Question

long-term Commonwealth bonds’ rate is 2.50%p.a.the return (standard deviation) for market-index is 9.65% p.a. (17% p.a.)

	Fund STR	Fund SHP	Fund ENT	Fund GLX
Average Return (% p.a.)	10.50	20.70	12.30	18.40
Standard deviation (% p.a.)	3.40	5.60	7.40	5.85
Beta	1.00	1.97	0.73	1.19

Required

I. Which fund has the lowest overall risk versus its return?

II. Which funds following Jensen’s alpha outperformed the market?

Answer 1

I). Lowest overall risk vs return can be measured by using Sharpe ratio which is calculated as

(Fund return - risk-free rate)/standard deviation of the fund

Fund STR Sharpe ratio = (10.50%-2.50%)/3.40% = 2.35

Fund SHP Sharpe ratio = (20.70%-2.50%)/5.60% = 3.25

Fund ENT Sharpe ratio = (12.30%-2.50%)/7.40% = 1.32

Fund GLX Sharpe ratio = (18.40%-2.50%)/5.85% = 2.72

As can be seen, Fund SHP has the highest excess return per unit risk (or in other words, the lowest risk vs return).

II). Jenson's alpha = average fund return - expected return where

expected return (using CAPM) = risk-free rate + beta*(market return - risk-free rate)

Jenson's alpha for Fund STR = 10.50% - (2.50% + 1*(9.65%-2.50%)) = 0.85%

Jenson's alpha for Fund SHP = 20.70% - (2.50% + 1.97*(9.65%-2.50%)) = 4.11%

Jenson's alpha for Fund ENT = 12.30% - (2.50% + 0.73*(9.65%-2.50%)) = 4.58%

Jenson's alpha for Fund GLX = 18.40% - (2.50% + 1.19*(9.65%-2.50%)) = 7.39%

All four funds have a positive Jenson's alpha so all four funds have outperformed the market.