Answer:
1. Weight of A=0.5, Weight of B= 0.5
2. Asset A has the highest shape ratio. The weight of A and B in the optimal risky portfolio that has the highest shape ratio is:
Weight of A= 0.105, Weight of B= 0.895
Explanation:
Expected return of Asset A= 5%Expected return of Asset A= 5%
Expected return of Asset B= 3%
Annual volatilities of Asset A= 20%
Annual votalities of Asset B= 20%
1. Correlation coefficient = 30% = 0.3 < 1
Risk Free Rate = 1% =0.01
1. Weight of A and B in portfolio with minimal risk is:
Weight of A= β^2B - Cov (XAXB) /β^2A + β^2B - 2Cov (XAXB)
Therefore,
CovXAXB = PAB (Volatility of A) (Volatility of B)
= 0.3 × 0.2 × 0.2
= 0.012
Hence,
Weight of A= (0.2)^2 - 0.012 / (0.2)^2 + (0.2)^2 - 2(0.012)
Weight of A= 0.04 - 0.012 / 0.04 + 0.04 - 0.024
= 0.028/ 0.08 - 0.024
= 0.028/ 0.056
=0.5
Weight of A = 0.5
Weight of B= 1 - Weight of A
Weight of B= 1 - 0.5
Weight of B= 0.5
2. Shape ratio of A= RA - Rf / β
= 0.05 - 0.01 / 2
= 0.04/2
= 0.02 =20%
Shape ratio of B= RB - Rf / β
= 0.03 - 0.01/ 2
0.02 / 2
=0.01 = 10%
So, Asset A has the highest shape ratio
Cov (XAXB) = PAB (Volatility of A) (Volatility of B)
= 0.03 × 0.2 × 0.1
= 0.006
Weight of A= β^2B - Cov (XAXB) /β^2A + β^2B - 2Cov (XAXB)
Weight of A = (0.1)^2 - 0.006 / (0.2)^2 + (0.1)^2 - 2(0.006)
= 0.01 - 0.006 / 0.04 +0.01 - 0.012
= 0.004/ 0.05 - 0.012
= 0.004/ 0.038
= 0.105
Weight of A = 0.105
Weight of B= 1 - 0.105
Weight of B= 0.895
