Friday, 24 August 2012

Interpreting Mean Reversion: Time Varying Equity Premium

Next in this series of articles about equity prices, returns and mean reversion, preceded by Mean Reversion and Equity Prices: Background Research and Implications for InvestmentsCyclical Variation in Equity Prices and Interpreting Mean Reversion: Mispricing in Irrational Markets, is the interpretation of the time varying equity premium. As previously explained, the excerpts are taken from an academic paper I wrote back in 2001, but which I believe is as relevant as ever today.

Time Varying Equity Risk Premium

It is a general assumption in finance that investors are risk averse. It then follows, in theory, that there must always be a positive premium, i.e. a higher expected return than holding the risk free investment, for holding shares in order to induce such investors to buy shares given their higher risk. The cost of equity therefore consists of the rate offered by the risk free asset plus this premium, referred to as the equity risk premium (ERP). In this discussion, the ERP is defined according to the CAPM. However, there is a growing body of literature that uses valuation models to estimate expected returns (Fama and French (2001)). The ERP is perhaps the single most important number in financial economics (Welch (2000) and Pastor and Stambaugh (2001)). The importance of the number is evident from its use as an input in asset allocation models, and asset pricing models such as the CAPM. Over the long term, for the U.S. stock market, the ERP is measured to be around 6.6 percent (Siegel (1998)). In an earlier study, Siegel and Thaler (1997) find that the premium has increased with time in the U.S. stock market. Over a 193-year period, the excess return on equity has been 5.3 percent per year and the premium has risen from 2.9 percent (1802-1871) to 4.7 percent (1872-1925) and finally 8.1 percent over the most recent period (1926-1997). However, since the mid 1970s the premium has declined significantly in response to a fundamental shift in the relative riskiness of stocks and bonds. Bond returns became almost as variable as stock returns in the 1980s and remained so into the 1990s. In recent years, the risk premium has declined, not because stocks have become less volatile, but because bonds have become more volatile. The difference in risk between the two asset classes is for this reason less than before and so the spread has declined (Reilly and Brown (1997)). Although written some years back, Woolridge (1995) conclude “for a given level of interest rates, investors appear to be willing to pay a higher price for equities today than, say, in the1960s and early1970s”. At the end of 1997 the premium was about 4 percent and approaching the 2 to 3 percent range (Siegel (1998)). Pastor et al (2001) estimate the ERP in the U.S. to have fluctuated between 3.9 and 6.0 from January 1834 through June 1999 with a sharp drop in the last decade. Finally, Claus and Thomas (2001) estimate that the premium has been 3 percent or less for each year between 1985 and 1998 for in the US and five other large stock markets. Since the rate of arrival of new information is time varying, we should expect the variance of the rates of return on shares and the covariance among them, to be time varying. Thus, stationary components of long-horizon returns can also result from time-varying equilibrium expected returns generated by rational pricing in inefficient market. If stock returns are mean reverting, Campbell (2000) interprets this as if investment opportunities are time varying. Furthermore, this mean reversion in returns slows the growth of conditional variances of long horizon returns, making equities appear less risky at long horizons relative to the short-term (Barberis (1999) and Campbell (2000)). The equity risk premium, being an integral part of the expected return equation, also varies with changes in market consensus, and Chen (1991) explains that higher expected future levels of economic activity will generally lead to higher expected stock market returns. More specifically, he finds evidence for his hypothesis that the market premium is negatively related to the recent growth rate and positively related to the expected future growth rate in GNP. Furthermore, in a depressed state where consumption is low, relative risk aversion and hence the market’s risk premium, tends to be high. This points in the direction that the ERP tends to increase during recessions as opposed to during bull markets when the premium tends to be very small. Perez-Quiros and Timmermann (2000) show evidence of such movements in the expected equity risk premium, especially for small firms. In harmony with Chen (1991), the ERP is found to be small and even negative prior to and during the early recession phase, followed by a sharp increase during later stages of most recessions. They argue that a possible interpretation of this finding is that, as recessions grow deeper, small firms rapidly lose collateral and their assets then become more risky. This in turn causes investors to require a higher premium for holding their shares. Theory predicts that the same holds for larger companies as well since the equity beta increases with leverage (Fama (1991)) and leverage ratios tend to increase during recessions when the market value of equity decreases. How much higher premium investors demand during recessions for investing in individual shares depends on two factors: the market premium and the equity beta. This deserves a closer discussion. The former is a market measure, meaning it is affected only by the expected returns of the market as a whole. Assuming equilibrium in capital markets, the risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the representative investor (Bodie et al (1999)). The higher the perceived risk of the market portfolio and the more risk averse the representative investor, the higher the market premium becomes. The equity beta is a measure of how the market portfolio and the individual asset move together and can be viewed as a risk premium on individual assets. As for the factors affecting the equity beta, Brealey and Myers’ (2000) suggest that cyclicality and operating leverage are its main determinants. First, the strength of the relationship between the firm’s earnings and the aggregate earnings of the market is considered to be of outmost importance. The prediction is that firms with high accounting or cash-flow betas should also have high stock betas. Beaver and Manegold (1979) confirm this. This means that cyclical firms, firms whose revenues and earnings are strongly dependent on the state of the business cycle, tend to be high-beta firms. Second, operating leverage, the degree of fixed costs to total costs, influences the equity beta. Lev (1974) confirms that companies with relatively high operating leverage indeed have higher betas.

