to overly focus on such a short time period.

Of course, the next thought and/or comment that comes up is “what if the stock market is too high and I should sell to avoid the downturn?”. I will not deny that this instinct is very real and will never go away for individual investors. In fact, a good deal of financial media television coverage and news publications are devoted to advising people on this very topic every single day. It is termed “market timing”. In the third and last article in this series on becoming a successful long-term investor, I am going to examine “market timing” with the same stock market data from the S&P 500 Index. You will clearly see why trying to time the market and buy/sell or sell/buy at the right time is extremely difficult to do (despite what the financial pundits might have you believe given the daily commentary).

Bonds Have Risks Other Than Rising Interest Rates. Dividend Stocks are not Substitutes for Bonds.

24 Sunday Jul 2016

Posted by wmosconi in academics, asset allocation, bond basics, bond market, Bond Mathematics, Bond Risks, bonds, Fabozzi, finance, finance theory, financial advice, Financial Advisor, financial goals, financial markets, Financial Media, financial planning, financial services industry, Fixed Income Mathematics, foreign currency, Frank Fabozzi, Individual Investing, individual investors, interest rates, investing, investing advice, investing information, investing tips, investment advice, investments, math, MBS, personal finance, rebalancing, rebalancing investment portfolio, rising interest rate environment, rising interest rates, risk, risks of bonds, Search for Yield, statistics, types of bonds, volatility, yield

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The main reason why Financial Advisors are recommending that individual investors sell bonds is that interest rates are likely to rise over the next 3-5 years or more. Although those sentiments have been a familiar refrain over the last 3-5 years though. Well, I would tend to agree that interest rates are poised to rise at some point toward the end of this decade. However, interest rate risk is only one of the risks of bonds. In fact, the size of the bond market dwarfs the stock market. When Financial Advisors are talking about bonds, they tend to be referring only to US Treasury bonds, corporate bonds, and municipal bonds. Interest rate risk greatly affects these bonds indeed. With that being said, they tend to conflate the interest rate risk of these bonds with the entire bond market. Remember that interest rates have dropped from 16.30% on the 1-month US Treasury bill back in 1981 to roughly 0.25% today. Therefore, bond prices have been rising for over 35 years and most financial professionals outside of the fixed income markets have forgotten (or if they are younger than 50) how bonds normally work, especially in a rising interest rate environment.

But does it even matter really? Yes. Here is an urgent note to all individual investors: “Beware of financial professionals that recommend dividend stocks or other equities as replacements for your fixed income allocation”. What I mean by this is that the volatility of stocks is far greater than bonds historically. Yields may be very low in money market funds, US Treasuries, and in bond mutual funds now. However, your risk tolerance must be taken into account at all times. While it is true that many dividend-paying stocks offer yields of 3% or more with the possibility of capital appreciation, there also is significant downside risk. For example, as most people are aware, the S&P 500 index (which represents most of the biggest companies in America) was down over 35% in 2008. Many of those stocks are included in the push to have individual investors buy dividend payers. With that being said, stock market declines of 10%-20% in a single quarter are not that uncommon. If you handle the volatility of the stock market well, there is no need to be concerned. However, a decline of 10% for a stock paying a 3% dividend will wipe out a little more than 3 years of yield. Individual investors need to realize that swapping traditional bonds or bond mutual funds is not a “riskless” transaction, meaning a one-for-one swap. The volatility and riskiness of your portfolio will go up commensurately with your added exposure to equities. Sometimes financial professionals portray the search for yield by jumping into stocks as the only option given the low interest rate environment.

While your situation might warrant that movement in your portfolio allocation, you need to be able to accept that the value of those stocks is likely to drop by 10% or more in the future just taking into account normal volatility in the stock market historically (every 36 months or so in any given quarter). Are you able to handle that volatility when looking at your risk tolerance, financial goals, and age?The purpose of this blog post is to discuss the risk factors associated with bonds in greater detail. Most bonds, such as Treasury notes and bonds, corporate bonds, and municipal bonds, will go down in value when interest rates go up. Conversely, they will go up in value when interest rates decrease. This characteristic of these types of bonds is called an inverse relationship. For a primer on how most bonds function normally, I have posted supplementary material alongside this post. You can refer to it to brush back up on bonds and how they work, and I also provide a historical look at interest rates over the last 35 years. Here is the link to that prior blog post:https://latticeworkwealth.com/2014/01/02/a-bond-is-a-bond-is-a-bond-right-should-you-sell-bonds-to-buy-stocks-supplementary-information-on-how-bonds-work/

