Question

An investors wishes to allocate his funds among stocks A and B. Stock A has an expected return of 8.17%8.17% and stock B of 3.11%3.11%. The investor wishes to achieve an expected target return of 8.77%8.77% on his portfolio. What are the portfolio weights for stock A and B in order to achieve this target performance? (rounded to two decimal places)

Select one:

a. 111.86%111.86%; −11.86%−11.86%

b. −111.86%−111.86%; 211.86%211.86%

c. 49.82%49.82%; 50.18%50.18%

d. −16.86%−16.86%; 116.86%116.86%

e. 50.18%50.18%; 49.82%

Please explain!

Answer 1

Option a

Expected return on portfolio=weighted average of expected return on individual stocks.

Let the weight of stock A in portfolio be x, total weight of a portfolio is always , hence weight of B in portfolio=1-x.

Hence expected return on portfolio=8.17*x+3.11*(1-x).

now, according to problem,

8.77=8.17*x+3.11*(1-x)

or, 8.17*x+3.11*(1-x)=8.77

or, 8.17x+3.11-3.11x=8.77

or, 5.06x=8.77-3.11

or, 5.06x=5.66

or, x=5.66/5.06

or, x=1.11857=111.857%=111.86%(approx)

Hence weight of A=111.86%

Weight of B=1-x=1-1.11857=-0.11857=-11.857%=-11.86%(approx.)