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Monthly Archives: September 2013

How Risky Are Stocks? Do You Understand Volatility? Part 2 of 2

20 Friday Sep 2013

Posted by wmosconi in asset allocation, bonds, business, Charlie Munger, Education, finance, financial planning, Individual Investing, interest rates, investing, investing, investments, stocks, bonds, asset allocation, portfolio, investments, math, personal finance, portfolio, risk, statistics, stock prices, stocks, volatility, Warren Buffett

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asset allocation, bonds, business, Charlie Munger, education, Fed taper, finance, financial planning, investing, investments, long term investing, mathematics, Modern Portfolio Theory, MPT, portfolio, retirement, risk, statistics, stocks, Warren Buffett

In the first part of this discussion, I talked at length regarding the volatility of stock prices.  Most investors are fearful of stock prices jumping all around for seemingly random or unknown reasons.  Many times extreme volatility can be explained.  Other times different news sources will attribute these fluctuations to totally different or even opposite reasons.  No wonder it is frustrating for individual investors.  Now traders and speculators need volatility to make money.  Additionally, Wall Street trading desks generate purchase and sale orders if stock prices are constantly in flux.  However, if you have a longer timeframe for holding the underlying components of your portfolio, it is quite easy to get hung up in this daily “circus”.  It is hard to have what I term “intestinal fortitude”, which is a fancy way to say guts, in the face of this environment of information overload.

Most financial professionals will construct a portfolio and recommend purchases/sales based upon Modern Portfolio Theory (MPT).  If you have heard the terms beta, alpha, r-squared, and tracking error, you are already familiar with MPT.  I will not get into the history behind the construction of MPT, but it started over 50 years ago.  Harry Markowitz is credited with creating the outline of the theory, and there has been a plethora of academic work done since then by some of the greatest academicians of all time.  With that being said, coming up with an academic theory and applying it to the real world are two different stories.  In brief, MPT talks about how to create a portfolio on the efficient frontier which maximizes return and minimizes risk (where risk is defined as the volatility of stock prices).  The portfolio consists of a combination of the risk free asset (Treasury debt) and an additional percentage of stocks.  However, there are a number of assumptions which underlie the theory.  In order to get the mathematics to work, a number of simplifying assumptions need to be made.  Otherwise, the calculations are so difficult that only a handful of mathematicians and statisticians would be able to understand the theory.  For some background information on the issue of stock price volatility, I encourage you to reread the first part of this article:  https://latticeworkwealth.com/2013/09/08/how-risky-are-stocks-do-you-understand-volatility-part-1-of-2/.

Let’s take a look at the six key underlying assumptions of MPT as described by Dr. John C. Hull who is the Maple Financial Group Chair in Derivatives and Risk Management at the Joseph L. Rotman School of Management, University of Toronto in his book entitled Risk Management and Financial Institutions Third Edition.  As an aside, most students with an MBA in Finance or MS in Financial Engineering will recognize Dr. Hull’s name from his book on Options, Futures, and Other Derivatives, which is a standard text in most programs:  http://www.amazon.com/Options-Futures-Derivatives-DerivaGem-Package/dp/0132777428/ref=sr_1_1?ie=UTF8&qid=1379691849&sr=8-1&keywords=john+hull+options+futures+and+other+derivatives+9th .  Dr. Hull lays out the assumptions on pages 10-11 of the aforementioned book.  They are as follows:

1)       Investors only care about the expected returns and the standard deviation of their portfolios assuming the standard normal distribution (bell curve).  He admits that many academics and practitioners believe that the expected returns of stock prices are non-normal and exhibit skewness and excess kurtosis.  Without giving a formal definition of the two, suffice it to say that skewness depicts whether or not more observations are above or below the average.  Kurtosis is simply whether or not there are observations than the simple bell curve would not predict.  Investors are more concerned with extreme negative returns above and beyond what the bell curve would predict;

2)      The second assumption is that stock price changes are not correlated to each other.  However, think about the industry factors that affect Apple and Samsung.  It is likely to be that global demand for smartphones will affect both these stocks in similar ways;

3)      The time horizon for all investors is one period which is typical one calendar year;

4)      All investors can borrow and lend at the same risk free interest rate;

5)      All investors are taxed at the same rate in all locations;

6)      All investors make the same calculations about the estimated expected returns, standard deviations, and correlations between returns for all investments available to investors.

