Question

E[R] and σ(R) and Standard Deviation of a Portfolio. Assume that ABC is selling for $10 per share, XYZ is selling for $20 per share, and XYZ has an expected return of 8% and a standard deviation of 30%.

(a) Over the past four years, ABC has returned 10%, 0%, -5%, and 15%. Assuming these past returns are representative of what ABC might return in the future, what are ABC’s expected return and standard deviation?

(b) You decide to buy 10,000 shares of each company. If the covariance between ABC and XYZ is 0, what is the expected return and standard deviation of your portfolio over the next year?

Answer 1

a.

Expected Return of ABC = (10 + 0 + (-5) + 15)/4

Expected Return of ABC = 5%

Standard Deviation = 9.13%

b.

Covariance = 0

Expected Return of XYZ = 8%

Standard Deviation of XYZ = 30%

So,

Weight of ABC = 100000/300000 = 0.3333

Weight of XYZ = 200000/300000 = 0.6667

Expected Return = Weight average return of Stocks

Expected Return = 0.3333(0.05) + 0.6667(0.08)

Expected Return = 0.016665 + 0.053336

Expected Return of Portolio = 7.0%

Standard Deviation = [ w²_A*σ²(R_A) + w²_B*σ²(R_B)]^1/2 (As correlation = 0)

Standard Deviation of Portfolio = 20.23%