Question

You are given the following information from your boss: Stock Bond E(r.) - Port Stan. Dev. Sharpe Ratio 100% 0% 8.00% 15.00% 0.400 80% 20% 7.20% 12.70% 0.409 60% 40% 6.40% 11.01% 0.399 40% 60% 5.60% 10.25% 0.351 20% 80% 4.80% 10.62% 0.264 0% 100% 4.00% 12.00% 0.167 Min Var. 36.36% 63.64% 5.45% 10.23% 0.338 Optimal 77.2% 22.8% 7.09% 12.42% 0.410 The information was calculated assuming a 2% risk free rate and a 0.20 correlation co-efficient. Assume your client would like to earn 6% on her money. What is the standard deviation of your clients 6% returning portfolio? Answer in percentages with 1 decimal point.m

Answer 1

Expected Return of Stock (ER_S ).= 8%

  as given in question if 100% invest in Stock and 0% in Bond we get 8% return, it means expected return of stock is 8%.

Expected Return of Bond (ER_B ).= 4%

  as given in question if 0% invest in Stock and 100% in Bond we get 4% return, it means expected return of stock is 4%

Client wants to earn 6% on her money. It means expected return of Portfolio (ER_P ) = 6%

Now we find weights of stock and bond to earn 6% return on portfolio.

ER_P = W_S * ER_S + W_B * ER_B

W_S = weight of stock = w (assumed)

W_B = weight of bond = 1 - w

6% = w * 8% + (1 - w ) * 4%

0.06 = 0.08w + 0.04 - 0.04w

0.06 - 0.04 = 0.08w - 0.04w (by solving equation)

0.02 = 0.04w

w = 0.02 / 0.04

w = 0.5 Or 50%

w = W_S = 50%

W_B = 1 - w = 1 - 0.5 = 0.5 Or 50%

Standard Deviation of Stock (SD_S ).= 15%

  as given in question if 100% invest in Stock and 0% in Bond we get 15% standard deviation, it means standard deviation of stock is 15%.

Standard Deviation of Bond (SD_B ).= 12%

  as given in question if 0% invest in Stock and 100% in Bond we get 12% standard deviation, it means standard deviation of bond is 12%.

r = 0.20 (given)

SD_P = 10.5%

Standard Deviation of Client is 10.5% of 6% returning portfolio.