We can clearly see that these assumptions severely limit the practical application of MPT to constructing a portfolio of investments that will provide a satisfactory rate of return given ones risk tolerance and financial goals.  Why are these assumptions made?  Well, I can assure you that even with these assumptions the math gets quite complicated.  For example, ask your Financial Advisor how William Sharpe proved that you can eliminate the covariance between stocks in order to come up with portfolios that lie on the efficient frontier to “simplify” Markowitz’s original theory.  Note this is just one “easy” part of coming up with the expected return of a portfolio composed of percentages of the risk free asset and all stocks.  If your Financial Advisor can explain that concept to you, you need not read any further.  I would be quite impressed and listen more to what he/she says.  If not, I would urge you to continue reading.

If some or all of the six assumptions do not apply to you, why would you want a portfolio custom made for you that uses a 50 year-old theory?  Personally, I do not know either.  So let’s proceed with how it relates to individual investors.  I will concentrate on investors in or near retirement or saving for retirement in my discussion below.

If your time horizon is longer than one year, you can make some modifications to MPT in order to fit your financial goals, risk aversion, and timeframe.  How?  Well, if you are an individual investor, you can choose to see the world in a different manner when it comes to investing.  The day-to-day and even quarterly fluctuations of stock prices should not concern you too much.  Yes, I realize it is easier said than done.  However, you can choose to make tactical and strategic decisions about the composition of your portfolio.  Most financial professionals would tell you to invest for the long term anyway, right?  Well, tactical decisions should be made in the context of an annual review of your portfolio.  Strategic decisions should be made with an outlook on the next five years or so.  This is probably what you have heard anyway.  Here is the twist though:  if you look at the stock price fluctuations of the S&P 500 index over the last 50 years, there will be some scary results.  If we take the period April 1, 1957 through June 28, 2013 and use MPT statistics, you can expect that 1 out of every 10 quarters your quarterly return from the S&P 500 index will be less than -11.5% or greater than 15.1%.  Note the returns are based upon quarterly fluctuations.  You can expect to experience a return in any given quarter which is less than -11.5% every 5 years or so.  Given your risk tolerance, how would you feel if your portfolio lost this amount in a single quarter?  Most investors, especially retirees, would have a difficult time accepting this volatility in expect returns.  Should you sell all your stocks at this point?  Well, I try never to give portfolio advice, but, if you are fearful of losing more than 10% of your money investors in stocks, I think you should strongly reconsider your risk tolerance.  That negative return is any given quarterly window is not too extraordinary in the real world.

I talked about the standard deviation of stocks on an annual basis at great length in the first part of this article.  How can we use the same statistical techniques to look at a portfolio over the long term?  Your Financial Advisor is used to speaking with you once a quarter and at the end of the year to review the performance of your portfolio.  What if you are wondering what you should do over the next five years? If you are 43 years old, why should you worry about daily stock price returns in 2014?  You should think about stock price returns but not to the extent of watching the stock market every single day, month, or quarter to try to glean magical insight into the future direction of stock prices.  I have been investing in the stock market since 1987, and the history of the stock market is littered with incorrect predictions about the stock market.  In fact, it can be dangerous to listen to some of the market prognosticators of “gloom and doom”.  For example, if you hear that you should buy gold because the entire financial system is going to collapse, I would ask you to perform a thought experiment.  If the financial system breaks down such that we are bartering for goods with gold and silver coins, ask yourself how long that money will last.   How long will it be until there is a scene out of NBC’s television show Revolution?  If there is an armed gang of thugs roaming the streets, I am pretty sure that your coins will not be in your possession for very long.  Note that is my personal opinion, but, if you construct your portfolio based upon extreme scenarios, you have to perform extreme scenarios to “stress” your portfolio.  I think it is a better use of time to think about uncertainty as being an ongoing component of investing.  There will never be 100% certainty about economic and financial events.

We can use the same statistics invoked by the academicians who created MPT to our advantage if the time horizon is extended to five year increments.  For example, over the time period 1961-2010, the average annual return for stocks in the S&P 500 index over each five-year period was 9.7% per year.  Now the minimum and maximum annual returns for each five-year increment were 0.5% (2001-2005) and 18.2% (1996-2000), respectively.  Now please observe that the annual returns of 1973, 1974, 1987 (as shown in part 1 of 2 was actually positive), 2001, and 2008 are included in that time series.  How does this occur?  The extreme increases and decreases of stock returns are smoothed out over a long period of time.  We had the Internet Bubble in 2001 which was preceded by the period of time in the late 1990’s which former Federal Reserve Chairman, Alan Greenspan termed irrational exuberance (note that this term was coined by him in December 1996; please refer to this link for Greenspan’s famous speech:  http://www.federalreserve.gov/boarddocs/speeches/1996/19961205.htm).  The fluctuation of stocks over a particular year can be quite volatile and can persist for much longer than expected by top-notch economists and asset managers.  However, if you look at these observed returns, you come up with much smoother results.  Your financial professional encourages you to invest for the long term, so why don’t you look at the expected returns over the long term for stocks when creating your portfolio?  If you are making tactical (medium term) and strategic (long term) changes to your portfolio, doesn’t it make sense to ignore the daily changes in stock prices?  To me, these are rhetorical questions.  Given the financial advice you receive or information you receive from the financial media now, does it sound like they consider these questions to be rhetorical?

