Introducing the Minimum Acceptable Return (MAR)

I repeated my procedures using one-year and two-year January P/E10 values. This time, I introduced Minimum Acceptable Return (MAR) requirements to see how they affect results.

The Tools

I used the Forsey-Sortino model throughout this section. It comes in a CD when you purchase Managing Downside Risk in Financial Markets by Frank Sortino and Stephen Satchell. The book describes methods that are light-years ahead of traditional Mean-Variance Optimization.

Books Section
Managing Downside Risk in Financial Markets

I include the probability of falling below the Minimum Acceptable Return (MAR), the below target deviation and the upside potential. The below target deviation formula is the square root of the integral or sum of w(x)*f(x)*(x-MAR)^2, where f(x) is the probability density function for a return of x, the weighting function w(x) is 1 whenever x is below the MAR and zero whenever x is above the MAR. The upside potential is the integral of (1-w(x))*f(x)*(x-MAR).

One-Year January Values of P/E10

I listed the data according to dates. I made lists that kept the first value of P/E10 the same for intervals of one year for every month. That is, the list for January used the January value of P/E10 for the eleven months that followed. I updated the next year by using the new January value of P/E10. And so on.

I collected summary data for the month of January. The results were similar to before but not exactly the same. This is because of the random selection of months to generate 2500 simulated years.

I collected a complete set of data from the same set of simulated years.

Two-Year January Values of P/E10

I repeated my procedures using two-year values of P/E10.

I made lists that kept the first value of P/E10 the same for intervals of two years. I only made twelve (not twenty-four) lists, one for each month in the first year as a matter of convenience.

Using a two-year interval was similar to using a one-year interval. P/E10 displayed predictive power.

Minimum Acceptable Return (MAR) Thresholds

I set the Minimum Acceptable Returns equal to 0%, 1% and 2%.

All of my returns are adjusted for inflation. They are real returns.

A real return of 0% matches inflation exactly. A real return of 1% matches today’s ibond interest rate. A real return of 2% is very close to today’s interest rates on TIPS. (Today, rates are just above 2.0% for all maturities and well below 2.5%.)

1921-1980 Data

I ordered all 720 months (sixty years). I grouped them in three equal parts: those with the 240 (20 years) lowest values of P/E10, those with the 240 (twenty years) middle values of P/E10 and those with the 240 (twenty years) highest values of P/E10.

Here are the means and plus and minus one standard deviation as displayed on the lognormal plot (using default values) and at the MAR thresholds of 0%, 1% and 2%.

January Single-Year Ordering

Here are the means and plus and minus one standard deviation as displayed on the lognormal plot (using default values):
1-yr Low P/E10: -6.1%, 17.7% and 41.5%.
1-yr Middle P/E10: -10.4%, 6.8% and 24.1%.
1-yr High P/E10: -11.9%, 3.4% and 18.7%.

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 0.0%:
1-yr Low P/E10: 76.1%, 7.2%, 17.7% and 20.3% (MAR = 0.2%).
1-yr Middle P/E10: 63.3%, 7.8%, 6.8% and 10.6% (MAR = 0.0%).
1-yr High P/E10: 55.7%, 8.4%, 3.4% and 7.7% (MAR = 0.2%).

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 1.0%:
1-yr Low P/E10: 74.6%, 7.5%, 17.7% and 19.5% (MAR = 1.2%)
1-yr Middle P/E10: 60.7%, 8.3%, 6.8% and 9.9% (MAR = 1.1%).
1-yr High P/E10: 53.1%, 9.0%, 3.4% and 7.2% (MAR = 1.2%).

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 2.0%:
1-yr Low P/E10: 73.1%, 8.0%, 17.7% and 18.8% (MAR = 2.2%)
1-yr Middle P/E10: 58.1%, 8.9%, 6.8% and 9.3% (MAR = 2.2%).
1-yr High P/E10: 50.5%, 9.5%, 3.4% and 6.7% (MAR = 2.2%).

These are the P/E10 thresholds:
1-yr Low P/E10: 5.12 to 11.44
1-yr Middle P/E10: 11.47 to 16.72
1-yr High P/E10: 17.09 to 27.08

January Two-Year Ordering

Here are the means and plus and minus one standard deviation as displayed on the lognormal plot (using default values):
2-yr Low P/E10: -1.1%, 15.4% and 31.9%.
2-yr Middle P/E10: -10.3%, 12.6% and 35.6%.
2-yr High P/E10: -16.2%, -0.5% and 15.2%.

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 0.0%:
2-yr Low P/E10: 82.3%, 3.9%, 15.4% and 16.6% (MAR = 0.1%).
2-yr Middle P/E10: 69.1%, 8.7%, 12.6% and 16.4% (MAR = 0.1%).
2-yr High P/E10: 46.1%, 10.7%, -0.5% and 6.0% (MAR = -0.1%).

