Question
Could someone help me with b)? The answer for a) is: (A) Given, Beta of mutual fund: 1.5 Expected Return of mutual fund: 9% Risk
Could someone help me with b)?
The answer for a) is: (A)
Given,
Beta of mutual fund: 1.5
Expected Return of mutual fund: 9%
Risk free rate 1%
Market Return 5%
1) Fund's Alpha
Alpha = Expected return - CAPM return
CAPM return = risk free rate + Beta (Market return - risk free
return)=0.01 + 1.5*(0.05-0.01)
CAPM return = risk free rate + Beta (Market return - risk free
return)=0.01 + 1.5*(0.05-0.01) 7.00%
Alpha = 9% - 7% = 2%
2) Yes, we should invest in a fund as it is generating positive
alpha that means it is generating returns higher than the systematic risk
involved in the fund due to superior investing.
3) Passive portfolio
As passive portfolio is a porfolio based on market index. Beta
of such passive portfolio invested 100% in the market is 1. The required beta
of the mutual fund is 1.5 so this portfolio needs to be invested more in market
by borrowing at risk free rate.
So to get the beta of 1.5 foloowing weights are required:
150% on market portfolio
-50% on riskfree asset
4) Return on passive portfolio
Return = 1.5*(5%) -0.5*(1%) = 7%
5) Difference between the returns:
Difference = Expected return on mutual fund - Expected Return on
passive fund = 9% - 7% = 2%
This difference arises because mutual fund is generating higher
return than the systematic return undertaken because of positive alpha but the
passive fund is just generating the required return according to the level of
the systematic risk undertaken.
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