Does Tactical Allocation Based On Prior Returns Pay Off?  
 

There is little question that the financial markets can be profoundly irrational. Over long time periods, asset valuations and returns can gyrate wildly. At times stocks may become absurdly overvalued, and at other times they cannot be given away. It would seem axiomatic that the alert and disciplined investor could take advantage of this phenomenon with some ease.

Consider, for example, the behavior of large US stocks over the past several decades. There is fairly good data on the price to book ratio, dividend yield, and price to earnings ratio of the Dow Jones Average going back 80 years. Until recently, anyway, the P/B ratio of the Dow has correlated fairly well with the 5 year future return of large US stocks. For almost all of the 1926-94 period the DJIA has been priced at between 1 and 3 times book value. Had one simply bought and held large stocks (proxied as the S&P) for the 1926-94 period one would have garnered a return of 10.19% with a standard deviation of 20.30%.

Now, consider a strategy where equity exposure is allotted according to P/B -- e.g., 100% stock at a PB of 1, 50% at 2, 25% at 2.5, and 0% at 3. This determination is made at the beginning of each year; whatever not allotted to stocks is invested in 5 year treasuries. This strategy yields an annualized return of 10.96% with an SD of 15.34% -- a slightly higher return with much less risk.

It can be argued that we are cheating by employing an allocation rule using P/Bs of 1 and 3 as our border values; in 1926 we had no way of knowing that these would be the "correct" values. Fine -- let's say we guessed wrong and used P/Bs of 0.5 and 6 as our border values (100% stock at 0.5, zero stock at 6.0). As this is being written the P/B of the DJIA/S&P is actually approaching this upper limit. This rule yields a return of 10.39% and an SD of 16.36% -- still better than buy and hold 100% stock. The point is this; any strategy that slightly increases the portfolio exposure of an asset as it gets cheaper, and slightly decreases it as it gets more expensive seems quite likely to both increase return while reducing risk.

One ought to be able to expand this sort of strategy to international investing. Unfortunately, it is difficult, if not impossible, to compare P/B, P/E, and dividend yields across borders.

Some other kind of approach is needed.  There is ample evidence that a wide range of assets mean revert -- i.e., a period of outperformance by any one asset is likely to be followed by a period of underperformance.

Anthony Richards, from the IMF, in an article to be published in December's Journal of Finance, looked at the 16 MSCI countries from 1970 to 1995, and examined the performance of portfolios made up of the 4 "winners" and "losers" over varying time periods. Here are the results over different horizons, relative to the average of all of the countries studied:
 

	Winner Portfolio (annualized relative return)	Loser Portfolio (annualized relative return)
3 months	+6.4%	+3.3%
6 months	+1.5%	-1.9%
12 months	-0.4%	-2.7%
24 months	-4.0%	+1.2%
36 months	-3.2%	+3.2%
48 months	-3.0%	+2.7%
60 months	-1.6%	+1.8%

(The time periods are both forward and backward looking. I.e., "12 months" refers to the forward 12 month performance of the winners/losers over the previous 12 months.)

As you can see, there is a strong tendency for past winners to produce above average short term performance, and below average longer term performance. The opposite is true of past losers. (Be careful with the 3 month data -- remember that this is annualized.)

For those of you who want to look at the piece yourselves, it can be found at http://www.cob.ohio-state.edu/~fin/journal/archive_papers/issdec97/ms5314.pdf

Unfortunately, switching back and forth between different national index portfolios is not practical for small investors. As an alternative, I've calculated the "autocorrelations" for 5 year returns for a range of global regional assets. An "autocorrelation" is simply the correlation of a time series with itself, lagged by one period. So, an autocorrelation of +1 means that an above average result in one period always predicts the same above average result in the next period. (This is mathematically impossible.) An autocorrelation of -1 predicts the opposite result, and a value of zero is seen when the return for a given period has no predictive value. Put another way, a high positive autocorrelation favors momentum strategies, a high negative correlation favors contrarian strategies, and a zero autocorrelation defines a "random walk," in which a fixed, mechanically rebalanced policy is most effective.

