We can quantify that uncertainty using probability distributions. For example, suppose you are considering investing some of your money, now all in- vested in a bank account, in a stock market index fund. The price of a share in the fund is cur- rently $100, and your time horizon is one year. You expect the cash dividend during the year to be $4, so your expected dividend yield (dividends earned per dollar invested) is 4%. Your total holding-period return (HPR) will depend on the price you expect to prevail one year from now. Suppose your best guess is that it will be $110 per share. Then your capital gain will be $10 and your HPR will be 14%. The definition of the holding-period return in this context is capital gain income plus dividend income per dollar invested in the stock at the start of the period: HPR Endingprice of a share Beginningprice Cashdividend Beginning price   In our case we have     $110 $100 $4 $100 .14, or 14%   This definition of the HPR assumes the dividend is paid at the end of the holding period. To the extent that dividends are received earlier, the HPR ignores reinvestment income be- tween the receipt of the payment and the end of the holding period. Recall also that the per- cent return from dividends is called the dividend yield, and so the dividend yield plus the capital gains yield equals the HPR. There is considerable uncertainty about the price of a share a year from now, however, so you cannot be sure about your eventual HPR. We can try to quantify our beliefs about the state of the economy and the stock market in terms of three possible scenarios with probabilities as presented in Table 5.1. How can we evaluate this probability distribution? Throughout this book we will char- acterize probability distributions of rates of return in terms of their expected or mean return, E(r), and their standard deviation, . The expected rate of return is a probability- weighted average of the rates of return in each scenario. Calling p(s) the probability of each scenario and r(s) the HPR in each scenario, where scenarios are labeled or "indexed" by the variable s, we may write the expected return as   E(r) p(s)r (s) s (5.1) I. Introduction 5. History of Interest Rates and Risk Premiums The McGraw−Hill Companies, 2001