chapter 5 note - Fin 4320: Investments Risk and Portfolio...

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1 Fin 4320: Investments Risk and Portfolio Management Chapter 5 By M. Metghalchi Expected and Unexpected Returns The return on a security can be expressed as: Total return = Expected return + Unexpected return R = E(r) + U E(r) = expected return and U = unexpected return Note : the average value of the unexpected return is zero. E(r) = E(D) / P + E(g) E(r) = expected return as percentage E(D) = expected dividend E(g) = expected growth rate in the stock (capital gain) Announcements and News: The same way an announcement can be broken into two parts, the anticipated or expected part, and the surprise part: Announcement = Expected part + Surprise The expected part is the part of the information that is included in the E(R) that the market was expecting. And the surprise part is the news that influences the unanticipated return on the stock, U. The current price reflects relevant publicly available information, or the expected information. . So when we speak of news, we mean the surprise part of the announcement. The expected return is the return the investor anticipates when the investment is made. The required return is the return necessary to induce the investor to make the investment. The expected return must be equal to or greater than the required return in order to induce the investor to purchase the asset. The realized return is the return the investor actually earns. This realized return may differ considerably (in either direction) from the expected return. Expected Return Expressed as Probability
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2 E(r) = n i=1 r i P(r i ) (1) Where n = the number of possible states of the economy r i = the cash flow in the ith state of the economy P(r i ) = the probability of the ith return Example: Consider three stocks, A,B, and C in Table 1 and assume the following return possibilities for different economic conditions for the coming year: Table 1 State of the economy Returns if the state of the economy occurs Probability Stock A Stock B Stock C Deep recession .20 8% 16 % 8 % Mild recession .20 10 % 14 % 10 % Average economy .20 12 % 12 % 12 % Mild boom .20 14 % 10 % 14 % Strong boom .20 16 % 8 % 16 % Using equation 1 above, estimate the expected returns for A,B and C. E(r) = n i=1 r i P(r i ) = r 1 P 1 + r 2 P 2 + r 3 P 3 + r 4 P 4 + r 5 P 5 Stock A: E(r) = .20* 8 % + .20*10% +.20*12%+.20*14%+.20*16% E(r) = 12 % Do as an exercise for B and C and you should find that their expected returns are also 12%. Note: the above formula uses subjective probability (the returns and probabilities of each economic condition is given subjectively by the researcher). Subjective probabilities are set by the researcher. If we don’t want to use subjective probability, we can determine the expected return of a stock as an average of past returns of that stock or:
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3 E(r) = n i=1 r i / n (2) Example: Assume stock D had the following returns over the past 5 years: 10%, -6%, 30%, 20%, 14%; what is the expected return for stock D? E(r
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chapter 5 note - Fin 4320: Investments Risk and Portfolio...

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