There are many risk factors associated with investments in bonds. A great overview of those risks can be found in Fixed Income Mathematics the Fourth Edition by Dr. Frank Fabozzi who teaches at Yale University’s School of Management. Most fixed income traders, portfolio managers, and risk managers use his Handbook of Fixed Income Securities as their general guidebook for approaching dealing with the trading, investing, and portfolio/risk management of owning fixed income securities. Suffice it to say that he is regarded as one of the experts when it comes to the bond markets. Dr. Fabozzi summarizes the risks inherent in bonds on page 109 of the first text referenced above. The risks are as follows:

Interest-rate risk;
Credit risk;
Liquidity risk;
Call or prepayment risk;
Exchange-rate risk.

Most of fixed income folks and myself would add inflation risk, basis risk, and separate credit risk into two components. Bonds have two types of risk as it relates to payment of principal and interest. The first risk is more commonly thought of and referred to as default risk. Default risk is simply whether or not the company will pay you back in full and with timely interest payments. Credit risk also can be thought of as the financial strength of the company. If a company starts to see a reduction in profits, much higher expenses, and drains of cash, the rating agencies may downgrade their debt. A downgrade just means that the company is less likely to pay back the bondholder.Here is an example to illustrate the difference more fully: a company may have a AA+ rating from Standard & Poor’s at the beginning of the year, but, due to events that transpire during the year, the company may get downgraded to A- with a Negative Outlook. Now the company is still very likely to pay back principal and interest on the bonds, but the probability of default has gone up. As a point of reference, AAA is the highest and BBB- is the lowest Standard & Poor’s ratings to be considered investment grade. You will note that the hypothetical company would need to be downgraded four more times (BBB+, BBB, BBB- to BB+) to be considered non-investment grade or a “junk” bond. Bond market participants though will react to the downgrade though because new potential buyers see more risk of default given the same coupon. So even though the company may not default eventually on the actual bond, the price of the bond goes up to compensate for the interest rate required by the marketplace on similarly rated bonds to attract buyers.Now I will address the full list of risks affecting bonds outlined by Dr. Fabozzi above. Any bond is simply an agreement between two parties in which one party agrees to pay back money to the other party at a later date with interest.

All bonds have what is referred to as credit (default portion) risk. Credit risk in general is simply the risk one runs that the party who owes you the money will not pay you back (i.e. default). What is lesser known or thought about by individual investors is interest-rate risk and inflation risk. These two risks are usually missed because investors tend to think that bonds are “safe”. Interest-rate risk relates to the fact that interest rates may rise, while you hold the bonds (spoken about at length in the beginning of this blog post). When financial pundits make blanket statements about selling bonds, they are referring to this one risk factor normally. Inflation risk means that inflation may increase to a level higher than your interest rate on the bond. Thus, if the interest rate on your bond is less than inflation or closer to inflation from when you bought the bond, your purchasing power goes down. The prices of goods and services go up faster than the interest you earn on the bond. Call risk refers to instances where some companies have the option to redeem your bonds in the future at an agreed upon price. This is normally done only when interest rates fall. Prepayment risk is a more specialized case of call risk and refers to people paying their mortgages (or credit cards, home equity loans, student loans, etc.) back sooner than expected. Most people group these two risks into a category called reinvestment risk. Think about the concept in this manner: many people refinanced their mortgages because interest rates went down. They did so because they could lower their total mortgage payment. Well, companies do the same thing if they have the option. Companies can redeem bonds at higher interests and issue new bonds at lower interest rates. Chances are that, if you are the owner of the redeemed bonds, you will be unable to find as high of an interest payment currently if you want to buy a bond with similar characteristics of the company issuing the bonds you own before.The other three risks I mentioned above are less commonly discussed and not quite as important.

Exchange-rate risk exists because sometimes a company issues bonds in a currency other than its own. For example, you will sometimes hear the terms Yankee bonds or Samurai bonds. Since the company is paying you interest and principal in a foreign currency that money may be worth more or less depending on what happens in foreign exchange markets in the future.

Liquidity risk refers to the phenomenon that there are certain crisis times in the market where very few, if any bond market participants, are willing to buy the bonds you are trying to sell. Therefore, you might have to take a bigger loss in order to entice someone to buy the bonds given the current macro environment.