The last point I will leave you with is a brief look at the annual returns you might expect over any five-year holding period in stocks.  Looking at the ten observations of five-year annual returns between 1961-2010 for the S&P 500 index, you can expect that 1 year in every 100 your five-year annual return will be outside -5.9% and 25.2%.  Therefore, every 200 years, there should be a five-year annual return less than -5.9% which is otherwise thought of as downside risk.  The worst five-year annual return for stocks since 1931 was 1936-1940 in which the average annual return was a bit less than -0.5%.  The five-year annual return for stocks between 1931-1935 was 2.2% which incorporated the height of the Great Depression.  Therefore, I would argue that you are thinking about investing as a long-term exercise in helping you reach your financial goals, stocks may be less risky than you think.  Or at the very least, you should ask your Financial Advisor why they do not use annual and five-year annualized (geometric basis of course) expected returns for stocks when recommending how you should position your portfolio.  It is a valid question if you are a long-term investor.  Note that I did not even include diversification in this discussion.  Since you are able to choose small cap stocks, international stocks, high yield bonds, and real estate, you can look at an individual portfolio in an even more positive light.

How Risky Are Stocks? Do You Understand Volatility? Part 1 of 2

08 Sunday Sep 2013

Posted by wmosconi in bonds, business, Education, finance, Individual Investing, investing, investing, investments, stocks, bonds, asset allocation, portfolio, investments, math, statistics, stock prices, stocks, volatility, Warren Buffett

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asset allocation, bonds, business, finance, investing, investments, math, portfolio allocation, standard deviation, statistics, stocks, Warren Buffett

Investors are told over and over that stocks are risky investments.  How true is that though?  If you watch the financial news each day, it seems like there is no reason why stocks go up, down, or remain unchanged at times.  For every financial pundit that gets the direction of the market correct, there are many others that predicted things incorrectly or have been saying that the “sky will fall” for the past five years.  I will admit that stocks are very risky on a daily basis.  However, if you are not running a hedge fund or are a trader on a Wall Street firm’s proprietary desk, the “vicissitudes and vagaries” of the daily moves in the stock market are of no concern to you.  In fact, being too concerned about daily/weekly/monthly/quarterly movements in stock prices will actually hurt your long-term performance.  Investing is not a sprint.  It is a marathon!  If it seems as though the professionals on Wall Street do better than you, please keep in mind that the financial media rarely interviews people that were totally wrong on the market.

I do not like to pick on anyone; however, I will provide one example just to make a point.  Mark Faber, a long-time fixture on Wall Street, predicted that the S&P 500 index would drop to the 1266 level back in November 2012.  Refer to http://moneymorning.com/2012/11/08/stock-market-today-why-marc-faber-predicts-a-20-slide/.   He was recently on CNBC in August 2013 and predicted that the S&P 500 index would by 20% this year.  So is he actually more bullish on his bearish prediction about one year later?  Who knows how to characterize that one?  It is important to learn about stock price movements which are termed volatility in the jargon of Wall Street.  Your Financial Advisor will refer to it over and over when he/she advises you on how to construct your portfolio.

Why does volatility matter to you?  Well, in the very short run, stocks are one of the riskiest investments.  I recently read that over the last 50 years stocks were up 53% of the time and down 47% of the time.  So your odds of being right about one day is essentially a bit better than calling a coin flip.  Now hopefully you are not a speculator.  If you are trying to double your money this year or in even a shorter period of time, you need not read any further.  However, if you would like to learn how volatility affects portfolio construction and portfolio performance over the long term, please read on.

