8-14. The Fruit Investment Fund has a total investment of $60 million in three s

Question

8-14. The Fruit Investment Fund has a total investment of $60 million in three stocks: Orange Tangerine $20 million $30 million $10 million The current risk-free rate is 6%. The expected and required rate of return for the market portfolio is based upon the following probability distribution: .10 .10 .35 .25 .20 -.05 .00 .10 .20 .30 o.o 0.05 Information on the stock's systematic risk is the following: O· BETA 1.72 0.97 1.63 Apple Orange Tangerine The expected returns on three stocks are the following PROBABILm APPLERETURN ORANGERETURN TANGERNERETURN .10 .25 .35 .30 -.05 .05 .10 .15 -.10 .00 .15 .25 -.30 .05 .20 .40 a. Compute the expected rate of return separately for Apple, Orange,& Tangerine stock. b. Compute the expected rate of return for the Fruit Investment Fund. c. Compute the Fruit Investment Fund's portfolio beta. d. What is the required rate of return for the Fruit Investment Fund? e. Should Fruit Investment fund be purchased? YES or NO? WHY? f. CDRAW THE SML PLOT AND POINTS QUESTION2 Draw a SML and provide the following labeled points and axis for the Fruit Investment Fund: 1. Risk-free rate of return 2. Required market rate of return 3. Required rate of return for the Fruit Investment fund 4. Expected rate of return for the Fruit Investment fund

Explanation / Answer

a) Computation of Expected rate of return of individual securities:

Apple Return = (0.10x-0.05) + (0.25 x 0.05) + (0.35x0.10) +(.30 x 0.15) = 0.0875 or 8.75%

Orange Return= (0.10x-0.10) + (0.25 x 0.00) + (0.35x0.15) +(.30 x 0.25) = 0.1175 or 11.75%

Tangerine Return = (0.10x-0.30) + (0.25 x -0.05) + (0.35x0.20) +(.30 x 0.40) = 0.1475 or 14.75%

b) Expected Rate of return of a portfolio is the weighted avg of the stocks return taking investment value as weighted.

Therefore Expected return of portfolio is = [(8.75 x 20) + (11.75 x 30) + (14.75 x 10)] / (20+30+10)

= 11.25%

c) Beta of a portfolio is the weighted avg of the stocks return taking investment value as weighted.

Portfolio beta = [(1.72 x 20) + (0.97 x 30) + (1.63 x 10)] / (20+30+10) = 1.33

d) Required Rate of Return = Risk free rate + (Market Premium x Beta)

= 6 + [(14 - 6)x1.33]

= 16.64%

e) No, The Fruit Investment fund should not be purchased because our required return is more than the expected return of the portfolio.

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