In: Finance
Telecom Italia has a beta of 1.25 and an expected return of 14%. Assume that the return on an Italian risk-free asset is 2.1%. a) If a portfolio of the two assets has a beta of 0.93, what are the portfolio weights? b) If a portfolio of two assets has an expected return of 9%, what is its market risk premium? c) If you construct a different portfolio containing a different combination of the previous two assets that results in a Beta equal to 2.5, what are the portfolio weights? How do you interpret the weights for the two assets in this case?
Beta of Telecom Italia =1.25
Return on Telecom Italia = 14%
Risk Free Rate = 2.10%
a) Beta of Risk free Asset is 0 (Zero)
Beta of portfolio is weighted average beta of individual security
Therefore, Beta of Portfolio = Weight of Telecom Italia * Beta of Telecom Italia + Weight of Risk free * Beta of Risk free
0.93 = W1*1.25+W2*0
W1=0.93/1.25
W1 i.e. Weight of Telecom Italia = 74.40%
W2 Weight of Riskfree = 100% -74.40% = 25.60%
b)
Return of portfolio = Weight of Telecom Italia * Return of Telecom Italia + Weight of Risk free * Return of Risk free
9% = W1*14%+(1-W1)*2.1%
9% = 14%W1+2.1%-2.1%W1
(9%+2.1%)/11.90% = W1
W1 = 93.28%
W2 = 6.72%
Beta of the portfolio = 93.28% *1.25 = 1.166
As per CAPM,
Expected Return = Risk free Rate + Beta x Market Risk Premium
9% = 2.10% + 1.166 * Market Risk Premium
Market Risk Premium = (9%-2.1%)/1.166
Market Risk Premium = 5.92%
c)
Beta of portfolio is weighted average beta of individual security
Therefore, Beta of Portfolio = Weight of Telecom Italia * Beta of Telecom Italia + Weight of Risk free * Beta of Risk free
2.50 = W1*1.25+W2*0
W1=0.93/2.50
W1 i.e. Weight of Telecom Italia = 37.20%
W2 Weight of Riskfree = 100% - 37.20% =62.80%
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