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September 27, 2004

Valuations and Risk-Adjusted Returns

John P. Hussman, Ph.D.
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One of the interesting distinctions in the financial markets is the one between risks and efficient risks. Risk alone has no necessary relationship with investment return, because some risks can be diversified away, or avoided altogether in cases when securities are not properly valued. For instance, you don't get a higher expected return for holding a poorly diversified portfolio, regardless of how risky it is (yes, the range of returns will be wider, but the average return is not correspondingly higher). So when we talk about there being a positive relationship between expected return and risk, we're already assuming that the selection, diversification, and optimization has been done – that is, we already have a portfolio that provides the highest expected return for a given level of risk, and no information exists that would allow that portfolio to be beaten over time. Taking greater risk as a strategy to earn higher expected returns is not useful unless the existing portfolio is already efficient and can't be improved upon while still holding risk constant.

To say “the market portfolio is efficient,” then, is to say that the expected return of every stock lines up in a way that no investor has an incentive to hold any stock in a different percentage than its weight in the market (you can derive the CAPM this way). It also effectively means that the expected return per unit of risk in the market is constant through time, so that no investor has an incentive to increase risk-adjusted returns by holding more of the market portfolio in one period than in another.

To some investors, market efficiency seems so implausible that they scoff at finance theory and abandon it altogether. I don't know any good investor who has succeeded this way. A good investor respects finance theory first, and then looks for the departures. As charming and simple as Warren Buffett might appear, anybody who carefully reads his comments knows that he understands valuation in exacting detail. Interestingly, his investment record also exhibits higher returns and lower volatility than the S&P over a convincingly long period.

Valuation – higher returns at lower risks

If you look at historical data carefully, you'll notice something that might seem peculiar. The periods of highest returns (say, over 5-year periods) are also generally the least volatile, while the periods of poorest returns are among the most volatile. Once you consider the mathematics of compounding, that result isn't quite so surprising. High compound returns almost require the avoidance of large losses. Take three consecutive years of 20% returns, and you've got a 20% compound annual return. Add one year with a 20% loss and the compound annual return plunges to 8.43%.

The question is whether any information would have allowed an investor to discern the likely profile of returns and risks in advance. With that in mind, I put together the chart below, using data since 1950. It shows the price/peak earnings multiple of the S&P 500, along with the compound annual total return over the subsequent 5-year period, the annualized standard deviation (volatility), and the annualized Sharpe ratio [a measure of return per unit of risk calculated as (annualized return – Tbill yield)/annualized standard deviation].

Stare at that chart. The Sharpe ratio for the S&P 500 index has averaged about 0.50 in data since 1950. Notice that very low valuations (price/peak earnings below 9) are associated with a Sharpe ratio nearly twice that historical norm, resulting both from a much higher-than-average annual return (18.9%) and lower-than-average volatility (13.9%). Since 1950, those periods have comprised about 20% of the data.

Though the 15-18 P/E range appears to have an average Sharpe ratio, that's actually thanks to observations in the 15-16 range. Even before the P/E ratio reaches 17, the prospective Sharpe ratio drops in half versus the historical norm, and continues to plunge as valuations increase further. Once valuations move above average, they begin to add insult to injury, with expected 5-year returns falling sharply while 5-year volatility actually increases. In a more complete analysis, of course, market action and other factors can be used to define market conditions more finely. But even an investor using valuations alone would have historically been well served to take proportionately less risk as valuations increased beyond the normal range.

The same pattern holds in data from 1900-1950, except that valuation levels were generally lower (about 40% of observations were at a price/peak earnings multiple below 9, owing largely to the post-depression valuations in the 1930's and 1940's). In short, the link between valuations and risk-adjusted returns (realized Sharpe ratios decline as valuations rise) is very clear in the historical data, regardless of how far back one cares to look.

Maximizing long-term risk-adjusted returns

If we consider the Sharpe ratio (investment return over and above the risk-free rate, per unit of volatility) as a desirable object to maximize over the long-term, the appropriate strategy immediately suggests itself: take a larger exposure to market risk when the expected return per unit of risk is high, and take a smaller exposure to market risk when the expected return per unit of risk is low. In other words, the long-term Sharpe ratio is simply a weighted-average of a whole series of shorter term Sharpe ratios. If the market's expected Sharpe ratio varies systematically with valuation, it makes sense to take more market risk during periods with higher expected Sharpe ratios (for example, by using a limited amount of leverage during very undervalued periods), and to take less market risk during periods with lower expected Sharpe ratios (for example, by hedging or avoiding market risk during very overvalued periods).

