You are considering investing $1,000 in a complete portfolio. The complete portf

Question

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 3% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 80% and 20%, respectively. X has an expected rate of return of 12%, and Y has an expected rate of return of 7%. The dollar values of your positions in X, Y, and Treasury bills would be _________, __________, and __________, respectively, if you decide to hold a complete portfolio that has an expected return of 9%
a) $500, $150, $350
b) $150, $500, $350
c) $150, $600, $250
d) $600, $150, $250

please show your work! :)

Explanation / Answer

Answer is d) $600 , $150 & $250

Step 1 Weighted average return on Risky Portfolio = 80% * 12% + 20% * 7% which is = 11%

Step 2 :- now its given that weighted average return on complete portfolio is 9%

therefore weight of Treseary bills is x then 9% = 3% * x + 11% * (1-x)

x = 0.25

so Weights of Treseary bills = 25% , Wight of X is 75% * 80% i.e. 60% & Y is 75% * 20% i.e. 15%

therefore now muliply these weights to Investment

X = $1000 * 60% = $600

Y = $1000 * 15% = $150

Treasury bills = $1000 * 25% = $250

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.