Question

Use the following information to answer the next FOUR (4) questions: The following data are available relating to the performance of Zeta Stock Fund and the market portfolio: Zeta Market Average Return 0.13 0.15 Std. Dev. of Returns 0.35 0.3 Beta 0.9 Tracking Error 0.11 Average PE The risk-free rate during the sample periods was 0.07 18 18. Calculate the Jensen measure of performance for Zeta Fund. 19. Calculate the Treynor measure of performance for Zeta Fund. 20. Calculate the Information Ratio measure of performance for Zeta Fund. 21. Calculate the M2 measure of performance for Zeta Fund.

Answer 1

18. Formula to calculate Jensen measure

Jensen's alpha of zeta fund = expected return of zeta fund – [risk free rate + beta of the zeta fund* (expected market return – risk free rate)]

Where,

Return of zeta fund = 0.13

Risk free rate = 0.07

Beta of zeta fund = 0.9

Market return = 0.15

Therefore,

Jensen's alpha of zeta fund = 0.13 - [0.07 + 0.9 *(0.15 – 0.07)]

= 0.13– 0.142 = - 0.012

19. Treynor Measure

Treynor Measure of zeta fund = (expected return of zeta fund – risk free rate)/ Beta of zeta fund

Where,

Return of zeta fund = 0.13

Risk free rate = 0.07

Beta of zeta fund = 0.9

Therefore,

Treynor’s measure of zeta fund = (0.13 – 0.07)/0.9 = 0.06/0.9 = 0.067

20. Information ratio = (Return of the zeta fund – Return of the Market)/ Tracking error of zeta fund

Where,

Return of the zeta fund = 0.13

Return of the Market = 0.15

Tracking error of zeta fund = 0.11

Therefore,

Information ratio of zeta fund = (0.13 -0.15)/0.11

= - 0.1818

21. M^2 Measure

M^2 Measure of zeta fund = (Std. Dev. of market /Std. Dev. Of zeta fund) *(expected return of zeta fund – risk free rate) + risk free rate

Where,

Std. Dev. of market = 0.3

Std. Dev. Of zeta fund = 0.35

Return of zeta fund = 0.13

Risk free rate = 0.07

Therefore,

= (0.3/0.35) * (0.13 – 0.07) + 0.07

= 0.1214