Basis risk is a more obtuse type of risk that institutions deal with. Basis risk essentially refers to anytime when interest rates on your bond are pegged to another interest rate that is different but normally behaves in a certain way (referred to as correlation). Now most of the time, the behavior will follow the historical pattern. However, during times of stress like a liquidity and/or credit crisis, the correlations tend to break down. Meaning you can think you are “hedged” but, if the historical relationship does not hold up, your end return will be nothing like what you had expected. These two risks are not something that individual investors need to focus on for the most part, since these types of bonds are not normally owned by them.I will admit that this list is quite lengthy and, quite possibly, a bit too detailed and/or complicated. However, I wanted to lay them all out for you. Why? When you hear Financial Advisors recommend that you sell a large portion of your bonds, and/or hear the same investment advice from the financial media, they normally are really only referring to interest-rate risk primarily and secondarily inflation risk as well. As you can see from the description above, the bond market is far more complex than that to make a blanket statement.Now, as I usually say, I would never advise individual investors to take a certain course of action in terms of selecting specific bonds or not selling bonds to move into more stocks. However, I am saying that you should feel comfortable enough to ask your Financial Advisor why he/she recommends that you sell a portion of your bonds. If the answer relates only to interest-rate risk, I would probe the recommendation further. You can explain that you know that is the case for Treasury notes/bonds, municipal bonds, and corporate bonds. However, there are a whole host of other fixed income securities with different characteristics and risks. Now I am not referring solely to Mortgage Backed Securities (MBS), although the residential and commercial markets for these are in the trillions of dollars. There are bonds and notes that have floating interest rates which means that as interest rates go up, the interest rate you receive on that security goes up. Not to mention that different countries are experiencing different interest rate cycles than the US (stable or downward even).The complete list is too in-depth to cover in a single blog post. My goal was to provide you with enough information to at least ask the question(s). Your risk tolerance and financial goals might make a move from bonds to stocks the best course of action. With that being said, you also have the option of selling bonds and keeping the money in cash or investing in the different types of bonds offered in the fixed income markets while keeping your total allocation to fixed income nearly the same. Thinking holistically about your portfolio, you may be increasing the riskiness of your portfolio beyond your risk tolerance or more than you are aware unbeknownst to you by moving from bonds into stocks. This is something you definitely want to avoid. It can turn out to be a rude awakening and hard lesson to learn one or two years from now.

Are Stocks Currently Overvalued, Undervalued, or Fairly Valued? Answer: Yes.

10 Tuesday May 2016

Posted by wmosconi in academia, academics, asset allocation, Average Returns, business, CAPE, CAPE P/E Ratio, Consumer Finance, Cyclically Adjusted Price Earnings Ratio, Education, finance, finance theory, financial advice, financial goals, financial markets, Financial Media, Financial News, financial planning, financial services industry, Forward P/E Ratio, Individual Investing, individual investors, interest rates, investing, investing advice, investing information, investing tips, investment advice, investments, Nobel Prize, Nobel Prize in Economics, P/E Ratio, passive investing, personal finance, portfolio, risk, Robert Shiller, Schiller, Shiller P/E Ratio, statistics, stock market, Stock Market Returns, Stock Market Valuation, stock prices, stocks, Valuation, volatility

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Confusing and frustrating as it may be, the answer about the current valuation of stocks will always be different depending on who you ask. Various economists, mutual fund portfolio managers, research analysts, financial news print and TV personalities, and other parties seem to disagree on this very important question. Financial professionals will offer a wide range of financial and economic statistics in support of these opinions on the current valuation of stocks. One of the most often cited statistics in support of a person’s opinion is the P/E ratio of the stock market at any given point in time. Many financial professionals use it as one of the easiest numbers to be able to formulate a viewpoint on stock valuation. However, when it comes to any statistic, one must always be skeptical in terms of both the way the number is calculated and its predictive value. Any time one number is used to describe the financial markets one must always be leery. A closer examination of the P/E ratio is necessary to show why its usage alone is a poor way to make a judgement in regard to the proper valuation of stocks.

The P/E ratio is short for Price/Earnings ratio. The value is calculated by taking the current stock price divided by the annual earnings of the company. When it is applied to an entire stock market index like the S&P 500 index, the value is calculated by taking the current value of the index divided by the sum of the annual earnings of the 500 companies included in the index. One of the very important things to be aware of is that the denominator of the equation may actually be different depending on who is using the P/E ratio. Some people will refer to the P/E ratio in terms of the last reported annual earnings for the company (index). Other people will refer to the P/E ratio in terms of the expected earnings for the company (index) over the next year. In this particular case, the P/E ratio is referred to as the Forward P/E ratio. Both ratios have a purpose. The traditional P/E ratio measures the reported accounting earnings of the firm (index). It is a known value. The Forward P/E ratio measures the profits that the firm (index) will create in the future. However, the future profits are only a forecast. Many analysts prefer to use the Forward P/E ratio because the value of any firm (or index of companies) is determined by its future ability to generate profits for its owners. The historical earnings are of lesser significance.

