Question

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?

Answer 1

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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