Question

Your client has invested $100,000 in an existing portfolio (called "original portfolio") that gives an expected monthly return of 3.1% with a standard deviation of monthly returns of 6%. Your client decides to add $400,000 of stock Y to this portfolio. Stock Y has an expected monthly return of 12.9% with a standard deviation of monthly returns of 19%. The coefficient of correlation between the stock Y and the original portfolio is -0.9.

1) Calculate the expected return and standard deviation of your client's new portfolio (which includes the original portfolio and the stock Y). Explain the difference, if any, you observe comparing the original portfolio and the new portfolio.

2) Explain without calculation, how your client's expected return and standard deviation would change if they used the $400,000 to purchase US Treasury Bills with an expected monthly return of 0.23%, instead of stock Y. Explain why.

Answer 1

1. Expected return and  standard deviation of client's new portfolio:

Expected Return:

Investment proportion of original portfolio =100000/500000 = .2

Investment proportion of stock Y =400000/500000 = .8

ER = 3.1%*.2 + 12.9%*.8 = 10.94%

standard deviation:

Portfolio Variance = w²_A*σ²(R_A) + w²_B*σ²(R_B) + 2*(w_A)*(w_B)*Cov(R_A, R_B); Where: w_A and w_B are portfolio weights, σ²(R_A) and σ²(R_B) are variances and
Cov(R_A, R_B) is the covariance

Varience = 232.192

Standard Deviation = Sqare root of Variance = 15.24

Observation: Both return and standard deviation is increased.

2) Expected return will be 0.8% and standard deviation will be 1.07 ( If the covariance is considered as same)

In case of Treasury bills Standard deviation will be 0