Question

1. Assume you are considering investing your personal portfolio in only two possible risky assets: 60% invested in Asset Y and the rest in Asset Z. The characteristics of these two risky assets are as follows:
   • Asset Y has an Expected Return of 12% and a standard deviation of 15%
   • Asset Z has an Expected Return of 9% and a standard deviation of 12%
   • Correlation between the returns of Asset Y and Asset Z is 0.20

1. Find the Expected Return of this 2-Asset Portfolio.

2. What is the Standard Deviation of this 2-Asset Portfolio?

3. Finally, if the correlation were to suddenly drop to -0.3 and all other inputs stayed the same, in what direction would you expect this portfolio’s Sharpe Ratio to change? Why?

Answer 1

a. Expected return of the portfolio = 10.8%
b. Expected standard deviation of portfolio= 11.01%
c. It increases.

As the correlation decreases, the risk of the portfolio(standard deviation) also decreases.
Sharpe ratio = expected risk minus risk-free rate/ standard deviation

Hence the Sharpe ratio increases.

Asset 4 y = 12 % 2 = 9.). Asset 2 Ty = 15% - 18./. correlation - 0.20 (2) wy= 0.6 Wzo 1-0.6 - 0.4 a. Return of portfolio - wy dy + werz = 0.6(12) + (0.4) a z 10.8% b. Standard deviation of portfolio tp = wyty) 7 (Wete) 7 auguz (80g on) v (0.6x)} (0-4x12)72 (0-6x0.4)(0.2x15x12) = 1.01./ c.) see text.