Question

ALLLLL 23. You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio Rp Qe Bp 12.0% 33% 1.95 11.0 28 1.25 7.3 18 0.60 Market 11.4 1.00 Risk-free 6. 8 0 0 What are the Sharpe ratio, Treynor ratio, and Jensen's alpha for each portfolio?

Answer 1

1. Sharpe Ratio = E(R) - RF (S.R) o 5. R of x = 12-6-8- - = 0.1575 33 SR of u = 11-6.8 28 - nuo SR of a = 7.3-6.8 = 0.02778 2. Treynor Ratio = E(R)-RF ToR of x = 12-6.8 .. = 2.667 1.95 T-R of y= 11-6.8 1.25 = 3.36 TR of a = 7.3-6.8 0.60 = 0.8333

Capital Asset pricing model:

As per CAPM model:
Re= Rf+(Rm-Rf)B

Re= required rate of return.
Rf= Risk-free rate.
Rm =Market Risk Premium.
B = Beta, systematic risk.

E(R) = Expected Return of X, Y, Z = 12, 11, 7.3%

3. Jensen Alpha (x) = E(R)-Re As per CAPM; Re- RA+ (Rm - Rp) ß x of x = 12 -6.8+(11-4-6-8)1.95] = -3.77% x of 4 = 11-[ 6.8+ (1-4-6.8) 1.25 - = - 1. 55% x of 2 = 7.3 - [ 6.8 + (1.4-6-8) 0-6] = - 2.26%