Question

You decided to invest your wealth of $10,000 in a portfolio of three stocks. You also decided to sell stock 1 short and collect $3,000. After the short sale you will invest $8,000 of your cash in stock 2 and the remainder in stock 3. The expected rate of return of stock 2 is R₂ = 18% and of stock 3 is R₃ = 22%. What should the rate of return on stock 1 be for the portfolio rate of return to equal 19%?

a.

21.33%

b.

-6.22%

c.

26.44%

d.

9.88%

Answer 1

Weights of each Stock = Invested in that Stock/Total Investment

Stock A = -3000(negative, because shorted)/10000 = -0.3

Stock B = 8000/10000 = 0.8

Stock C = (10000+3000-8000)/10000 = 5000/10000 = 0.5

Expected Return of Portfolio = Weighted Average Return = Sum of (Weights*Returns)

Therefore,

19 = (-0.3*R)+(0.8*18)+(0.5*22)

19 = -0.3R+14.4+11

0.3R = 25.4-19

Therefore, Return on Stock 1 = R = 6.4/0.3 = 21.33%