Question

The expected return of Bonita is 15.3 percent, and the expected return of Windsor is 23.3 percent. Their standard deviations are 10.3 percent and 23.3 percent, respectively, and the correlation coefficient between them is zero. What is the expected return and standard deviation of a portfolio composed of 25 percent Bonita and 75 percent Windsor? (Round intermediate calculations to 6 decimal places, e.g. 31.212564 and final answers to 2 decimal places, e.g. 15.25%.) The expected return % Standard deviation of portfolio 0% What is the expected return and standard deviation of a portfolio composed of 75 percent Bonita and 25 percent Windsor? (Round intermediate calculations to 6 decimal places, e.g. 31.212564 and final answers to 2 decimal places, e.g. 15.25%.) The expected return Standard deviation of portfolio % Would a risk-averse investor hold a portfolio made up of 100 percent of Bonita?

Answer 1

1) Bonita 25% and Windsor 75%

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

(wxox)2 + (wyoy)2 + 2 * 0x *0x *W, * Wy* P1,2

where x and y are the securities

Expected return = 0.25*0.153+0.75*0.233 = 0.213 = 21.30%

Standard deviation = ((0.25*0.103)^2 + (0.75*0.233)^2 + 2*0.25*0.75*0.103*0.233*0)^0.5 = 0.1766

Standard deviation = 17.66%

2) Bonita 75% and Windsor 25%

Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)

Standard deviation of portfolio =

(wxox)2 + (wyoy)2 + 2 * 0x *0x *W, * Wy* P1,2

where x and y are the securities

Expected return = 0.75*0.153+0.25*0.233= 0.1730 = 17.30%

Standard deviation = ((0.75*0.103)^2 + (0.25*0.233)^2 + 2*0.25*0.75*0.103*0.233*0)^0.5 = 0.0968

Standard deviation = 9.68%

3) NO

This is because the standard deviation of the portfolio consisting of Bonita 75% and Windsor 25% is less than that of Bonita alone. Along with lower standard deviation (risk), the expected return is also higher. Hence, a risk averse investor would invest in a combination portfolio (like in part b) to reap the diversification effects.