Baran

 

18、The minimum amount of money that one could expect to lose with a given probability over a specific period of time is the definition of:

A) delta. 

B) the hedge ratio. 

C) value at risk (VAR). 

D) the coefficient of variation. 

Baran

 

The correct answer is C

 

This is an often-used definition of VAR.

Baran

 

19、The Westover Fund is a portfolio consisting of 42 percent fixed income investments and 58 percent equity investments. The manager of the Westover Fund recently estimated that the annual VAR(5 percent), assuming a 250-day year, for the entire portfolio was $1,367,000 based on the portfolio’s market value of $12,428,000 and a correlation coefficient between stocks and bonds of zero. If the annual loss in the equity position is only expected to exceed $1,153,000 5 percent of the time, then the daily expected loss in the bond position that will be exceeded 5 percent of the time is closest to:

A) $72,623. 

B) $55,171. 

C) $46,445. 

D) $21,163.

Baran

 

The correct answer is C

 

Begin by using the formula for dollar portfolio VAR to compute the annual VAR(5%) for the bond position:

VAR2portfolio = VAR2Stocks + VAR2Bonds + 2VARStocksVARBonds ρStocks, Bonds

(1,367,000)2 = (1,153,000)2 + VAR2Bonds + 2(1,153,000)VARBonds(0)

VARBonds = [(1,367,000)2 – (1,153,000)2]0.5 = 734,357

Next convert the annual $VARBonds to daily $VARBonds:

734,357 / (250)0.5 = 46,445

Baran

 

20 Hugo Nelson is preparing a presentation on the attributes of value at risk. Which of Nelson’s following statements is not correct?

A) VAR can account for the diversified holdings of a financial institution, reducing capital requirements.

B) VAR(10%) = $0 indicates a positive dollar return is likely to occur on 90 out of 100 days.

C) VAR was developed in order to more closely represent the economic capital necessary to ensure commercial bank solvency.

D) VAR(1%) can be interpreted as the number of days that a loss in portfolio value will exceed 1%.

Baran

 

The correct answer is D

 

VAR is defined as the dollar or percentage loss in portfolio value that will be exceeded only X% of the time. VAR(10%) = $0 indicates that there is a 10% probability that on any given day the dollar loss will be greater than $0. Alternatively, we can say there is a 90% probability that on any given day the dollar gain will be greater than $0. VAR was developed by commercial banks to provide a more accurate measure of their economic capital requirements, taking into account the effects of diversification.

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.