40. Nuada Airgetlam wants to create a $75,000 portfolio comprised of two stocks

Question

40. Nuada Airgetlam wants to create a $75,000 portfolio comprised of two stocks plus a risk-free security. Stock A has an expected return of 13.58 percent and stock B has an expected return of 11.39 percent. Nuada wants to own $27,000 of stock B. The risk-free rate is 4.07 percent and the expected return on the market is 9.87 percent. If Nuada wants the portfolio to have an expected return equal to that of the market, how much should he invest in the risk-free security?

Part B  Lugh owns a portfolio valued at $23,693. The portfolio consists of four stocks. Stock A is worth $4,858, stock B is worth $3,937, and stock C is worth $12,410. What is the portfolio weight (in percents) of stock D?

Explanation / Answer

Total Investment = 75,000

Stock B investment = 27,000 => Weight of B = 27,000 / 75,000 = 36%

Remaining investment = 75,000 - 27,000 = 48,000 in Stock A and Risk-free asset.

Assume y% in A and 1 - y in riskfree asset.

E(Ra) = 13.58%, E(Rb) = 11.39%, Rf = 3.07%, Rm = 9.87%

Portfolio Returns = wa x E(Ra) + wb x E(Rb) + wrf x Rf

=> 9.87% = y x 13.58% + 36% x 11.39% + (1 - y) x 3.07%

=> y = 25.69%, i.e Invest 25.69% x 48,000 = 12,329 in Stock A

and 1 - y = 74.31%, ie. Invest 48,000 - 12,329 = 35,671 in risk-free asset.

b) Stock D worth = 23,693 - 4,858 - 3,937 - 12,410 = $2,488

=> Weight of Stock D = 2,488 / 23,693 = 10.50%

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