The P/E ratio is essentially a measure of how much investors value $1 worth of earnings and what they are willing to pay for it. For example, a firm might have a P/E ratio of 10, 20, 45, or even 100. In the case of a firm that is losing money, the P/E ratio does not apply. In general, investors are willing to pay more per each $1 in earnings if the company has the potential to grow a great deal in the future. Examples of this would be companies like Amazon (Ticker Symbol: AMZN) or Netflix (Ticker Symbol: NFLX) that have P/E ratios well over 100. Some companies are further along in their life cycle and offer less growth opportunities and tend to have lower P/E ratios. Examples of this would be General Motors or IBM that have P/E ratios in the single digits or low teens, respectively. Investors tend to pay more for companies that offer the promise of future growth than for companies that are in mature or declining industries.

When it comes to the entire stock market, the P/E ratio applied to a stock market index (such as the S&P 500 index) measures how much investors are willing to pay for the earnings of all the companies in that particular index. For purposes of discussion and illustration, I will refer to the S&P 500 index while discussing the P/E ratio. The average P/E ratio for the S&P 500 index over the last 40 years (1966-2015) was 18.77. When delivering an opinion on the valuation of the S&P 500 index, many financial professionals will cite this number and state that stocks are overvalued (undervalued) if the current P/E ratio of the S&P 500 index is above (below) that historical average. If the current P/E ratio of the S&P 500 index is roughly in line with that historical average, the term fairly valued will usually be used in relation to stocks. The rationale is that stocks are only worth what their earnings/profits are over time. There is evidence that the stock market can become far too highly priced (as in March 2000 or December 2007) or far too lowly priced (as in 1982) based upon the P/E ratio observed at that time. Unfortunately, the relative correlation between looking at the difference between the current P/E ratio of the stock market and the historical P/E ratio does not work perfectly. In fact, it is only under very extreme circumstances and with perfect hindsight that investors can see that stocks were overvalued or undervalued in relation to the P/E ratio at that time.

Here are the historical P/E ratios for the S&P 500 index from 1966-2015 as measured by the P/E ratio at the end of the year. Additionally, the annual return of the S&P index for that year is also shown.

Year	P/E Ratio	Annual Return
2015	22.17	1.30%
2014	20.02	13.81%
2013	18.15	32.43%
2012	17.03	15.88%
2011	14.87	2.07%
2010	16.30	14.87%
2009	20.70	27.11%
2008	70.91	-37.22%
2007	21.46	5.46%
2006	17.36	15.74%
2005	18.07	4.79%
2004	19.99	10.82%
2003	22.73	28.72%
2002	31.43	-22.27%
2001	46.17	-11.98%
2000	27.55	-9.11%
1999	29.04	21.11%
1998	32.92	28.73%
1997	24.29	33.67%
1996	19.53	23.06%
1995	18.08	38.02%
1994	14.89	1.19%
1993	21.34	10.17%
1992	22.50	7.60%
1991	25.93	30.95%
1990	15.35	-3.42%
1989	15.13	32.00%
1988	11.82	16.64%
1987	14.03	5.69%
1986	18.01	19.06%
1985	14.28	32.24%
1984	10.36	5.96%
1983	11.52	23.13%
1982	11.48	21.22%
1981	7.73	-5.33%
1980	9.02	32.76%
1979	7.39	18.69%
1978	7.88	6.41%
1977	8.28	-7.78%
1976	10.41	24.20%
1975	11.83	38.46%
1974	8.30	-26.95%
1973	11.68	-15.03%
1972	18.08	19.15%
1971	18.00	14.54%
1970	18.12	3.60%
1969	15.76	-8.63%
1968	17.65	11.03%
1967	17.70	24.45%
1966	15.30	-10.36%

Average 18.77

The P/E ratio for the S&P 500 index has varied widely from the single digits to values of 40 or above. The important thing to observe is that very high P/E ratios are not always followed by low or negative returns, nor are very low P/E ratios followed by very high returns. In terms of a baseline, the S&P 500 index returned approximately 9.5% over this 40-year period. As is immediately evident, the returns of stocks are quite varied which is what one would expect given the fact that stocks are known as assets that exhibit volatility (meaning that they fluctuate a lot because the future is never known with certainty). Thus, whenever a financial professional says that stocks are overvalued, undervalued, or fairly valued at any given point in time, that statement has very little significance. Whenever only one data point is utilized to give a forecast about the future direction of stocks, an individual investor needs to be extremely skeptical of that statement. The P/E ratio does hold a very important key for the future returns of stocks but only over long periods of time and certainly not over a short timeframe like a month, quarter, or even a year.

