Baran

6、 firm has a portfolio of traded assets worth $400 million with a VAR of $30 million. The standard deviation of the return on the portfolio is 0.60. The firm is considering the sale of a position worth $2 million in an asset that has an expected return of 6 percent and a covariance of return with the portfolio of 0.40. The position that would be added has an expected return of 10 percent and a covariance of return with the portfolio of 0.80. The VAR is based on a 95 percent confidence level.

The impact of the trade on the volatility of the portfolio is a(n):

A) increase of 0.0022.
 
B) increase of 0.0044.
 
C) decrease of 0.0080.
 
D) increase of 0.0033.
 

Baran

The correct answer is D

The beta, relative to the overall portfolio, of the proposed position is βip = 0.80/0.602 = 2.22, and the beta of the replaced position is βjp= 0.40/0.602=1.11. The volatility impact of the trade is equal to (βip - βjp) × Δw × Vol(Rp) = (2.22 – 1.11) × (2/400) × 0.60 = 0.0033.

 

Baran

The impact of the trade on the expected return of the portfolio is a(n):
A) increase of $80,000.
 
B) increase of $40,000.
 
C) decrease of $120,000.
 
D) increase of $160,000.

Baran

The correct answer is A

The impact on the expected return is (E(Ri)-E(Rj)) × Δw = (0.10 - 0.06) × (2/400) ×$400,000,000 = $80,000.

Baran

The impact of the trade on the VAR of the portfolio is a(n):
A) decrease of $2.20 million.
 
B) increase of $2.12 million.
 
C) decrease of $2.28 million.
 
D) increase of $2.70 million.

Baran

 The correct answer is B

 

Impact on VAR = -{(E(Ri)-E(Rj)) × Δw × W} + [(βip - βjp) × 1.65 × Vol(Rp) × Δw × W] = - {(0.10 -0.06) × (2/400) × 400} + [(2.22 - 1.11) × 1.65 × 0.60 × (2/400) × 400] = 2.12.

Baran

7、For a diversified portfolio, the VAR impact of a trade depends on the:

      I. betas of the traded assets.
     II. expected returns of traded assets.
    III. correlation between the returns of the risky assets.
    IV. size of the position in the traded assets.

A) I and II.
 
B) I, II, and IV.
 
C) I, II, and III.
 
D) II, III, and IV.
 

Baran

The correct answer is B

The VAR impact of a trade in a diversified portfolio can be calculated based on the asset betas, the size of the trade, and the expected returns of each assets. Correlation between the assets does not enter into the calculation. Note that if the portfolio were not well-diversified, standard deviation would be the relevant measure of risk rather than beta, and correlation would explicitly enter the calculation.

Baran

8、For a trade that is small relative to portfolio size, which of the following tends to decrease the VAR of the portfolio?

Purchasing an asset that has a higher beta relative to the portfolio than the asset sold.
Purchasing an asset that has a higher expected return relative to the portfolio than the asset sold.
Purchasing an asset that has a lower beta relative to the portfolio than the asset sold.
Purchasing a low volatility asset.
A) I and II only.
 
B) II and III only.
 
C) III only.
 
D) II, III, and IV only.

Baran

The correct answer is B

A trade decreases VAR if the asset bought has a lower beta coefficient with respect to the portfolio than the asset sold, or if it has a higher expected return. The impact of volatility alone cannot be determined without knowledge of the correlation with other portfolio assets.