Baran

 

26、Which of the following statements about value at risk (VAR) is TRUE?

A) VAR increases with longer holding periods.

B) VAR decreases with lower probability levels.

C) VAR is not dependent on the choice of holding period.

D) VAR is independent of probability level.

Baran

 

The correct answer is A

 

VAR measures the amount of loss in the left tail of the distribution. It increases with lower probability levels and increases in holding period.

Baran

 

27、Tim Jones is evaluating two mutual funds for an investment of $100,000. Mutual fund A has $20,000,000 in assets, an annual expected return of 14 percent, and an annual standard deviation of 19 percent. Mutual fund B has $8,000,000 in assets, an annual expected return of 12 percent, and an annual standard deviation of 16.5 percent. What is the daily value at risk (VAR) of Jones’ portfolio at a 5 percent probability if he invests his money in mutual fund A?

A) $1,668.

B) $1,924.

C) $13,344.

D) $38,480.

Baran

 

The correct answer is B

 

The expected outcome is $20,000. Given the standard deviation of $45,000 and a z-score of 1.65 (95% confidence level for a one-tailed test), the VAR is –54,250 [=20,000 – 1.65 (45,000)].

Baran

 

24、A $2 million balanced portfolio is comprised of 40 percent stocks and 60 percent intermediate bonds. For the next year, the expected return on the stock component is 9 percent and the expected return on the bond component is 6 percent. The standard deviation of the stock component is 18 percent and the standard deviation of the bond component is 8 percent. What is the annual VAR for the portfolio at a 1 percent probability level if the correlation between the stock and the bond component is 0.25?

A) $126,768.

B) $149,500.

C) $303,360.

D) $152,250.

Baran

 

The correct answer is C

Weight of Stock = WS=0.40; Weight of Bonds = WB = 0.60

Expected Portfolio return = E(RP) = 0.40(9)+0.60(6) = 7.20%

Portfolio Standard deviation =

σP = [(WS)2(σS)2+ (WB)2(σB)2+2(WS)(WB)rSBσSσB]0.5

= [(0.40)2(0.18)2+(0.60)2(0.08)2+2(0.40)(0.60)(0.25)(0.18)(0.08)]0.5

= (0.009216)0.5

= 9.6%

VAR = Portfolio Value [ E(R) -zσ]

= 2,000,000[0.072 – (2.33)(0.096)] = $303,360.

Baran

 

21、A large bank currently has a security portfolio with a market value of $145 million. The daily returns on the bank’s portfolio are normally distributed with 80% of the distribution lying within 1.28 standard deviations above and below the mean and 90% of the distribution lying within 1.65 standard deviations above and below the mean. Assuming the standard deviation of the bank’s portfolio returns is 1.2%, calculate the VAR(5%) on a one-day basis.

A) $2.87 million.

B) $2.23 million.

C) $2.04 million.

D) cannot be determined from information given.

Baran

 

The correct answer is A

VAR(5%) = z5% × σ × portfolio value

                   = 1.65 × 0.012 × $145 million

                   = $2.871 million

Baran

 

22、The accuracy of a value at risk (VAR) measure:

A) is included in the statistic.

B) can only be ascertained after the fact. 

C) is complete because the process is deterministic. 

D) is one minus the probability level. 

Baran

 

The correct answer is B

 

This is a weakness of VAR. The reliability can only be known after some time has passed to see if the number and size of the losses is congruent with the VAR measure.