Lessons from history and math

By Tom Anderson / Guest Editorial

Nobody knows the future.

In part one of this three-part series, I proposed that one potential way to gain insight is through basic math and financial history. While we don’t know the future, we know that discipline and process are likely to be rewarded in the long-run. When investors otherwise may be tempted to abandon a process in favor of something else, a grounding in math and history may help maintain discipline.

Previously, I overlaid two basic math facts with some lessons from history. Math Fact 1: If a position goes up 40 percent and then down 40 percent, you were better off being in cash. Math Fact 2: In any given series, the starting value matters in determining total return.

And the history lessons: From 1996 through the spring of 2009, Treasury bills beat the NASDAQ’s return series. In Greece, Argentina and throughout the world over the past 100 years, significant busts have tended to follow significant booms. In all of these scenarios, investors could have had vastly different outcomes within a single return series depending on when they were buying and when they were selling.

Here, I will apply this framework of simple math facts and history to the current landscape and valuation of U.S. stocks and bonds.

First, we need a quick math lesson in how bonds work. A bond provides a fixed return per year based on the interest rate and term at which you purchased it, assuming it does not default. If you buy a 10-year bond at 3 percent, it would provide a return of 3 percent per year for 10 years. Accordingly, the best predictor of bonds’ future returns is current yield to maturity.

In today’s landscape, 5-year bonds are yielding 1.18 percent for AAA municipal bonds to 2.12 percent for riskier A-rated corporate bonds according to http://bondsonline.com at the time of publication. Applying basic math to the current landscape, investors would predict a return on bonds in the 1.18 to 2.12 percent range for the next five years. But for purposes of our discussion, let’s assume an expected return of 2 percent, excluding taxes, fees and inflation.

Now let’s look at the history of the U.S. stock market. The average bull market in the United States has lasted 31 months with a median price increase of 73.53 percent. The bear markets that follow have been 10 months long and 35.43 percent deep on average according to Bank of America Merrill Lynch Global Research, Bloomberg. The size of the upswing in a bull market has not predicted the result of the subsequent correction.

The recent bull market started in March 2009, which makes it the sixth longest since 1929. Its 166 percent price increase ranks as the fourth biggest percentage movement in that same period. “The experts” think the rally is likely to continue. Let’s assume they are right. What happens?

If the S&P advances another 40 percent to 2,520 over the next 48 months, it would be the second longest and second biggest bull market since 1929. If the rally is followed by an average bear market over the subsequent 12 months, the S&P’s ending value 60 months from today would be 9 percent lower than today. In this scenario, the 5-year expected return for U.S. equities is roughly zero.

Our discussion so far gives us a 5-year return on U.S. stocks of 0 percent and a 5-year return on bonds of 2 percent. The good news is nothing really mattered all that much, including asset allocation and fund selection. The bad news is your returns are 0-2 percent.

So what does math tell us will happen under other scenarios? If we put some ranges around the cumulative 5-year price change (an initial movement up of 20, 30, 40, 50 or 60 percent followed by a subsequent move down of -20, -30, -40, -50 or -60 percent), we don’t get much good news. The best case scenario is if the market goes up 60 percent and down 20 percent, you are up 28 percent. However, 16 of 25 possible up-down scenarios lead to a loss of 9 percent or more. Only 4 of 25 scenarios lead to a gain of more than 10 percent. The average is a loss of 16 percent.

What if over the next five years, the market goes up another 20 percent then goes down 35 percent and then rallies up 10 percent per year for the final three years? This 5-year return rounds to zero. A study of 25 up-down-up scenarios looking at the cumulative 5-year price change after an initial 20 percent upward movement gives us 14 negative scenarios and only six scenarios with a gain over 10 percent. The average is -6 percent.

In the best case of these 50 scenarios, if you are 60 percent U.S. stocks and 40 percent U.S. bonds at 2 percent, then your annual return would be 5.3 percent – before taxes, fees and inflation.

Armed with this information, how do we move forward? My final piece in the series will look at what to do with this information, tie it back to what we know about valuation, and provide some strategies for investors.


For more information or if you’d like to see sources for all of my data, visit http://www.morganstanleyfa.com/theandersongroup and read my most recent commentary: Perspectives – Fall 2013 – Clarity from the College of Arts and Sciences: Lessons From History & Math – Part 2 found in the Anderson Group Economic Commentary.

NASDAQ Composite Index is a market-value-weighted index of all NASDAQ domestic and non-U.S. based common stocks listed on NASDAQ stock market. S&P 500 Index is an unmanaged, market value-weighted index of 500 stocks generally representative of the broad stock market. An investment cannot be made directly in a market index.

All opinions are subject to change without notice. Neither the information provided nor any opinion expressed constitutes a solicitation for the purchase or sale of any security. Past performance does not guarantee future results.



Tom Anderson is an executive director – wealth management, senior portfolio management director, family wealth director and financial advisor with Morgan Stanley. The views expressed herin are those of the author and do not necessarily reflect the views of Morgan Stanley or its affiliates.