Baran

 

13、Value at risk (VAR) is a benchmark associated with a given probability. The actual loss:

A) may be much greater. 

B) cannot exceed this amount. 

C) is expected to be the average of the expected return of the portfolio and VAR.

D) will have an inverse relationship with VAR.

Baran

 

The correct answer is A

 

VAR is a benchmark that gives an estimate of what magnitude of loss would not be unusual. The actual loss for any given time period can be much greater.

Baran

 

14、A global portfolio is comprised of European and Emerging market equities. The correlation of returns for the two sectors is 0.3. Based on the information below, what is the portfolio’s annual value at risk (VAR) at a 5 percent probability level?

Stock	Value	E(R)	σ
European	$800,000	9.0%	15.0%
Emerging	$200,000	18.0%	25.0%

A) $110,700.

B) $130,300.

C) $230,491.

D) $128,280.

Baran

 

The correct answer is D

 

Weight of European equities = W_A=0.80; Weight of Emerging = W_B = 0.20

Expected Portfolio return = E(R_P) = 0.8(9)+0.2(18) = 10.80%

Portfolio Standard deviation = 

 σ_P = [(W_A)²(σ_A)²+ (W_B)²(σ_B)²+2(W_A)(W_B)r_ABσ_Aσ_B]^0.5

    = [(0.8)²(0.15)²+(0.2)²(0.25)²+2(0.8)(0.2)(0.3)(0.15)(0.25)]^0.5

    = (0.0205)^0.5

    = 14.32%

VAR = Portfolio Value[E(R) - zσ]
    = 1,000,000[0.108 – (1.65)(0.1432)] = -$128,280.

Baran

 

15、Alto Steel’s pension plan has $250 million in assets with an expected return of 12 percent. The last thirty monthly returns are given below.

What is the 10 percent monthly probability VAR for Alto’s pension plan?

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

A) $1,200,000.

B) $3,000,000.

C) $1,950,000.

D) $36,125,850.

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.

Baran

 

The correct answer is A

 

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

-34.75%	-31.35%	-22.25%	-19.61%	-11.57%	-4.69%	0.57%	6.35%
-34.26%	-31.13%	-20.77%	-18.26%	-10.26%	-3.26%	0.95%	7.07%
-33.56%	-30.59%	-20.66%	-16.11%	-6.73%	-2.83%	1.17%	7.23%
-33.16%	-23.08%	-20.37%	-14.42%	-6.37%	-2.77%	1.58%	8.35%
-32.81%	-22.46%	-19.76%	-12.02%	-5.49%	-2.42%	4.75%	9.26%

The 5% lowest return is the 2^nd value (2/40 = 0.05), which is -34.26%%
Therefore 5% VAR for the portfolio = 0.3426*$20,000,000 = $6,852,000

Baran

 

17、Portfolio A has total assets of $14 million and an expected return of 12.50 percent. Historical VAR of the portfolio at 5 percent probability level is $2,400,000. What is the portfolio’s standard deviation?

A) 12.50%.

B) 14.65%.

C) 17.97%.

D) 15.75%.

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.