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 1.0%:
2-yr Low P/E10: 80.4%, 4.2%, 15.4% and 15.7% (MAR = 1.1%)
2-yr Middle P/E10: 67.4%, 9.1%, 12.6% and 15.7% (MAR = 1.1%).
2-yr High P/E10: 43.6%, 11.3%, -0.5% and 5.6% (MAR = 0.9%).

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 2.0%:
2-yr Low P/E10: 78.3%, 4.6%, 15.4% and 14.9% (MAR = 2.2%)
2-yr Middle P/E10: 65.7%, 9.6%, 12.6% and 15.1% (MAR = 2.0%).
2-yr High P/E10: 41.1%, 11.9%, -0.5% and 5.2% (MAR = 1.9%).

These are the P/E10 thresholds:
2-yr Low P/E10: 5.12 to 11.47
2-yr Middle P/E10: 11.50 to 16.71
2-yr High P/E10: 16.72 to 27.08

1921-1980 Summary

Single-year ordering strongly favors low values of P/E10. There is a general trend favoring lower valuations to higher valuations. The changes are gradual in terms of the downside. They are dramatic on the upside, especially when looking at the lowest P/E10 levels.

The two-year ordering continues to show the trend in favor of lower valuations. Here we see a consistent, strong effect in terms of exceeding the minimum acceptable return.

Using two-year intervals improves the performance at middle level valuations. It has similar means and upside potentials as at low valuations.

High valuations bring about lower returns, greater downside risk and limited upside potential.

January 1981-June 2004

I ordered all 282 months (twenty-three and one-half years). I grouped them in three almost equal parts: those with the 96 (eight years) lowest values of P/E10, those with the 96 (eight years) middle values of P/E10 and those with the 90 (seven and one-half years) highest values of P/E10. I kept the division as close to using complete years as possible to minimize seasonal effects.

I used January Single-Year Ordering. I used the January 2004 value of P/E10 for the six months of 2004.

January 1981-June 2004 Data

Here are the means and plus and minus one standard deviation as displayed on the lognormal plot (using default values):
1-yr Low P/E10: -3.7%, 11.0% and 25.7%.
1-yr Middle P/E10: 2.7%, 13.2% and 23.7%.
1-yr High P/E10: -8.6%, 6.0% and 20.6%.

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 0.0%:
1-yr Low P/E10: 76.1%, 4.5%, 11.0% and 12.5% (MAR = 0.2%).
1-yr Middle P/E10: 90.8%, 1.5%, 13.2% and 13.7% (MAR = -0.1%).
1-yr High P/E10: 64.1%, 6.4%, 6.0% and 9.2% (MAR = -0.1%).

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 1.0%:
1-yr Low P/E10: 73.9%, 4.8%, 11.0% and 11.8% (MAR = 1.1%)
1-yr Middle P/E10: 88.5%, 1.8%, 13.2% and 12.7% (MAR = 1.0%).
1-yr High P/E10: 60.7%, 7.0%, 6.0% and 8.4% (MAR = 1.1%).

Here are the probability above MAR, below target deviation, mean and upside potential when MAR = 2.0%:
1-yr Low P/E10: 71.5%, 5.2%, 11.0% and 11.2% (MAR = 2.0%)
1-yr Middle P/E10: 86.5%, 2.0%, 13.2% and 11.9% (MAR = 1.9%).
1-yr High P/E10: 58.1%, 7.5%, 6.0% and 7.8% (MAR = 2.1%).

These are the P/E10 thresholds:
Low P/E10: 7.39 to 14.92
Middle P/E10: 15.09 to 22.90
High P/E10: 24.76 to 43.77

January 1981-June 2004 Summary

The worse results occurred when P/E10 was high.

Middle values of P/E10 did better than the lowest values of P/E10. However, the low P/E10 values all occurred in the earliest years (in the 1980s). The calendar separated the low P/E10 data from the rest. Returns during the 1990s were higher than returns during the 1980s.

Since the early 1990s, lower levels of P/E10 have produced better results than high levels of P/E10.

Remarks

This is my second survey using the Forsey-Sortino model.

We had already learned to be wary of monthly return data. They strip away the effects of valuations. Single-year and two-year data restores the main effects at high and low valuations and produce similar trends. They differ in terms of the details associated with middle level valuations. Using two-year data groupings helps at middle level valuations.

To be precise, what we are learning has to do with Monte Carlo models. Conclusions do not necessarily translate into real world results. Still, relationships produced from the longer sequences probably are more representative of what happens in actual markets.

It makes sense that high valuations produce bad outcomes and low valuations produce good outcomes when holding periods are one year or longer. It makes sense that the ability to benefit at middle level valuations is better over a time period of two years than over a time period of one year.

In normal times, valuations have had a tremendous influence on upside potential. Using single-year data, we see this as strong only at low valuations. Two-year data (with a built-in longer holding period) demonstrate a strong result at middle level valuations as well.

Upside potential effects were dampened during the bubble. High valuations still reduced the upside potential, but not by much.

Have fun.

John Walter Russell
December 14, 2005