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Company X has a beta of 0.70, while Company Y's beta is 1.20. The required return...

Company X has a beta of 0.70, while Company Y's beta is 1.20. The required return on the stock market is 11.00%, and the risk-free rate is 4.25%. A fund has $3500 invested in company X stock and $4500 invested in the stock of company Y. a) What is fund's required rate of return? b) Suppose you sell all of your holdings in stock Y and invest $4500 in stock Z having beta of 1.5. What is the fund's new beta after this transaction?

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Expert Solution

Solution a) Beta of Stock X = 0.70

Investment in stock X = $3500

Beta of Stock Y = 1.20

Investment in stock Y = $4500

Total investment in the fund = Investment in stock X + Investment in stock Y

= $3500 + $4500 = $8000

Weight of stock X in the fund = Investment in stock X/Total investment in the fund

= 3500/8000 = 43.75%

Weight of stock Y in the fund = Investment in stock Y/Total investment in the fund

= 4500/8000 = 56.25%

Beta of the fund = ∑Weight of Individual Security in a Portfolio×Beta of Individual Security

Beta of the fund = 43.75%*0.70 + 56.25%*1.20 = 0.98125

According to the Capital Asset Pricing Model (CAPM), the required return of the fund = Risk-free rate + Beta*(Market return - Risk-free rate)

Required return of the fund (using CAPM) = Rf + beta* (Rm - Rf)

where Rf = risk-free rate = 4.25%;

Rm = market return = 11%

Hence, the required return of the fund = 4.25% + 0.98125*(11% - 4.25%)

= 4.25% + 0.98125*6.75%

= 4.25% + 6.6234375%

= 10.87%

Solution b) All of the holdings in stock Y are sold and $4500 are invested in stock Z having beta of 1.5.

Beta of Stock X = 0.70

Investment in stock X = $3500

Beta of Stock Z = 1.50

Investment in stock Z = $4500

Total investment in the fund = Investment in stock X + Investment in stock Z

= $3500 + $4500 = $8000

Weight of stock X in the fund = Investment in stock X/Total investment in the fund

= 3500/8000 = 43.75%

Weight of stock Z in the fund = Investment in stock Z/Total investment in the fund

= 4500/8000 = 56.25%

Beta of the fund = ∑Weight of Individual Security in a Portfolio×Beta of Individual Security

Beta of the fund = 43.75%*0.70 + 56.25%*1.5 = 1.15

Hence, beta of the new portfolio = 1.15

jeff jeffy answered 1 year ago

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