You have $136,000 to invest in a portfolio containing Stock X, Stock Y, and a ri

Question

You have $136,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 16 percent and that has only 86 percent of the risk of the overall market. If X has an expected return of 42 percent and a beta of 1.6, Y has an expected return of 21 percent and a beta of 1.3, and the risk-free rate is 7 percent, how much money will you invest in Stock Y? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

You have $136,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 16 percent and that has only 86 percent of the risk of the overall market. If X has an expected return of 42 percent and a beta of 1.6, Y has an expected return of 21 percent and a beta of 1.3, and the risk-free rate is 7 percent, how much money will you invest in Stock Y? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Explanation / Answer

We will have to use the equations for Expected Return and Beta of the Portfolio to determine the amount to be invested in Stock Y. The equations are given below:

Expected Return of the Portfolio = Investment Percentage in Stock X*Expected Return on Stock X + Investment Percentage in Stock Y*Expected Return on Stock Y + Investment Percentage in Risk Free Stock*Expected Return on Risk Free Stock

Beta of the Portfolio = Investment Percentage in Stock X*Beta of Stock X + Investment Percentage in Stock Y*Beta of Stock Y + Investment Percentage in Risk Free Asset*Beta of Risk Free Asset

Let us assume Investment Percentage in Stock X is "X" and Investment Percentage in Stock Y is "Y". Investment Percentage in Risk Free Asset will, therefore, be (1-X-Y)

_______

Using the information provided in the question, we get,

16% = X*42% + Y*21% + (1-X-Y)*7% {Equation 1}

and

.86 = X*1.6 + Y*1.3 + (1-X-Y)*(0) [The beta of Risk Free Asset is 0] {Equation 2}

Solving the equations, we get,

Y = (.86 - 1.6X)/1.3 = .6615 - 1.2308X

Substituting this value of Y in equation 1, we get,

.16 = .42X + .21*.(6615 - 1.2308X) + (1-X-(.6615 - 1.2308X))*.07

.16 = .42X + .1389 - .2585X + .07 - .07X -.0463 + .0862X

X = (.16 -.1389 -.07 + .0463)/(0.42-0.2585-0.07+0.0862) = -.01463

Now, we can determine the investment percentage for Stock Y and Risk Free Stock

Investment Percentage in Stock Y = .6615 - 1.2308*(-.01463) = .6795

Investment Percentage in Risk Free Stock = 1- (-.01463) - .6795 = .3351

________

The total amount of money to be invested in Stock Y is 136,000*.6795 = $92,412.90 (there can be a slight difference in the final answer on account of rounding off intermediate values)

Answer is $92,412.90.

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