Here are the autocorrelations for 5 year periods for some regional global assets:
 

Asset	1970-94	1972-96
S&P 500	-0.12	+.14
US small stocks	-0.39	-0.45
Japanese stocks	-0.50	-0.12
Pacific Rim stocks	-0.73	-0.62
European stocks	-0.45	-0.39
UK stocks	-0.66	-0.26
Precious Metals stocks	+0.44	+0.07

 

I've used the two overlapping periods to judge the reproducibility of the data. Note that for both periods US small stocks and all foreign stock groups fairly strongly mean revert. Large US stocks exhibit a random walk, and precious metals stocks may actually have nonregressing behavior -- at least over 5 years.

Over shorter periods of time, this negative autocorrelation tends to disappear, and at very short periods, tends to be positive. For example, the average autocorrelation for the above assets over 1 month periods is about +0.1. Extensive studies have tended to confirm the short term positive and long term negative autocorrelation of US equity prices. Lakonishok et. al. have recently demonstrated positive excess returns generated by short term momentum strategies, and discuss why this is not necessarily inconsistent with longer term contrarian strategies.

The overwhelming acceptance of the "random walk" behavior of stock prices is seen to stem from the fact that most of the data is derived from large US securities. Look at almost any other equity class, however, and there is fairly strong evidence for mean reversion over long time periods.

I've looked at the data yet another way. Let's use the database of global equity assets for the 1970-94 period (the above, except that the EAFE-E is used to combine UK and European stocks.) The "relative 5 year return" for each asset is calculated as the difference between for the return for the asset and for the average of all 6. This "relative return" is then compared with the "relative" return for the same asset for the next 5 years. It turns out that if you aggregate all of the nonoverlapping 5 year autocorrelations (24 in all, there are 4 data points for each of 6 assets) the average autocorrelations is -0.44. In other words, if Japanese stocks have underperformed global equities for the past 5 years, the odds are that they will outperform global equities in the next 5 years.

In summary, then, the performance of a wide group of global assets seems to mean revert, with a mean 5 year autocorrelation of about -0.4 to -0.5, either in absolute or relative terms.

Can the individual investor make this pay?

For some time I've experimented with models which examine different allocation strategies for overweighting/underweighting global asset categories which underperform/outperform. The results have been disappointing. Those which work best involve "all or none" paradigms, similar to the technique used by Richards. . Consider the 1970-96 allocation model discussed in last month's issue, consisting of 6 assets:

• S&P500
• US Small
• EAFE-E
• EAFE-PXJ
• EAFE-Japan
• Gold Stocks

The 5 year returns are calculated every 5 years, and the best performing asset is dropped for the next 5 years, resulting in an equally weighted portfolio of the remaining 5 assets. Thus, this portfolio covers the 22 year period 1975-96, with portfolio revisions being made in 1975, 1980, 1985, 1990, and 1995. This portfolio returned 19.20% annually, with an SD of 17.44%. The "coward's portfolio" consisting of equal amounts of all 6 assets yielded a return of 17.57% with an SD of 15.68%. The Sharpe ratios, assuming a 7.11% t bill yield for the period, are 0.697 for the dynamically allocated portfolio, versus 0.667 for the coward's statically allocated portfolio.

What if you rebalance every year based on the previous 5 year's performance, dropping the winner each year ? The results are worse -- a 22 year return/SD of 17.64/18.44, with a Sharpe of 0.559.

What to make of all this? Although I've identified a few methods of increasing risk adjusted yield slightly, I've also identified many more which have failed. I would bet that the successful techniques (using P/B and dividend yield with the S&P, eliminating the best global performer every 5 years) were more the result of data snooping than of a genuine efficacy.

The lesson? Don't get too cute with your allocations. Keep them fairly constant over the long haul, and don't count on reversion to the mean to increase your returns by very much. Even Richard's method, which uses the white-knuckle strategy of picking the 4 nations with the worst preceding 3 year returns, produces an excess return of only 3.2%. It's a good bet that a fair chunk of this advantage was extracted from the old data mine.

If you must change your allocations, do so very slowly and infrequently, by very little, and always in a contrarian manner.
 
 

 

copyright (c) 1997, William J. Bernstein