Question

Assume you have two investment opportunities.

1. Corporate Disasters (CD) has expected returns ?(?_CD) = 4% and standard deviation of

   returns 9%.

2. Nevada beach front properties (NBF) has expected returns ?(?_NBF) = 10% and standard

   deviation of returns 18%

Risk free rate is R_f = 1%.

1. a) Calculate Sharpe ratios of these two portfolios.

2. b) Assume you can invest only in one of those companies (and a risk free rate). Assume

   your target rate of return is 6%. Calculate portfolios with CD&RF and NBF&RF which

   would deliver this return. Which portfolio has smaller standard deviation and why?

3. c) Assume you have a portfolio which is not efficient. Assume Corporate Disasters have

   market beta of ?_CD = 0.5 and Nevada beach front properties have market beta
   ?_NBF = 4. Calculate Treynor measures for those securities. Which one should you add to

   your portfolio to increase the Sharpe ratio.

Answer 1

a) Sharp Index = (Portfolio average return - Risk free rate of interest) / Strandard deviation of the portfolio return

Corporate disasters(CD) Sharp index= (4%-1%)/9% = 0.3333

  Nevada beach front properties (NBF) Sharp index= (10%-1%)/18% = 0.5

b) Portfolio with Corporate disasters(CD)= target return/CD return =6%/4% =1.5 CD

Risk of portfolio CD = 1.5 * standard deviation CD = 1.5*9% = 13.5%

Portfolio with Nevada beach front properties (NBF) = target return/NBF return =6%/10% =0.6 CD

Risk of portfolio Nevada beach front properties (NBF) = .6 * standard deviation NBF = .6*18% = 10.8%

So,Portfolio with Nevada beach front properties having smaller standard deviation while comparing with Portfolio with Corporate disasters(CD).

c)Treynor Index = (Portfolio average return - Risk free rate of interest) / Beta of the portfolio

Corporate disasters(CD) Treynor Index = (4%-1%)/.5 = 6

Nevada beach front properties (NBF) Treynor Index = (10%-1%)/4 = 2.25