Question

You are managing a risky portfolio with an expected return of 15%, a variance of 0.0784, and a beta of 1.4. Suppose that the T-bill rate is 5% and the S&P500 stock index (as the market index) has an expected return of 10% and a variance of 0.04. Your client chose to invest 80% of her portfolio in your fund and the rest in a T-bill money market fund. What is the Treynor ratio of your client’s portfolio?

A. 0.3571

B. 0.1161

C. 0.0571

D. 0.0714

Answer 1

Answer

Treynor ratio of client's portfolio is OPTION D 0.0714

Calculation is below

Return on risky asset 15% or 0.15

Return on T-Bill 5% or 0.05

Investment : 80% in Risky Asset & 20% in T Bill

Return on Investment : 0.80 * 15% + 0.20 * 5% = 12% + 1 % = 13% or 0.13

Beta of risky investment : 1.4

Beta on T-Bill : 0 ( Beta is not provided in question but but of Risk free asset is 0)

Beta of Investment : 1.4*0.8 + 0 *0.2 = 1.12

Treynors Ratio : Return on Investment - Risk free return i.e. return on T Bill divided by Beta of Investment.

= (0.13 - 0.05 ) / 1.12

= 0.08 /1.12

= 0.7142