EQUITY RISK PREMIUM: EXPECTATIONS GREAT AND SMALL

North American Actuarial Journal,  Jan 2004  by Derrig, Richard A,  Orr, Elisha D

• E-mail
• Print
• Link

2 According to CAPM, investors are compensated only for nondiversifiable, or market, risk. The market beta becomes the measurement of the extent to which returns on an individual security co-vary with the market. The market beta times the ERP represents the nondiversifiable expected return from an individual security.

3 Campbell, Lo, and MacKinlay (1997, pp. 307-308) performed a similar analysis and found a risk-aversion coefficient of 1 9, larger than the reasonable level suggested in Mehra and Prescott's paper.

4 see Appendix C.

5 For a complete discussion of the arithmetic/geometric choice, see lbbotson Associates (2003b, pp. 71-3). see also Dimson et al. (2002, p. 35), and Brennan and Schwartz (1985).

6 The arithmetic difference is the geometric difference multiplied by 1 + Risk Free.

7 THe reason for this is two-fold, hirst, when issued, the yield is the expected market return for the entire horizon of the bond. No net capital gains are expected for the market return for the entire horizon of the bond. No capital gains are expected at the default-free maturity. second, historical annual capital gains on long-term government bonds average near zero (0.4%) over the 1926-2002 period (lbbotson Associates 2003a, tables 6-7).

8 One qualitative difference can arise from the collapse of equity markets during war time.

9 For the lbbotson analysis of the small stock premium, the NYSE/ AMEX/NASDAQ combined data are used, with the S&P 500 data falling within deciles 1 and 2 (lbbotson Associates 2003b, pp. 66 and Chapter 7.)

10 A more recent alternative is Wilson and Jones (2002), as cited by Dimson et al. (2002, p. 39).

11 Using Wilson and Jones' 1871-2002 data series, time series analyses show no significant ERP difference between the 1871-1925 period and the 1926-2002 period; one cannot distinguish the old from the new. The overall average is lower with the additional 1871-1925 data, but on a statistical basis, they are not significantly different. Assuming the equivalency of the two data series for 1871-1925 (Goetzmann et al. 2001 and Wilson and Jones 2002), the risk difference found by Goetzmann et al. must be determined by a significantly different ERP in the pre-1871 data. The 1871-1913 return that is prior to personal income tax and that appears to be about 35% lower than the 1926-2002 period average of 11.8%, might simply reflect a zero valuation for income taxes in the pre-1914 returns. Adjusting the pre-1914 data for taxes would most likely make the ERP for the entire period (1871-2002) approximately equal to 7.5%, the 1926-2002 average.

12 The low risk-free return is indicative of the "risk-free rate puzzle," the twin of the ERP puzzle. For details see Weil (1989).

13 The nominal and real ERPs are identical in Table 5 because the ERPs are calculated as arithmetic differences, and the same value of inflation will reduce the market return and the risk-free return equally. Geometric differences would produce minimally different estimates for the same types.