An improvement on the P/E ratio was developed by Dr. Robert J. Shiller, the Nobel Prize winner in Economics and current professor of Economics at Yale University. The P/E ratio that Dr. Shiller developed is referred to as the Shiller P/E ratio or the CAPE (Cyclically Adjusted Price Earnings) P/E ratio. This P/E ratio takes the current value of a stock or stock index and divides it by the average earnings of a firm or index components for a period of 10 years and also takes into account the level of inflation over that period. The general idea is that the long-term earnings of a firm or index determine its relative valuation. Thus, it does a far better job of measuring whether or not the stock market is fairly valued or not at any given point in time. However, another very important piece of the puzzle has to do with interest rates. Investors are generally willing to pay more for stocks when interest rates are low than when interest rates are high. Why? If it is assumed that the future earnings stream of the company remains the same, an investor would be willing to take more risk and invest in stocks over the safety of bonds. A quick example from everyday life is instructive. Imagine that your friend wants to borrow $500 for one year. How much interest will you charge your friend on the loan? Let’s say you want to earn 5% more than what you could earn by simply buying US Treasury Bills for one year. A one-year US Treasury Bill is risk free and, as of May 10, 2016 yields interest of 0.50%. Therefore, you might charge your friend 5.5% on the loan. Now back in the early 1980’s, one-year US Treasury Bills (and even savings accounts at banks) were 10% or higher. If you were to have provided the loan to your friend then, you would not charge 5.5% because you could simply deposit the $500 in the bank. You might charge your friend 15.5% on the loan assuming that the relative risk of your friend not paying you back is the same in both time periods. It is very similar when it comes to investing in stocks. Due to the fact that stocks are volatile and future profits are unknown, investors tend to prefer bonds over stocks as interest rates rise. This phenomenon causes the value of stocks to fall. Conversely, as interest rates fall, the preference for bonds decreases and investors will choose stocks more and prices go up. Now this assumes that the future earnings of the company or index constituents stay the same in either scenario.

With that information in mind, a better way to gauge the relative valuation of stocks in terms of being overvalued, undervalued, or fairly valued, would be to look at the Shiller P/E ratio in combination with interest rates. It is most common for investors to utilize the 10-year US Treasury note as a proxy for interest rates. Here are the historical values for the Shiller P/E ratio and the 10-year US Treasury note over the same 40-year period (1966-2015) as before:

Year	CAPE Ratio	10-Year Yield
2015	24.21	2.27%
2014	26.49	2.17%
2013	24.86	3.04%
2012	21.90	1.78%
2011	21.21	1.89%
2010	22.98	3.30%
2009	20.53	3.85%
2008	15.17	2.25%
2007	24.02	4.04%
2006	27.21	4.71%
2005	26.47	4.39%
2004	26.59	4.24%
2003	27.66	4.27%
2002	22.90	3.83%
2001	30.28	5.07%
2000	36.98	5.12%
1999	43.77	6.45%
1998	40.57	4.65%
1997	32.86	5.75%
1996	28.33	6.43%
1995	24.76	5.58%
1994	20.22	7.84%
1993	21.41	5.83%
1992	20.32	6.70%
1991	19.77	6.71%
1990	15.61	8.08%
1989	17.05	7.93%
1988	15.09	9.14%
1987	13.90	8.83%
1986	14.92	7.23%
1985	11.72	9.00%
1984	10.00	11.55%
1983	9.89	11.82%
1982	8.76	10.36%
1981	7.39	13.98%
1980	9.26	12.43%
1979	8.85	10.33%
1978	9.26	9.15%
1977	9.24	7.78%
1976	11.44	6.81%
1975	11.19	7.76%
1974	8.92	7.40%
1973	13.53	6.90%
1972	18.71	6.41%
1971	17.26	5.89%
1970	16.46	6.50%
1969	17.09	7.88%
1968	21.19	6.16%
1967	21.51	5.70%
1966	20.43	4.64%

