As long as the probability distribution is more or less symmetric about the mean, is an adequate measure of risk. In the special case where we can assume that the probability distribution is normal-represented by the well-known bell-shaped curve-E(r) and are perfectly adequate to characterize the distribution.

Getting back to the example, how much, if anything, should you invest in the index fund? First, you must ask how much of an expected reward is offered for the risk involved in investing money in stocks.

We measure the reward as the difference between the expected HPR on the index stock fund and the risk-free rate, that is, the rate you can earn by leaving money in risk-free assets such as T-bills, money market funds, or the bank. We call this difference the risk premium on common stocks.

If the risk-free rate in the example is 6% per year, and the expected index fund return is 14%, then the risk premium on stocks is 8% per year. The difference in any par- ticular period between the actual rate of return on a risky asset and the risk-free rate is called excess return. Therefore, the risk premium is the expected excess return.

The degree to which investors are willing to commit funds to stocks depends on risk aversion. Financial analysts generally assume investors are risk averse in the sense that, if the risk premium were zero, people would not be willing to invest any money in stocks. In theory, then, there must always be a positive risk premium on stocks in order to induce risk- averse investors to hold the existing supply of stocks instead of placing all their money in risk-free assets.

Although this sample scenario analysis illustrates the concepts behind the quantification of risk and return, you may still wonder how to get a more realistic estimate of E(r) and for common stocks and other types of securities. Here history has insights to offer.

I. Introduction 5. History of Interest Rates and Risk Premiums

The McGraw−Hill Companies, 2001

138 PART I Introduction

Table 5.2 Rates of Return, 1926-1999

Small Large Long-Term Intermediate- Year Stocks Stocks T-Bonds Term T-Bonds T-Bills Inflation

1926 8.91 12.21 4.54 4.96 3.19 1.12

1927 32.23 35.99 8.11 3.34 3.12 2.26

1928 45.02 39.29 0.93 0.96 3.21 1.16

1929 50.81 7.66 4.41