Baran

 

10、A portfolio comprises 2 stocks: A and B. The correlation of returns of stocks A and B is 0.4. Based on the information below, what is the portfolio’s value-at-risk (VAR) at a 5 percent probability level?

Stock	Value	E(R)	σ
A	$85,000	15.0%	18.0%
B	$15,000	12.0%	10.0%

A) $1,410.

B) $13,300.

C) $11,784.

D) $23,491.

Baran

 

The correct answer is C

Weight of stock A = WA= 0.85; Weight of stock B = WB = 0.15

Expected Portfolio return = E(RP) = 0.85(15)+0.15(12) = 14.55%

Portfolio Standard deviation =

           sP = [(WA)2(sA)2+ (WB)2(sB)2+2(WA)(WB)rABsAsB]0.5

            = [(0.85)2(0.18)2+(0.15)2(0.10)2+2(0.85)(0.15)(0.4)(0.18)(0.10)]0.5

            = (0.02547)0.5

            = 15.96%

VAR = Portfolio value [E(R) - zs] 

            = 100,000[0.1455 – (1.65)(0.1596)] = -$11,784

Baran

 

11、Derivation Inc. has a portfolio of $100 MM. The expected return over one year is 6 percent, with a standard deviation of 8 percent. What is the VAR for this portfolio at the 99 percent confidence level?

A) $2.0 MM.

B) $7.2 MM.

C) $12.1 MM.

D) $12.6 MM.

Baran

 

9、A portfolio comprises 2 stocks: A and B. The correlation of returns of stocks A and B is 0.8. Based on the information below, compute the portfolio’s annual VAR at a 5 percent probability level.

Stock	Value	E(R)	σ
A	$75,000	12.0%	15.0%
B	$25,000	10.8%	10.0%

A) $10,295.

B) $11,700.

C) $13,300.

D) $23,491.

 

Baran

 

The correct answer is A

 

Weight of stock A = WA=0.75; Weight of stock B = WB = 0.25

Expected Portfolio return = E(RP) = 0.75(12)+0.25(10.8) = 11.70%

Portfolio Standard deviation =

sP = [(WA)2(sA)2+ (WB)2(sB)2+2(WA)(WB)rABsAsB]0.5

= [(0.75)2(0.15)2+(0.25)2(0.10)2+2(0.75)(0.25)(0.8)(0.15)(0.10)]0.5

= (0.0178)0.5

= 13.33%

VAR = Portfolio value [E(R)-zs]

= 100,000[0.117 – (1.65)(0.1333)] = -$10,295

Baran

 

The correct answer is A

 

VAR measures the amount of loss in the left tail of the distribution and increases with lower probability levels. Conversely VAR decreases with lower confidence levels (which is 1 minus the probability level). VAR actually increases with increases in holding period.

Baran

 

8、For a $1,000,000 stock portfolio with an expected return of 12 percent and an annual standard deviation of 15 percent, what is the VAR with 95 percent confidence level?

A) $120,000.

B) $150,000.

C) $127,500.

D) $247,500.

Baran

 

The correct answer is C

 

VAR = Portfolio Value[E(R)-zσ]= 1,000,000[0.12 – (1.65)(0.15)] = -$127,500

Baran

 

The correct answer is A

 

The variance/covariance method relies on the assumption of normality.

Baran

 

6、Which value at risk methodology is most subject to model risk?

A) Parametric.

B) Variance/covariance.

C) Historical.

D) Monte Carlo simulation.