Average 19.80 6.44%

These two data points provide a much better gauge of whether or not stocks are currently overvalued or undervalued. For example, take a look at the Shiller P/E ratio in the late 1970’s and early 1980’s. The value of the Shiller ratio is in the single digits during this time period because interest rates were higher than 10%. Lately interest rates have been right around 2.0%-2.5% for the past several years. Therefore, one would expect that the Shiller P/E ratio would be higher. Now the historical average for the Shiller P/E ratio was 19.80 over this period. The Shiller P/E ratio was in the neighborhood of 40 during 1998-2000 which preceded the bursting of the Internet Bubble in March 2000. The Shiller P/E ratio was at its two lowest levels of 7 and 8 in 1981 and 1982, respectively which is when the great bull market began. However, while this Shiller P/E and interest rates are better than simply the traditional P/E ratio, there are flaws. The Shiller P/E in 2007 was 24.02 right (and interest rates were around 4.0% which is on the low side historically) before the huge market drop of the Great Recession between September 2008 and March 2009. In fact, the S&P 500 index was down over 37% in 2008, and the Shiller P/E did not provide an imminent warning of any such severe downturn. Therefore, even looking at these two measures is imperfect but better than the normal P/E ratio in isolation.

To summarize the discussion, individual investors will always be told on a daily basis by various sources that the stock market is currently overvalued, undervalued, and fairly valued at the same time. One of the most commonly used rationales is a reference to the current P/E ratio in relation to the historical P/E ratio. As we have seen, this one data point is a very poor indicator of the future direction and relative value of stocks at any given period of time, especially for short periods of time (one year or less). The commentary and opinions provided by financial “experts” to individual investors when the P/E ratio is mentioned normally relates to the short term. By looking back at the historical data, it is clear that this one data point is really only relevant over very long periods of time. The Shiller P/E ratio in combination with current interest rates is a great improvement over the traditional P/E ratio, but it is even imperfect when it comes to forecasting the future returns of the stock market. There are two general rules for individual investors to take away from this discussion. Whenever a comment is made about the current value of stocks and only one statistic is provided, the opinion should be taken with a “grain of salt” and weighed only as one piece of information in determining investment decisions that individual investors may or may not make. Additionally, and equally as important, if a financial professional cites a statistic about stock valuation that you do not understand (even after doing some research of your own), you should always discard that opinion in most every case. Individual investors should not make major investment decisions in terms of altering large portions of their investment portfolios of stocks, bonds, and other financial assets utilizing information that they do not understand. It sounds like common sense, but, in the sometimes irrational world of investing, this occurrence is far more common than you imagine.

The First Key to Successful Stock Investing is Understanding and Accepting Reality – Updated

16 Wednesday Mar 2016

Posted by wmosconi in asset allocation, Average Returns, bonds, business, college finance, Consumer Finance, Education, Emotional Intelligence, finance, finance theory, financial advice, financial goals, financial markets, financial planning, financial services industry, Geometric Returns, Individual Investing, individual investors, investing, investing advice, investing information, investing tips, investment advice, investments, math, personal finance, portfolio, risk, risk tolerance, statistics, stock market, Stock Market Returns, stock prices, stocks, Uncategorized, volatility

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This particular topic is so important that I decided to revisit it again. The discussion below adds further refinements and creates an even stronger tie to behavioral finance (i.e. how emotions affect investment decisions). Additionally, for those of you who desire more in-depth coverage of the math and statistics presented, I have included that at the very end of this article. Let’s delve deeper into this topic and what is meant by “reality”.

The first key to successful stock investing has more to do with your emotions than a fundamental understanding of what causes stocks to move up or down. Emotions about money can be a powerful thing and cause people to behave in irrational ways. One of the most common phrases passed on to investors as a piece of wisdom is to “buy low and sell high”. However, study after study has shown that most individual investors fail to heed that advice. Why does this happen? Well, I would submit the real cause is behavioral and based upon incomplete information.

Most individual investors are told when they start investing in stocks via mutual funds and/or ETFs to expect an annual return of 8% to 9% per year. You will find that many financial calculators to help you plan for retirement on the Internet have that as one of the inputs to calculate the growth of your portfolio over time. While that information is not too far off the mark based upon historical returns of the S&P 500 stock index, the actual annual returns of stocks do not cooperate to the constant frustration and consternation of so many investors.

That brings us to the first key to successful stock investing: The actual yearly returns of stocks very rarely equal the average expected. The most common term for this phenomenon is referred to as volatility. Stocks tend to bounce around quite a bit from year to year. Volatility combines with the natural instinct of people to extrapolate from the recent past, and investing becomes a very difficult task. I will get deeper into the numbers at the very end of the post for those readers who like to more fully understand the concepts I discuss. I do need talk in general about annual stock returns at this point to expand upon the first key.

