Playing with Risk 2.0

Posted on Saturday, March 20, 2010
Filed under Fundamentals

I just read an article (click here for original source) which perfectly describe how to play with risk as written in my previous blog.

Shame on me for selectively copied and pasted from the article into my blog. I give full credit to the author and hope that the share will benefit you as well.

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Imagine if I challenged you to a simple game: I fill a jar with 50 black marbles and 50 red marbles and propose to draw 10 marbles from the jar.  For each black marble in the draw, I agree to pay you whatever dollar amount you choose, provided that you will pay me the same amount for each red marble pulled from the jar.

Knowing that the distribution of black and red marbles is 50/50, most rational people would decline to play this game for real money.  But what if I agreed to remove 10 red marbles from the jar before we started?  With the distribution now 50/40 in favor of black marbles, it becomes sensible, even wise to play this game for money.  If I remove 20 red marbles to make the distribution 50/30, a rational person should be willing to raise the value of their wager.  And if I remove 40 red marbles before starting the game it becomes sensible to “bet big,” whatever “big” means for the player involved.

The logic of this sequence is straightforward – when the mix of marbles is 50/50, the likelihood of winning or losing the game is purely random, but once a few of the red marbles have been removed from the jar the distribution of possible outcomes becomes skewed – any given draw of 10 marbles is more likely to contain more blacks than more reds.  The most probable outcome is no longer random.

A recent article in this publication by Joseph A. Tomlinson reminds readers that the models used by most financial planners assume the distribution of future returns in the asset markets is always random, like drawing marbles from a jar with an equal mix of reds and blacks.  Tomlinson goes on to suggest that this assumption of randomness in the asset markets may be flawed.  He supports his point with a study of historical correlations between starting valuation and subsequent returns in the stock market over rolling periods of 1 and 10 years.

The table below shows the distribution of every possible three-year return in the U.S. stock market – measured as of each month-end – between January 1884 and June 2009.  This period encompasses 1,506 observations measured over rolling 36-month holding periods.

U.S Stock Market*
1884 – 2009
Rolling 3-Year Holding Periods
753 Observations

*U.S. stock market returns for the period 1884 through 1926 are derived from the Shiller market index at www.econ.yale.edu/~shiller/data.htm.  Returns from 1926 through 1969 represent the “Large Company Stocks” category from Ibbotson Associates.  Returns from 1970 onward represent the S&P 500 Index.

Sources: Robert J. Shiller, Standard & Poor’s; Ibbotson Associates; Capital Advisors, Inc.

These data prompt numerous worthwhile questions for professional investors and financial planners.  Here are three:

1. Do professionals do their clients a disservice if they offer similar advice about stocks regardless of whether the starting P/E ratio is high or low, as so many financial software platforms prescribe? 
2. If presented with this data today, when the Shiller P/E Ratio is over 20, how many investors would knowingly accept a nearly one-in-three chance of losing money over three years in exchange for an expected annualized return of 6.85% with a majority of their savings (taken from the distribution of outcomes associated with a Shiller P/E of 19.20 or higher)? 
3. Would it be irresponsible for investment advisors to encourage a widow or a retiree to tilt her portfolio more aggressively toward stocks whenever the Shiller P/E sinks below 12?

The evidence from the real-world history of asset markets suggests that market returns are not totally random.  Sometimes “Mr. Market” removes a few red marbles from the jar, and sometimes he removes blacks.  Simple indicators like the Shiller P/E Ratio can reveal which marbles have been removed at any given time.  It is our job as investors to pay attention and adjust our wagers accordingly.

”Investing Rule No. 1: Never Lose Money
Investing Rule No. 2: Never Forget Rule No 1”
~ Warren Buffett