I pulled down some annual returns from the S&P 500 for the period 1926-2012.  Note that the S&P 500 was preceded by a number of other indexes of smaller components, so it is unwise to use this data in full.  Whenever anyone uses statistics to make an argument (myself included), you always need to be very skeptical.  So do NOT make me an exception.  If you look at the S&P 500 index’s performance over the 50 year period from 1961-2010, the annualized performance is a bit less than 9.7%.  Wow, that sounds really good!  However, it seems counterintuitive because the S&P 500 was down over 36% in 2008.  Plus, you may have heard that the 2001-2010 period is often referred to as the “Lost Decade”.  Stocks earned basically nothing over that timeframe.  You need to remember that the 9.7% figure is composed of five decades with different characteristics.  For a primer on how compounding of returns works, you can refer to one of my earlier posts:  https://latticeworkwealth.com/2013/07/08/double-edged-sword-of-the-power-of-compounding/.  The aforementioned annualized return of the S&P 500 index over the last 50 years is composed of the following returns for each decade:  8.1% (1961-1970), 8.5% (1971-1980), 13.8% (1981-1990), 17.3% (1991-2000), and 1.4% (2001-2010).  You will most certainly remember the financial crisis of 2008 and the Internet Bubble of 2001.  These major events in the stock market took a huge toll on performance returns over the last decade in this series.  With that being said, Time magazine had a cover story in 1982 where they declared the de facto death of equities.  Oddly enough, it turned out to be the beginning of the strongest bull market in history.  Why is it important to decompose this data?

The importance lies in human nature.  An annualized return of 9.7% means that an investment in stocks should essentially double every five years.  Well, if your Financial Advisor invokes market history when building your portfolio, he/she may set your expectation that you can expect to double your money in stocks every 5 years.  What if it takes longer or you do not double your money after even a ten-year period like 2001-2010?  Humans tend to seek patterns and be risk averse.  Many of the great bubbles over time have come because financial professionals extrapolate from the past, be it with stock prices, corporate earnings, or housing prices more recently.  We look at the immediate past for a guide to the future.  This analysis is called ex post facto, and, as you can see above, it can get you into a lot of trouble.

Many investors used the 1980s and 1990s as a guide to what would happen in the 21st century.  In fact, there were books written and predictions of why the Dow Jones Industrial Average (Dow Jones) would reach 36,000 which is more than twice its current level as of September 2013.  I have met many investors that are still shying away from buying stocks because of the Internet Bubble of 2001 and the financial crisis of 2008.  Now I am not making a prediction about the future direction of the stock market, my only observation is that people tend to wait too long to get back into the market if they attempt to time the market properly.  Everyone wants to buy low and sell high.  Furthermore, they want to sell all their holding right when the market reaches its highs.  Buying stocks and holding them for the long term is not really all that much fun.  When I was 13 years old and buying stocks in the late 1980s, I know I wanted to double my money each year.  I got frustrated really quickly; however, I kept plugging away and investing more every month.

After the experience many had in the stock market from 1966-1982, they felt it was unwise to invest in stocks at all.  The Dow Jones was essentially unchanged during that period.  Very few Financial Advisors were recommending the purchase of stocks in the early 1980s.  Conversely, most every Financial Advisor was recommending the purchase of stocks throughout the late 1990s.  As humans, we tend to seek out patterns in history and, even subconsciously, think that the past will repeat itself.  You may think that you do not fall into that category, but I urge you to think about your experience with the stock market in 2001, 2002, and 2008.  Did you sell all your stocks, hold them, or buy more stocks during those years?  I can remember 2003 where it was very unfashionable to still invest in stocks.  It is easy to say that you will not succumb to the pressure to sell stocks, but, after the stock market fell over 35% in 2008, many investors just had enough.  Imagine you had $1,000,000 on January 1, 2008 and opened your brokerage statement on December 31, 2008 only to see the balance was $640,000.  Hard dollar figures are much more impactful than testing your risk tolerance by wondering if you would sell your stocks if the market went down 10%, 20%, or 30%.

Your Financial Advisor will talk to you about diversification and the benefit of holding securities in many different asset classes.  Moreover, you will be told over and over again that stock price volatility is bad and hurts your returns.  I will agree that stocks are volatile, but the assertion that Modern Portfolio Theory (MPT) makes about risk/return can lead to odd answers.  Here is a homework assignment.  Ask your Financial Advisor if he/she remembers how stocks performed during 1987.  Of course, everyone remember the huge crash in October, but very few remember that the stock market was actually up a bit over 2% that year (S&P 500 index).  Why does that even matter?

