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?

Answer 1

As per the relationship equation between r_i , r_m, r_RF and beta (b_i) ;

r_i = r_RF + b_i( r_m - r_RF)

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

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

r_inew = r_RF + b_inew (r_Mnew - r_RF)

r_inew = 5 + b_inew (14 - 5) = 5 + 9* b_inew . 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 r_inew = 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 r_M = 12, equation become

r_i = 5 + b_i (12-5) = 5 + b_i * 7, here b_i can be found by equating 8/2 = 7/ b_i , b_i = 14/8 = 1.75. So, r_i = 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%.