***Please Show All Work So I Can Learn*** An investor can design a risky portfol
ID: 455389 • Letter: #
Question
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An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.4. The risk-free rate (T-bill rate) of return is 5%.
(a) The proportion of the optimal risky portfolio that should be invested in stock B is what?
(b) The expected return on the optimal risky portfolio is what?
(c) The standard deviation of the returns on the optimal risky portfolio is what?
(d) Investor wants to have an expected return of 10% for a complete portfolio. What proportion of his investment is in T-bills?
(e) What proportion of the investor’s complete portfolio is in stock A and in stock B?
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Explanation / Answer
Answer: Given
E(Ra) = Expected return of stock A = 21%
a= Standard deviation of return of stock A = 39%
E(Rb) = Expected return of stock B = 14%
b = Standard deviation of return of stock B = 20%
= The correlation coefficient between the returns of A and B = 0.4
Rf = The risk-free rate (T-bill rate) of return = 5%
Wa = weight of investment in stock A
Wb = weight of investment in stock B
a)The proportion of the optimal risky portfolio that should be invested in stock B is what?
Wb =[ E(Ra)-Rf) * b²] - [ E(Rb)-Rf) * ] / [( E(Ra)-Rf) * b²]+ [(E(Rb)-Rf) * a²] – [( E(Ra)-Rf) + (E(Rb)-Rf)]* ]
Wb = [(21-5)*20²] – [ 14-5] * 40] / [(21-5)*20²] + [(14-5)*39²] – [(21-5)+(14-5)] *40
Wb = 6400 – 360 / 6400 + 13689 – 1000
Wb = 6040 / 19089
Wb = 0.3164
Wb 31.64%
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