optimal portfolio practice exam question


optimal portfolio practice exam question

Author
Message
NEAS
Supreme Being
Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)Supreme Being (5.9K reputation)

Group: Administrators
Posts: 4.5K, Visits: 1.6K


BM Ch9 optimal portfolio practice exam question

The market has only two risky securities, with expected returns, standard deviations, and market values of

    Expected Return    Standard Deviation    Market Value
Stock Y     9.19%    30.40%    45.59 million
Stock Z    13.80%    67.20%    18.97 million


The correlation of stocks Y and Z is 54.62%. Risk-free bonds yield 4.74%. An investor who can borrow or lend at the risk-free rate forms an optimal portfolio of risk-free bonds and risky securities.

Question 8.1: Expected return of market portfolio of risky assets

What is the expected return of the market portfolio of risky securities?

Answer 8.1: The expected return of the market portfolio of risky securities is a weighted average by market value:

    ( (9.19%) × 45.59 + (13.80%) × 18.97 ) / (45.59 + 18.97) = 10.54%


Question 8.2: Variance of market portfolio of risky assets

What is the variance of the market portfolio of risky securities?

Answer 8.2: The variance of the market portfolio of risky securities is

    ( (30.40%)2 × 45.592 + (67.20%)2 × 18.972 + 2 × (54.62%) × (30.40%) × 45.59 × (67.20%) × 18.97) / (45.59 + 18.97)2 = 13.14%



Question 8.3: Standard deviation of market portfolio of risky assets

What is the standard deviation of the market portfolio of risky securities?


Answer 8.3: The standard deviation of the market portfolio of risky securities is the square root of the variance

    (13.14%)0.5 = 36.25%


Question 8.4: Composition of optimal portfolio

What is the composition of the optimal portfolio with a standard deviation of 42.7%?

Answer 8.4: The optimal portfolio is a combination of risk-free bonds with a standard deviation of zero and the market portfolio of risky securities that have a standard deviation of 36.25%. For a standard deviation of 42.7%, we solve

36.25% × Z + 0 × (1 – Z) = 42.7%
➾ Z = (42.7%) / (36.25%) = 117.79%
➾ (1 – Z) = 1 – 117.79% = -17.79%

For an optimal portfolio with a standard deviation of 42.7% and a market value of 100, the investor sells 17.79 of risk-free bonds with a standard deviation of zero and buys 117.79 of the market portfolio of risky securities with a standard deviation of 36.25%. This investor wants a portfolio even riskier than the market portfolio.


Question 8.5: Expected return of optimal portfolio

What is the expected return on an optimal portfolio with a standard deviation of 42.7%?

The expected return on the optimal portfolio with a standard deviation of 42.7% is a weighted average of its two parts:

    117.79% × 10.54% + -17.79% × 4.74% = 11.57%


Question 8.6: Composition of optimal portfolio

What is the composition of the optimal portfolio with an expected return of 6.24%?

Answer 8.6: The optimal portfolio is a combination of risk-free bonds with an expected return of 4.74% and the market portfolio of risky securities that have an expected return of 10.54%. For an expected return of 6.24%, we solve

10.54% × Z + 4.74% × (1 – Z) = 6.24%

➾ Z = (6.24% – 4.74% ) / (10.54% – 4.74%) = 25.86%

➾ (1 – Z) = 1 – 25.86% = 74.14%

For an optimal portfolio with an expected return of 6.24% and a market value of 100, the investor

●    buys 25.86 of the market portfolio of risky securities with an expected return of 10.54% and
●    buys 74.14 of risk-free bonds with an expected return of 4.74%.


Question 8.7: Standard deviation of optimal portfolio

What is the standard deviation on an optimal portfolio with an expected return of 6.24%?


Answer 8.7: The risk-free bonds have a standard deviation of zero and are not correlated with the market portfolio of risky securities, which have a standard deviation of 36.25%. This optimal portfolio has a standard deviation of 25.86% × 36.25% = 9.37%.


Attachments
GO
Merge Selected
Merge into selected topic...



Merge into merge target...



Merge into a specific topic ID...





Reading This Topic


Login
Existing Account
Email Address:


Password:


Social Logins

  • Login with twitter
  • Login with twitter
Select a Forum....













































































































































































































































Neas-Seminars

Search