Monthly Returns

Our investigations into Managing Downside Risk in Financial Markets have led us to an unexpected conclusion: Much of academic investment research should be tossed out. I am not able to discern exactly how much.

The critical flaw is the use of monthly returns.

The Model

In my most recent Current Research initiative, I am applying the Forsey-Sortino model. [A compact disk with the model comes with the book Managing Downside Risk in Financial Markets by Frank Sortino and Stephen Satchell.]

The model constructs synthetic years from monthly return data. It links sequences of twelve monthly returns, each month being selected at random with replacement, to create 2500 synthetic years. It calculates statistics and makes plots from these data.

Introducing Valuations

I collected data for the S&P500 using Professor Robert Shiller’s database. This includes his measure of valuation, P/E10.

I initially investigated 1921-1980. I calculated real, total returns for each month and identified the values of P/E10. I ordered the data, broke it into thirds and construct three portfolios as inputs to the Forsey-Sortino model. I reported means and plus and minus one standard deviation.

I repeated the process, except that I restricted the P/E10 number to that of January of each year. I did the same thing, starting with April of one year and restricting the P/E10 value until April of the following year. [I have constructed the data tables for all twelve months. I have only looked at January and April.] I repeated the process starting in January 1921, this time restricting the P/E10 value for two years.

It’s All Different and It Makes Sense

The statistical behaviors of the three different periods all differ. The behavior using April is similar to using January.

The monthly statistics show almost no variation of returns to P/E10. Upon reflection, this lack of sensitivity makes sense. The monthly returns show only how well P/E10 predicts what happens exactly one month later. It is a short-term statistic.

The single-year statistics of January and April are similar. They show that the lowest levels of P/E10 result in high returns. Middle levels of P/E10 have returns not too far from the historical long-term rates of 6.5% to 7.0%. High levels of P/E10 result in low returns.

This general trend makes sense. It is what we would expect.

The two-year statistics still show that low P/E10 levels are best and high P/E10 levels are worse. The middle level is much better than with single-year statistics. It is almost as high as with low levels of P/E10.

This change also makes sense. The two-year groupings imply a longer time base. That is, the predictability of returns improves as you increase your holding period.

As might be expected, the benefits at the lowest levels of P/E10 diminish a little bit, not much, when using the two-year statistics. My interpretation is that the lowest levels of P/E10 represent substantial bargains. You should take advantage of such opportunities. Do not delay your purchases.

Implications

If using monthly returns strips off the effects of something as basic as valuations, a large amount of research based on monthly returns is flawed fatally.

Some conclusions are sure to hold up in spite of this flaw. I am not able to draw the lines. At this moment, all are suspect.

Have fun.

John Walter Russell
December 15, 2005