Baran

 

23、A portfolio manager determines that his portfolio has an expected return of $20,000 and a standard deviation of $45,000. Given a 95 percent confidence level, what is the portfolio's VAR?

A) $43,500.

B) $54,250.

C) $74,250.

D) $94,250.

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

 

The correct answer is C

 

VAR = Portfolio Value [E(R)-zσ] 
-2,400,000 = 14,000,000[0.125 – (1.65)(X)] 
-2,400,000 = 1,750,000 – 23,100,000(X)
X = 17.97%.
Note that VAR value is always negative.

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

 

Sorted monthly returns (from low to high, in columns) are as follows:

-21.50%	2.99%	9.68%	11.03%	17.44%	31.07%
-7.94%	6.97%	9.81%	11.77%	18.56%	31.76%
-0.78%	8.47%	9.82%	12.57%	19.55%	35.66%
2.54%	8.53%	10.00%	14.20%	21.84%	36.15%
2.71%	8.88%	10.97%	14.35%	22.25%	39.45%

The 10% lowest return is the 3rd value (3/30 = 0.10), which is -0.78%
Therefore 10% VAR for the portfolio = 0.0078*250,000,000 = 1,950,000

Baran

 

16、Super Hedge fund has $20 million in assets. The total return for the past 40 months is given below. What is the monthly value at risk (VAR) of the portfolio at a 5 percent probability level?

Monthly Returns
-22.46%	9.26%	-4.69%	-20.66%	-2.77%	1.17%	-16.11%	-6.73%
0.57%	12.56%	-18.26%	-32.81%	24.15%	-34.26%	-5.49%	-19.76%
-34.75%	-12.02%	32.74%	-31.35%	13.68%	-31.13%	7.07%	-33.56%
-20.37%	30.27%	31.09%	-3.26%	-14.42%	4.75%	15.63%	-11.57%
7.23%	-20.77%	-19.61%	-2.42%	-30.59%	28.83%	-22.25%	-10.26%

A) $6,852,000.

B) $7,200,000.

C) $9,000,000.

D) $16,725,000.