Below I have provided a chart of the annual returns of the S&P 500 index for every year in the 21^st century:

Year	% Return
2001	-11.90%
2002	-22.10%
2003	28.70%
2004	10.90%
2005	4.90%
2006	15.80%
2007	5.50%
2008	-37.00%
2009	26.50%
2010	15.10%
2011	2.10%
2012	16.00%
2013	32.40%
2014	13.70%
2015	1.40%

What is the first thing you notice when looking at the yearly returns in the table? First, you might notice that they really jump around a lot. More importantly, none of the years has a return that is between 8% and 9%. The closest year is 2004 with a return of 10.9%. If the only piece of information you have is to expect the historical average over time, the lack of consistency can be extraordinarily frustrating and scary. In fact, individual investors (and sometimes professional investors too) commonly look back at the last couple of years and expect those actual returns to continue into the future. Therein lies the problem. Investors tend to be gleeful when returns have been really good and very fearful when returns have been very low. Since the average never comes around very often, investors will forget what returns to expect over the long run and will “buy high and sell low”. It is common to sell stocks after a prolonged downturn and wait until it is “safe” to buy stocks again which is how the sound advice gets turned around.

I will not get too heavy into math and statistics, but I wanted to provide you will some useful information to at least be prepared when you venture out to invest by yourself or by using a financial professional. I looked back at all the returns of the S&P 500 index since 1928 (note the index had lesser numbers of stocks in the past until 1957). The actual annual return of the index was between 7% and 11% only 5 out of the 88 years or 5.7%. That statistic means that your annual return in stocks will be around the average once every 17 years. The 50-year average annual return for the S&P 500 index (1966-2015) was approximately 9.8%. Actual returns were negative 24 out of 88 years (27.9% of the time) and greater than 15% 42 out of 88 years (48.8% of the time). How does relate to the first key of stock investing that I mentioned earlier (“The actual yearly returns of stocks very rarely equal the average expected”)?

Well, it should be much easier to see at this point. If you are investing in stocks to achieve the average return quoted in so many sources of 8% to 9%, it is definitely a long-term proposition and can be a bumpy ride. The average return works out in the end, but you need to have a solid plan, either by yourself or with the guidance financial professional, to ensure that you stick to the long-term financial plan to reach the financial goals that you have set. Knowing beforehand should greatly assist you in controlling your emotions. I recommend trying to anticipate what you do when the actual return you achieve by investing in stocks is well below or quite high above the average in your portfolio. Having this information provides a much better way to truly understand and your risk tolerance when it comes to deciding what percentage of your monies to allocate to stocks in my opinion.

When you look back at the performance returns for stocks, it makes more sense why investors do what they do from the standpoint of behavioral finance. That is how emotions affect (all too often negatively) investment decisions. If an individual investor is told at the outset that he or she can expect returns of 8% or 9% per year, the actual annual returns of stocks can be quite troubling. Having that information only leads to a general disadvantage. When stock returns are negative and nowhere near the average, individual investors tend to panic and sell stocks. When stock returns are quite higher than the average, individual investors tend to be more euphoric and buy even more stocks. This affect is magnified when there are a number of consecutive years with one of those two trends. If stock returns are essentially unchanged, most individual investors become disengaged and really do not even see the point of investing in stocks at all.

I believe it is extremely important to know upfront that stocks are likely to hit the average return once every 17 years. That statistic alone is a real shocker! It lets individual investors truly see how “unusual” the average return really is. Plus, there is a better explanation for fear and greed. Stock market returns will be negative once every 4 years. Keep in mind this does not even include stock returns that are below the average yet still positive. Lastly, every other year the stock market returns will be above the average (in my case I was measuring above the average with the definition of that being a stock market return greater than 11%). It is no wonder why individual investors get greedy when it looks like investing in the stock market is so easy after seeing such great returns. Conversely, the occurrence of negative returns is so regular that it is only natural for individual investors to panic. Since the average only comes around approximately once every two decades, that is why confusion abounds and investors abandon their long-term financial plans.

I will readily admit sticking to a long-term financial plan is not easy to do in practice during powerful bull or bear markets, but I think it helps to know upfront what actual stock returns look like and prepare yourself emotionally in additional to the intellectual side of investing. Now I always mention that statistics can be misleading, conveniently picked to make a point, or not indicative of the future. Nevertheless, I have tried to present the information fairly and in general terms.

