46、A portfolio manager is constructing a portfolio of stocks and corporate bonds. The portfolio manager has estimated that stocks and corporate bond returns have daily standard deviations of 1.8% and 1.1%, respectively, and estimates a correlation coefficient of returns of 0.43. If the portfolio manager plans to allocate 35% of the portfolio to corporate bonds and the rest to stocks, what is the daily portfolio VAR (2.5%) on a percentage basis?

A) 2.71%.

B) 3.05%.

C) 2.27%.

D) 2.57%.

The correct answer is A

First, calculate the daily percentage VAR for stocks and corporate bonds:

Stocks: VAR(2.5%)Percentage basis = z2.5% × σ = 1.96(0.018) = 0.0353 = 3.53%

Bonds: VAR(2.5%)Percentage basis = z2.5% × σ = 1.96(0.011) = 0.0216 = 2.16%

Next calculate the portfolio VAR using weights of 35% for bonds and 65% for stocks:

[0.652(0.03532) + 0.352(0.02162) + 2(0.35)(0.65)(0.0353)(0.0216)(0.43)]0.5 = 0.0271 = 2.71%

47、An insurance company currently has a security portfolio with a market value of $243 million. The daily returns on the company’s portfolio are normally distributed with a standard deviation of 1.4%. Using the table below, determine which of the following statements are TRUE.

1. One-day VAR(1%) for the portfolio on a percentage basis is equal to 3.25%.
2. One-day VAR(10%) for the portfolio on a dollar basis is equal to $5.61 million.
3. One-day VAR(6%) > one-day VAR(10%).

 A) II and III only.

B) I and III only.

C) I only.

D) I, II, and III.

The correct answer is B

To find the appropriate zcritical value for the VAR(1%), use the two-tailed value from the table correspondnig to an alpha level of 2%. Under a two-tailed test, half the alpha probability lies in the left tail and half in the right tail. Thus the zcritical 2.32 is appropriate for VAR(1%). For VAR(10%), the table gives the one-tail zcritical value of 1.28. Calculate the percent and dollar VAR measures as follows:

VAR(1%)

 = z1% × σ

 = 2.32 × 0.014

 = 0.03248 ≈ 3.25%

VAR(10%)

 = z10% × σ × portfolio value

 = 1.28 × 0.014 × $243 million

 = $4.35 million

Thus, Statement I is correct and Statement II is incorrect. For Statement III, recall that as the probability in the lower tail decreases (i.e., from 10% to 6%), the VAR measure increases. Thus, Statement III is correct.