Question 1

Suppose that Ms.Lynch in Problem 1 can make up her portfolio using a risk-free asset that offers a surefire rate of return of 5% and a risky asset with an expected rate of return of 10%,with standard deviation 5.If she chooses a portfolio with an expected rate of return of 8.75%,then the standard deviation of her return on this portfolio will be

A) 7.50%.
B) 3.75%.
C) 1.88%.
D) 6.75%.
E) None of the above.

3.75%.

Accepted Answer

3.75%.

Question 2

Suppose that Ms.Lynch in Problem 1 can make up her portfolio using a risk-free asset that offers a surefire rate of return of 5% and a risky asset with an expected rate of return of 10%,with standard deviation 5.If she chooses a portfolio with an expected rate of return of 8.75%,then the standard deviation of her return on this portfolio will be

A) 7.50%.
B) 3.75%.
C) 1.88%.
D) 6.75%.
E) None of the above.

3.75%.

Accepted Answer

To calculate the standard deviation of Ms. Lynch's portfolio, we need to use the formula for the standard deviation of a two-asset portfolio:
σP = [(wA)^2σA^2 + (wB)^2σB^2 + 2wAwBσAσBρAB]^0.5
where σA and σB are the standard deviations of the two assets, ρAB is the correlation coefficient between the two assets, and wA and wB are the portfolio weights of the two assets.

Since Ms. Lynch is using a risk-free asset with a surefire rate of return, we can assume that the correlation coefficient between the risk-free asset and the risky asset is zero (i.e., ρAB = 0). Therefore, the formula simplifies to:
σP = [(wB)^2σB^2]^0.5

We know that Ms. Lynch wants to choose a portfolio with an expected rate of return of 20%, which means that the portfolio weights of the risk-free asset and the risky asset must add up to 1:
wA + wB = 1

We also know that the risky asset has an expected rate of return of 20% and a standard deviation of 5%. Therefore, the expected rate of return and standard deviation of Ms. Lynch's portfolio can be expressed as:
E(RP) = wAE(RF) + wBE(RB) = 0.1wA + 0.2wB = 0.2
σP = [(wB)^2(0.05)^2]^0.5

Using the two equations above, we can solve for wB:
wA + wB = 1
0.1wA + 0.2wB = 0.2

wA = 1 - wB
0.1(1 - wB) + 0.2wB = 0.2

0.1 - 0.1wB + 0.2wB = 0.2

0.1wB = 0.1

wB = 0.5

Therefore, the portfolio weights are wA = 0.5 and wB = 0.5. Plugging this into the formula for the standard deviation of the portfolio, we get:
σP = [(0.5)^2(0.05)^2]^0.5
σP = 0.025 = 2.5%

Therefore, the answer is (C) 5%.

Question 3

Suppose that Ms.Lynch in Problem 1 can make up her portfolio using a risk-free asset that offers a surefire rate of return of 5% and a risky asset with an expected rate of return of 10%,with standard deviation 5.If she chooses a portfolio with an expected rate of return of 8.75%,then the standard deviation of her return on this portfolio will be

A) 7.50%.
B) 3.75%.
C) 1.88%.
D) 6.75%.
E) None of the above.

3.75%.

Accepted Answer

The standard deviation of a portfolio that combines a risk-free asset and a risky asset is proportional to the amount invested in the risky asset. Since the expected return of the portfolio (20%) is exactly in the middle of the risk-free rate (15%) and the risky asset's expected return (25%), it implies that the portfolio is composed of equal parts of the risk-free and risky assets. Therefore, the standard deviation of the portfolio will be half of the standard deviation of the risky asset alone, which is 5%/2 = 2.5%.

Question 4

Suppose that Ms.Lynch in Problem 1 can make up her portfolio using a risk-free asset that offers a surefire rate of return of 5% and a risky asset with an expected rate of return of 10%,with standard deviation 5.If she chooses a portfolio with an expected rate of return of 8.75%,then the standard deviation of her return on this portfolio will be

A) 7.50%.
B) 3.75%.
C) 1.88%.
D) 6.75%.
E) None of the above.

3.75%.

Accepted Answer

The standard deviation of a portfolio that combines a risk-free asset and a risky asset is proportional to the amount invested in the risky asset. Since the expected return of the portfolio is 17.50%, which is 75% of the way from the risk-free rate of 10% to the risky asset's expected return of 20%, the standard deviation of the portfolio will be 75% of the risky asset's standard deviation. Thus, 0.75 * 5% = 3.75%.

Question 5

Suppose that Ms.Lynch in Problem 1 can make up her portfolio using a risk-free asset that offers a surefire rate of return of 5% and a risky asset with an expected rate of return of 10%,with standard deviation 5.If she chooses a portfolio with an expected rate of return of 8.75%,then the standard deviation of her return on this portfolio will be

A) 7.50%.
B) 3.75%.
C) 1.88%.
D) 6.75%.
E) None of the above.

3.75%.

Accepted Answer

We can use the formula for the standard deviation of a portfolio:
σp = [w1σ1^2 + w2σ2^2 + 2w1w2σ1σ2ρ12]^(1/2)

where σ1 is the standard deviation of the risk-free asset (0), σ2 is the standard deviation of the risky asset (5), ρ12 is the correlation coefficient between the two assets (-1 for a risk-free asset and a risky asset), w1 is the weight of the risk-free asset (1- w2), and w2 is the weight of the risky asset.

We are given that the expected rate of return on the portfolio is 15%, which means that the portfolio is a combination of the risk-free asset (with a return of 10%) and the risky asset (with a return of 15%) in some proportion. Let x be the proportion invested in the risky asset (and therefore, 1-x is invested in the risk-free asset). Then, we have:

E(rp) = xE(r2) + (1-x)E(r1)

15% = x(15%) + (1-x)(10%)

Solving for x, we get:

x = 0.5

So, the portfolio is made up of 50% risky asset and 50% risk-free asset.

Plugging in the values in the formula for σp, we get:

σp = [(0.5 x 5^2) + (0.5 x 0^2) + 2(0.5)(0.5)(5)(0)]^(1/2)

σp = [12.5]^(1/2)

σp = 3.54%

Therefore, the standard deviation of her return on the portfolio will be 3.54%, which is closest to choice (C).

Deck 13: B: Risky Assets