In summary, the higher the market premium, the more the company is exposed to the business cycle and the higher its operating leverage, the higher the equity premium becomes. We could therefore reasonably expect to find high equity risk premiums, e.g. low valuations, for small-sized, cyclical companies with a high degree of operating leverage facing a recession. Bernstein (1995) offers a practitioners view on this issue. He explains that when investor expectations are optimistic, meaning that nominal profit growth is expected to become increasingly abundant, investors will generally bid up the prices of stocks that comprise the riskier market segments. When expectations become more pessimistic, then investors will shun the riskier segments of the equity market, and will invest in safe haven segments, e.g. non-cyclical sectors. He indicates that markets are not fully rational when he concludes, “It is the perception or, better yet, the misperception and not the reality of what is safe or risky that presents the opportunity for the contrarian”. A contrarian investment strategy involves buying against sentiment, i.e. buying shares that most investors find unattractive or overly risky, and investing in companies with low earnings expectations (See Bernstein (1995) and Dreman (1998)). Perhaps even more important, PerezQuiros et al (2000) find that the premium per unit of risk, the price of risk, varies considerably over the economic cycle. They interpret this as the time variation in expected returns can be driven by either variations in the level of risk or by changes in the price of risk, and that both components need to be investigated. Since investors generally don not like uncertainty, they perhaps unsurprisingly find evidence that stock return volatility is highest during economic recessions. It therefore seems reasonable to believe that the equity premium is positively associated to at least some degree with equity volatility (Pastor et al (2001)). The price of risk can be thought of in terms of the Sharpe ratio. Both Whitelaw (1997) and Perez-Quiros et al (2000) find that the ratio tends to increase during recessions and to drop rapidly in the ensuing expansion states. The latter conclude by arguing that “the rapid increase during recessions in small and large firms’ expected returns appears to be the result of a rise in the level of risk confounded by an increase in the expected price of risk”. Whitelaw (1997) reports that peak ratios are on average 0.397 less than the ratios at troughs (-.106/ .291) and concludes “there appears to be striking cyclical variations in Sharpe ratios” and that, “almost without exception, business cycle peaks correspond to low Sharpe ratios and business cycle troughs to high Sharpe ratios”. Factors such as the credit risk premium are also thought to influence the ERP. The notion is that changes in the absolute or percentage spread between the yield on BAA and AAA bonds indicate a change in the required rate of return by the investors for accepting credit risk. It is based on current market results and reflects the investors’ attitudes. Thus, the larger the spread, the more riskaverse the investors and the larger the ERP. The two opposite views, irrational markets and time varying risk premia, can imply the same price behavior. Fama et al (1988) explains the intuition behind this. A short review of their interpretation follows. Expected returns correspond roughly to the discount rates that relate a current stock price to expected future dividends. Suppose that investor tastes for current versus risky future consumption and the stochastic evolution of the investment opportunities of firms result in time-varying equilibrium expected returns that are highly auto correlated but mean reverting. Suppose further that shocks to expected returns are uncorrelated with shocks to rational forecasts of dividends. It then follows that a shock to expected returns has no effect on expected dividends or expected returns in the distant future. The cumulative effect of shock on expected returns must then be exactly offset by an opposite adjustment in the current price. They conclude that auto correlated expected returns in such a scenario lead to slowly decaying components of prices that are indistinguishable from the temporary price components of an inefficient market. Finally, according to Bodie et al (1999), interest rates and corporate profits are perhaps the two factors with the greatest impact on share prices. Applying the P/E model, they show that the inverse of this ratio, the earnings yield, varies with the interest rates. This is as expected, since a general feature of any fundamental valuation models implies the discounting of future profits into present values. With this in mind, it has been argued that the volatility of stock prices is higher than warranted by changes in dividends (Shiller (1981,1989)). It should be noted that dividends are more stable than earnings (Lintner (1956) and Reilly et al (1997), especially for cyclical companies whose management often encourage the practice of averaging profits over the cycle by maintaining a constant dividend growth rate over the cycle (Hooke (1998)). Assuming rational investors apply the dividend discount model to their investment decisions, it follows that the numerator in the valuation equation cannot explain the volatility in stock returns through time. We are then left with the denominator in the equation, the cost of equity and growth in dividends, to explain the volatility. Real interest rates are too stable to explain large swings in stock prices (Shiller (1981)) and there is very little evidence that price-to-divided ratios predict future consumption growth, dividend growth, or real interest rates (Campbell (2000) and Poterba and Summers (1986)). In a CAPM framework, this suggests that the volatility of stock returns must be explained by time-varying changes in the equity premium itself. Campbell (2000) supports this reasoning and suggests, “the volatility of stock returns must be explained by variation in the equity premium itself”. This will be discussed in detail in the next article.