REQUIRED RATE OF RETURN Suppose rRF = 5%, rM = 13%, and bi = 2. What is ri, the

Question

REQUIRED RATE OF RETURN Suppose rRF = 5%, rM = 13%, and bi = 2. What is ri, the required rate of return on Stock i? Round your answer to two decimal places. C. Now assume that rRF remains at 5%, but rM increases to 14%. The slope of the SML does not remain constant. How would these changes affect ri? Round your answer to two decimal places. . Now assume that rRF remains at 5%, but rM falls to 12%. The slope of the SML does not remain constant. How would these changes affect ri? Round your answer to two decimal places. The new ri will be?

Explanation / Answer

As per the relationship equation between ri , rm, rRF and beta (bi) ;

ri = rRF + bi( rm - rRF)

So, here ri = 5 + 2(13-5) = 5 + 16 = 21%

If rm increases from 13 to 14, the slope of the SML and hence bi will also increase. Let us assume the new beta is binew where binew > bi . New equation will be;

rinew = rRF + binew (rMnew - rRF)

rinew = 5 + binew (14 - 5) = 5 + 9* binew . And since our new beta is greater than 2 , we can find it by equating 8/2 = 9/y, cross multiplying , y = 18/8 = 2.25 . So SML equation becomes rinew = 5 + 9*2.25 = 25.25 %. In short, we can say that return on stock will increase by increasing the market return and letting the risk free return same.

Now, if rM = 12, equation become

ri = 5 + bi (12-5) = 5 + bi * 7, here bi can be found by equating 8/2 = 7/ bi , bi = 14/8 = 1.75. So, ri = 5 + 1.75* 7 = 17.25.

In short, we can say that by decreasing the market return from 13 to 12 and letting risk free rate remain same at 5%, return on stock will also decrease from 21% to 17.25%.

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