That said, there is a serious difficulty in following an approach like that, focusing on valuations alone. In order for a value-only strategy to be effective over time, you must have a long enough investment horizon to believe that stocks will both visit and leave at least one period of undervaluation during that investment horizon. Very simply, you don't benefit from an undervalued period that occurs after your investment horizon is already over.

For example, suppose that an investor has a brief investment horizon of say, 5 years, and stocks are steeply valued. If that investor takes a defensive position and the market happens to continue higher (as it did between 1996 and 2000, despite absurdly high valuations), the investor will be unconditionally worse off.

So value investors who take defensive positions also need long investment horizons and a lot of patience. Unfortunately, investors have a natural tendency to favor short-term comfort over long-term discipline, and even disciplined investors can abandon their strategy in frustration during periods when stocks are moving higher despite valuations that already seem ridiculous. The fact is, one needs to have an investment horizon of about 20 years in order to count on deep undervaluation to emerge and resolve itself.

One of the ways we get around that is to define investment conditions on the basis of both valuations and market action. Historically, there have been many periods in which stocks were overvalued and still continued higher. Yet there are other periods in which stocks were overvalued and subsequently plunged. In my work, the main factor that distinguishes between these two possibilities is the quality of market action. Robust advances tend to have an “in-sync” character about them, with very few divergences. Vulnerable markets tend to have internal turbulence and divergence that suggests a growing skittishness of investors toward risk. By taking both valuations and market action into account, favorable Market Climates emerge with much more regularity than relying on valuation alone. Still, the basic approach is the same – take more market risk in Climates that are associated with relatively high Sharpe ratios, and take less market risk in Climates that are associated with relatively low Sharpe ratios.

Market Climate

The Market Climate for stocks remains characterized by unfavorable valuations and tenuously favorable market action. Even with apparent sideways movement in the major averages, there is an important amount of turbulence in the finer structure of the market. For example, the S&P 500 has been tracing out a well-defined pattern of declining peaks and declining troughs, financials and consumer staples conglomerates have encountered abrupt difficulties, and for those who respect Dow Theory at any level (which includes us), the Dow Industrials have persistently failed to confirm new highs in the Transports (Richard Russell of Dow Theory Letters has remarked extensively on this). Earnings growth is projected to come in at 14% growth year-over-year, but there's no evidence that stock returns are correlated at all with short-horizon earnings growth, and in any event, negative preannouncements continue to swamp positive ones at a rate last seen near the 2003 low.

The main positive for the stock market right now is that market action continues, for whatever reason, to reflect a continued willingness of investors to speculate. That's a fairly tenuous willingness however, but it is enough to keep the Strategic Growth Fund holding a modest position (less than 1% of portfolio value) in index call options carrying past the election, capable of expanding our exposure to market risk to about 35% of portfolio value in the event of a substantial market advance. At present, implied option volatilities are very low, so I consider the cost of this “contingent” position very reasonable. In any event, with market action still tenuously favorable, our investment approach requires us to take at least some exposure to market fluctuations, and at current implied volatilities, the call options strike me as a more effective way to do that than lifting off a portion of our hedge outright.

In bonds, the Market Climate remains characterized by modestly unfavorable valuations and modestly unfavorable market action. As I've noted recently, the economic outlook has softened measurably, and though it would be a large surprise to see the ISM Purchasing Managers Index weaken to 50 in the next month or two, it is an important factor to watch.

Though the bond market has benefited from heavy short-covering among speculators and buying on speculation about economic weakness, both inflation risks and U.S. dollar risks currently seem underestimated. Unless we begin to see defaults or other panics that raise the desirability of holding cash (which would drive a corresponding decline in monetary velocity), it is unlikely that the rate of inflation will slow substantially. For that reason, my impression is that soon enough, the bond market will be dealing with sources of pressure (velocity- and energy-induced inflation and dollar weakness) unrelated to economic growth. Inflation protected securities, though not as exciting on rallies, appear to be better situated than nominal bonds here. The Strategic Total Return Fund also continues to carry about 14% of assets in precious metals shares.


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