Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 19%. L has an expected rate of return of 10% and a standard deviation of 16%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

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DeniceSandidge DeniceSandidge · Answer 1 · 2019-11-05T08:48:43+01:00

Answer:

risk free rate of return is = 11.37 %

Explanation:

given data

K expected rate of return = 13%

K standard deviation = 19% = 0.19

L expected rate of return = 10%

L standard deviation = 16% = 0.16

to find out

risk-free portfolio rate of return

solution

first we find here weight of each portfolio

weight of K = [tex]\frac{L standard deviation}{K standard deviation+ L standard deviation}[/tex] ..................1

weight of K = [tex]\frac{0.16}{0.19+0.16}[/tex]

weight of K = 0.4571 = 45.71%

and

weight of L = 1 - 0.4571

weight of L = 0.5428 = 54.28 %

so that

risk free rate will be here

risk free rate = ( weight of K × K expected rate of return ) + ( weight of L + L expected rate of return ) ..........................2

risk free rate = ( 45.71 % × 13 % ) + ( 54.28 % + 10% )

risk free rate = 11.37 %