Expected Returns by SML

The optimism of investors towards the economy and corporate earnings is signified by a drop in risk aversion. A drop in predicted returns reflects this optimism. Prices are inversely proportional to interest rates and hence a drop in the projected rate of return leads to stock price upsurge. The risk spread between bonds and stocks drops corresponding to a reduction in return on stocks (Poon, Stapleton, 2005, p. 35). The intercourse between Expected Returns and Beta is illustrated by the Security Market Line (SML) equation (Poon & Stapleton, 2005, pp. 25-126).
The y-axis represents Expected Returns whereas the x-axis signifies Beta. Expected Returns are equal to Market Risk Premium (Beta) plus Risk-free Rate. Risk-Free Rate of return is the return on government securities with the least risk. Market Risk Premium is arrived at by subtracting the risk-free rate of return from the Return on Market portfolio. Beta is an indication of systematic risk signifying covariance between Return on Market Portfolio and Return on Security or Return on Market Portfolio variance.
Expected Returns = Risk-free Rate + Market Risk Premium (beta). Beta is constant since it signifies systematic risk that cannot be altered. The risk-free Rate of Return is also constant since the analysis doesn’t incorporate risk. Market Risk Premium or the slope of the SML indicates risk aversion levels. The steeper the SML slope, the more the risk aversion and vice versa (Poon, Stapleton, 2005, p. 50). Arithmetic or Geometric Average Return represents the annual cumulative Return on Equities.

Serially uncorrelated returns’ arithmetic mean is the optimum prediction for future returns in any future year. The best prediction over long periods is the correctly derived arithmetic mean. Siegel in 1998 documented a US equities’ geometric mean of 7. 0% for the years 1802-1997 and 1871-1997. The arithmetic means the return is the mean of a year’s past returns. The arithmetic average return is more than the geometric mean return that is 8. 5% (1802-1997) and 8. 7% (1871-1997). A 75-year prediction will arrive at 1. 085 cumulative returns for the period between 1802 and 1997.