Additional Information on Stock Market Returns (Discussion of Math and Statistics):

Please note that this information may be skipped by individual investors that are scared off by math in general or have no desire to dive deeper into the minutiae. One of the first things to be aware of is what expected returns for stocks are. An expected return is what the most likely outcome would be in any particular year. Expected returns provide misleading results when there is a high degree of variability in the entire dataset. In the case of stock market returns, there is an incredible amount of variability. The industry term for variability, which is the statistical term, is volatility. Due to the fact that the expected return almost never happens, it would be wise for the financial services industry to truly and better define volatility. Most individual investors do not know that there is far more of a range of possible outcomes for stock market returns. Individual investors associate hearing average returns with some volatility from Financial Advisors or financial media in the same way as the classic “bell curve”. As discussed in further detail above, the outcomes do not even come close to approximating the “bell curve”.

One important thing to be aware of when it comes to actual performance returns of an individual’s investment portfolio is that average/expected values are not very important. In fact, they really lead to a distorted way of looking at investing. Average/expected values are based on arithmetic returns, where the overall growth in one’s investment portfolio is tied to geometric returns. The concept of geometric returns is overlooked or not fully explained to individual investors. Here is the perfect example of how it comes into play. Let’s say you own one share of a $100 stock. It goes down 50% in the first year and then up 50% in the second year. How much money do you have at the end of the second year? You have the original $100, right?

Not even close. You end up with $75. Why? At the end of the first year, your stock is worth $50 ($100 + $100*-50%) after decreasing 50%. Since you begin the second year with only that $50, that is why you end up having $75 ($50 + $50 * 50%). The average annual return is 0% ((-50% + 50%) divided by 2)) for the two-year period. Whereas your geometric return is negative 13.4%. Essentially that number shows what happened to the value of your portfolio over the entire timeframe and incorporates the ending value. Think of it as having $100 + $100 * -13.4% or $86.60 at the end of year one and then $86.60 + $86.60 * -13.4%) or $75. Note that you never actually have $86.60 as the portfolio’s value at any time, but the geometric return tells you how much money you actually earned (or lost) over the entire period and how much money you end up with, otherwise known as the terminal value of your portfolio. The geometric return will ALWAYS differ from the arithmetic return when a negative return is introduced as one of the outcomes. As an individual investor, your primary concern is the terminal value of your portfolio. That is the dollar value you see on your brokerage statement and is the actual amount of money you have.

Financial professionals forget to focus on geometric returns or even bring them up to clients. This omission is important to individual investors because negative returns have an outsized effect on the terminal value of an investment portfolio. For example, in the example above, it is quite clear that losing 50% and then gaining 50% do not “cancel each other out”. The negative percent weighs down the final value of the portfolio. That is why it is extremely important to use the geometric return of the portfolio. This result is due to the fact that the compounding of interest is not linear. It is a geometric equation which is why the geometric mean comes into play. Without going fully into the explanation of those equations, the main takeaway for investors when it comes to annual returns is that negative returns have more of an effect than positive returns.

Taken together, it is important to utilize the concept of multi-year geometric averages. Individual investors never want to simply add up the annual returns of a series of years and then divided by the number of years. That result will overstate the amount of money in the investment portfolio at the end of the period. The preferred approach is to use the geometric average which is referred to as the annualized average return. That percentage is the number most relevant to investors. Additionally, longer timeframes of these returns are best to look at given the extreme amount of volatility in yearly stock market returns. It gives a better picture of how the stock market has moved.

When looking at the stock market returns for the S&P 500 index over five-year periods using the period 2001-2015, they yield surprising yet informative results. The five-year returns from 2001-2005, 2006-2010, and 2011-2015 were 0.54%, 2.30%, and 12.57%, respectively. Valuable information comes from looking at extended periods of time using the same time increment. The overall return during 2001-2015 was 5.01%. The effect of these longer timeframes smooths the stock market return data, but even then the stock market returns vary quite a bit. Note that the overall return from the entire historical period of the S&P 500 index is roughly 9.50%. These three selected chunks show two periods of underperformance and one year of outperformance. The reason stock market returns tend to hover around the historical average is due to the fact that these returns are tied to the overall growth the economy (most commonly Gross Domestic Product – GDP) and corporate profits. In the meantime though, stock market returns can vary a lot from this expected return. However, they are unlikely to do so for incredibly long periods of time.

By incorporating the understanding of volatility and geometric returns into your understanding of the “reality” of stock market returns, you will be able to better refine your own risk tolerance and how to craft your long-term financial plan. A better grasp of these concepts makes one far less likely to react emotionally to the market, either with too much fear or too much greed.

Latticework Wealth Management, LLC

~ Information for Individual Investors

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