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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.