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The Stock Market Correction in Context: Are Equities Cheap or Expensive?

股市调整:股票是便宜了还是贵了?

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【来源】: PIIE
【时间】: 2018-11-05
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October was a bad month for the US stock market. The S&P 500 index fell nearly 7 percent in the month, erasing most of its year-to-date gains. This large swing in the market has left many wondering where we stand; are equities cheap or expensive? The analysis here shows that stocks are expensive relative to their historical average, but they are still likely to outperform bonds over the next 10 years.
One commonly used measure for the valuation of stocks is Robert Shiller’s cyclically adjusted price to earnings ratio (CAPE). The CAPE is calculated as the S&P 500 equity price index divided by the 10-year average of inflation-adjusted earnings per share. The 10-year average is used to smooth out short-term earnings fluctuations related to the business cycle.
At the end of October, the CAPE was 31, which is higher than its historical average, but lower than the dot-com boom of the late 1990s. (See figure 1.) One factor contributing to the high value of the CAPE is the Great Recession of 2008-09, which depressed earnings by more than any time since the 1930s. As 2008 and 2009 drop out of the 10-year average earnings, the CAPE is likely to fall. Figure 1 shows that a CAPE based on 8-year average earnings (thus excluding 2008 and 2009) would be noticeably lower, but still above its historical average. [1]
However, any assessment of stock prices must take into consideration the alternative investments available. The primary alternative investment is bonds. Because stocks are riskier than bonds, they normally provide a higher rate of return. The excess return to holding stocks relative to bonds is called the equity premium (EP). An EP calculated using returns for a period in the past is called an ex post EP, whereas an EP calculated using expected returns for a period in the future is called an ex ante EP. The question is whether the ex ante EP is a good predictor of the future ex post EP – that is, does the expected return of stocks in excess of bonds help predict the actual return to stocks in excess of bonds?
As in a previous blog post, the ex ante EP is constructed as the cyclically adjusted earnings-price ratio (the reciprocal of the CAPE) minus the inflation-adjusted yield on the 10-year Treasury note.[2] The ex post EP is the nominal rate of return to holding the S&P 500 index and reinvesting all dividends for 10 years minus the yield on the 10-year Treasury note at the start of the holding period.
Figure 2 shows the relationship between the ex post and ex ante EP over two different periods: 1881 to present and 1945 to present. Each point refers to returns calculated over the same holding period. For example, the ex ante EP in 2000 is based on the earnings-price ratio in 2000, whereas the ex post EP in 2000 is based on actual earnings and stock prices over the following 10 years. The plot suggests a positive relationship between the ex post EP and the ex ante EP, which is stronger for the more recent sample period. As shown in Table 1, regressions confirm that the ex ante EP is a highly significant predictor of the ex post EP. A 1 percentage point increase in the ex ante EP is associated with a 0.4 percentage point increase in the ex post EP over the full sample period, and a 0.9 percentage point increase in the post-war period.
Table 1. Regression of ex post equity premium (1)
1881–2007 (2)
1945–2007 Ex Ante 0.443**
(3.21) 0.927***
(4.71) Constant 2.324*
(2.44) 0.593
(0.45) ARMA Residuals
AR(1) 0.892***
(22.41) 0.826***
(9.15) MA(10) -0.521***
(-4.11) -0.395**
(-2.78) R2 0.233 0.658
Note: t statistics in parentheses. * p