Well, stock price volatility is measured by statistics.  Think of the bell curve in your days in school.  The bell curve has been used in education which basically states that most of the students will be average and get a grade of C.  There will be other students that get B’s and D’s as well.  Of course, there will be a small group of students that fail a class or exam or do extremely well and get an A.  MPT tells investors that volatility is bad.  It is bad in terms of the decisions you might make, but there are many odd answers given by the theory.  For example, the average daily return of stocks in was roughly 0.03%.  The main measure of volatility is standard deviation, and you do not need to worry how to calculate it.  Standard deviation simply measures how far from the average a series of numbers in a population is like daily stock returns.  The standard deviation for daily returns was about 2.0%.  The annualized standard deviation was 31.8% (just so you know standard deviation is not additive in nature, so it takes some mathematical manipulation to get to that answer).  Why did I present these numbers?  I presented them to make another observation.  In 1973 and 1974, the S&P 500 index was down 14% and 26%, respectively.  However, the annualized standard deviation for each of those years was 15.6% in 1973 and 21.6% in 1974.  Thus, those years were less volatile than 1987, but an investor would have lost a large amount of money in each year.  Would you rather make money during the course of a year or lose money over the course of the year with less volatility?  If you are a long-term investor, daily fluctuations in the stock market should not guide your decisions.  Otherwise, you will end up selling all your stocks just because prices are going up and down a lot.  The most important thing is the terminal value.  The terminal value just means what the return will be at the end of the period without regard to the volatility over the course of the year.

The validity or, more aptly usefulness, of MPT becomes more apparent when we look at daily returns.  MPT makes a lot of assumptions, one of which is that stock prices will follow the normal distribution.  That is just a fancy way of saying the bell curve.  Now if you know about statistics, you can make predictions about a set of data based upon the historical experience of that data.  I downloaded the daily returns of the S&P 500 from 1957-2012 because I had some extra time on my hands and was bored.  The average daily return of the index was 0.03% with a standard deviation of 0.98%.  If you assume the normal distribution holds, you can make the assertion that 99% of all observations should be within a low daily return of -2.25% and a high daily return of 2.31% (Formula is average – standard deviation * 2.33 and average + standard deviation * 2.33).  You might ask if that is really true.  This way to express the data means that the daily return for the stock market should be equal to or between those two figures 99 out of every 100 trading days.  In statistical terms, it is referred to as a 99% confidence interval.  What about the market crash in 1987?  The S&P 500 index dropped 20.5% on October 19, 1987.  How would you express that statistically?  In order to have a daily return that far away from the average, it equates to approximately 21 standard deviations from the average.  How likely is that?  It is pretty much the same odds of flipping a coin 20 times and having it come up heads each time.  Keep in mind that this date was not the only big drop over this period.  For example, there were over 20 times when the S&P 500 index dropped by 5% or more in a day during that period.  The likelihood of that happening over the course of 55 years (1957-2012) is infinitesimal.  If you would like to learn more about this type of odd result, I would encourage you to read the book, The (Mis)Behavior of Markets, http://www.amazon.com/The-Misbehavior-of-Markets/dp/B008A0LNBM/ref=sr_1_2?ie=UTF8&qid=1378664066&sr=8-2&keywords=The+Misbehavior+of+markets.

Suffice it to say that the path of stock prices does not follow the normal distribution.  Now academics will admit that is the case and have made modifications to MPT.  Additionally, most academics will use the lognormal distribution or other distributions to explain the volatility of stock prices.  However, the mathematics becomes exponentially more difficult and challenging.  With that being said, the financial advice given to you from your Financial Advisor is likely to be taken from the first iteration of MPT.  If you have heard your financial professional talk about beta, alpha, sigma, mean, r-squared, and the like, he/she is constructing your portfolio by making reference to the ideas laid out by MPT.  Now I will not go so far as to say MPT is incorrect.  Much smarter folks than me developed it.; believe me!  However, the great Warren Buffett gave a speech back in 1984 that encapsulated why MPT he does not subscribe its tenants.  To see a transcription of the speech, refer to:  http://www.bestinver.es/pdf/articulos_value/The%20Superinvestors%20of%20Graham%20and%20Doddsville%20by%20Warren%20Buffett.pdf.

In the next part of this discussion, I will attempt to show you how to look at the volatility of stock prices in the context of your portfolio.  If you do not need to withdraw money from your portfolio on a short-term basis, MPT has less and less applicability for you.  MPT assumes that all investors have a one-year time horizon.  Therefore, if you do not plan on needed to withdraw money over the course of a 12-month period, this discussion definitely will apply to you.  You should be looking at your portfolio in terms of one-year and five-year increments.

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