Question

In: Finance

A portfolio manager has a $10 million portfolio, which consists of $1 million invested in stock...

A portfolio manager has a $10 million portfolio, which consists of $1 million invested in stock X and $2million invested in stock Y seperate stocks. Stock X has a beta of 0.9 where as stock Y has a beta of 1.3. The risk-free rate is 5% and the market risk premium is 6%.

a. Calculate portfolio's beta

b. Calculate stock X and stock Y required returns.

c. Calculate portfolio's required return.

d. Calculate portfolio's required rate of return if risk aversion increases by 2%.

Note: This question is fully complete and there is nothing to be added.

Solutions

Expert Solution

Information given:

Total portfolio value - 10 million

Invested in Stock X - 1 million = 0.1 of the portfolio

Invested in Stock Y - 2 million = 0.2 of the portfolio

Beta of Stock X - 0.9

Beta of Stock Y - 1.3

Risk free rate - 5%

Market risk premium - 6%

Part a)

Calculating the portfolio beta assuming investment has been made only in the two given stocks:

Portfolio beta = sum of the stock's weighted beta values

Portfolio beta = 0.1*0.9 + 0.2*1.3 = 0.09 + 0.26 = 0.35

Thus portfolio beta value is 0.35.

Part b)

Calculating the required returns on the stocks, the formula is:

Required return = Risk free rate + beta * (market return - risk free rate)

Stock X:

Required return = 0.05 + 0.9 * ( 0.06 - 0.05 )

= 0.05 + 0.9*0.01

= 0.05 + 0.009

= 0.059 or 5.9%

Stock Y:

Required return = 0.05 + 1.3 * ( 0.06 - 0.05 )

= 0.05 + 1.3*0.01

= 0.05 + 0.013

= 0.063 or 6.3%

Part c)

Portfolio's required return is calculated by the following formula:

Portfolio return = Sum of weighted required returns

Portfolio return = 0.1*0.059 + 0.2*0.063 = 0.0059 + 0.0126 = 0.0185

Thus, portfolio's expected return from these two stocks = 1.85%

Part d)

When an investor is risk averse, they expect to get more returns for the same amount of risk taken. Thus, this can be factored in by calculating the return required with the following formula:

Return expected = risk free rate + beta* ( market risk premium + risk aversion - risk free rate)

Stock X : 0.05 + 0.9*(0.06+0.02 - 0.05) = 0.05 + 0.9 * 0.03 = 0.05 + 0.027 = 0.077

Stock Y : 0.05 + 1.3 *(0.06+0.02 - 0.05) = 0.05 + 1.3 * 0.03 = 0.05 + 0.039 = 0.089

Portfolio return required from these two stocks = 0.077*0.1 + 0.089 *0.2 = 0.0077+0.0178 = 0.0255

Thus, portfolio return required = 2.55%


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