Investments, tenth edition

  Excess Returns and Risk Premiums 

 How much, if anything, should you invest in our 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. The risk-free rate in our example is 4% per year, and the 

expected index fund return is 9.76%, so the risk premium on stocks is 5.76% per year. 

The difference in any particular period between the  actual  rate of return on a risky asset 

and the actual risk-free rate is called the    excess  return.    Therefore, the risk premium is the 

expected value of the excess return, and the standard deviation of the excess return is a 

measure of its risk. (See  Spreadsheet 5.1  for these calculations.) 

 The degree to which investors are willing to commit funds to stocks depends on    risk 

aversion.    Investors are risk averse in the sense that, if the risk premium were zero, they 

would not invest any money in stocks. In theory, 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 the 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  s   for 

common stocks and other types of securities. Here, history has insights to offer. Analysis 

of the historical record of portfolio returns makes use of a variety of concepts and statisti-

cal tools, and so we first turn to a preparatory discussion. 

 

   

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6/18/13   8:03 PM

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P A R T   I I

  Portfolio Theory and Practice

 You invest $27,000 in a corporate bond selling for $900 per $1,000 par value. Over the coming year, the 

bond will pay interest of $75 per $1,000 of par value. The price of the bond at year’s end will depend on 

the level of interest rates that will prevail at that time. You construct the following scenario analysis: