Baran

 

33、An investor has 60 percent of his $500,000 portfolio in Value fund and the remaining in Growth fund. The correlation of returns of the two funds is –0.20. Based on the information below, what is the portfolio’s VAR at a 5 percent probability level?

Fund	E(R)	σ
Value	12%	14.0%
Growth	16%	20.0%

 

A) $26,768.

B) $49,824.

C) $17,635.

D) $82,368.

Baran

 

The correct answer is C

Weight of Value Fund = WV=0.60; Weight of Growth Fund = WG = 0.40

Expected Portfolio return = E(RP) = 0.60(12)+0.40(16) = 13.60%

Portfolio Standard deviation =

σP = [(WV)2(σV)2+ (WG)2(σG)2+2(WV)(WG)rVGσVσG]0.5

= [(0.60)2(0.14)2+(0.40)2(0.20)2+2(0.60)(0.40)(-0.2)(0.14)(0.20)]0.5

= (0.010768)0.5

= 10.38%

VAR = Portfolio Value [ E(R) -zσ]

= 500,000[0.1360 – (1.65)(0.1038)] = -$17,635.

Baran

 

34、Kiera Reed is a portfolio manager for BCG Investments. Reed manages a $140,000,000 portfolio consisting of 30 percent European stocks and 70 percent U.S. stocks. If the VAR(1%) of the European stocks is 1.93 percent, or $810,600, the VAR(1%) of U.S. stocks is 2.13 percent, or $2,087,400, and the correlation between European and U.S. stocks is 0.62, what is the portfolio VAR(1%) on a percentage and dollar basis?

A) 1.90% and $2.67 million.

B) 2.07% and $2.90 million.

C) 1.90% and $2.90 million.

D) 2.07% and $2.67 million.

Baran

 

The correct answer is A

 

VAR for the portfolio on a percentage and dollar basis is calculated as follows:

Baran

 

35、If a 10-day VAR is $15,000,000, the 250-day VAR, assuming no change in confidence level, would be:

A) $237,000,000.

B) $23,700,000. 

C) $7,500,000.

D) $75,000,000.

Baran

 

The correct answer is D

Just back out the 1-day VAR by dividing by the square root of 10 and then multiply by the square root of 250 to get the 250-day VAR.

Just back out the 1-day VAR by dividing by the square root of 10 and then multiply by the square root of 250 to get the 250-day VAR.

Baran

 

36、Communities Bank has a $17 million par position in a bond with the following characteristics:

The bond is a 7-year, zero-coupon bond.

The market value is $12,358,674.

The bond is trading at a yield to maturity of 4.6%.

The historical mean change in daily yield is 0.0%.

The standard deviation of the position is 1%.

The one-day VAR for this bond at the 95% confidence level is closest to:

A) $105,257.

B) $203,918. 

C) $260,654.

D) $339,487.

Baran

 

The correct answer is B

 

VAR is the market value of the position times the price volatility of the position times the confidence level, which in this case equals ($12,358,674) × (0.01) × (1.65) = $203,918.

Baran

 

The 10-day VAR on this bond is closest to:

A) $866,111.

B) $644,845

C) $736,487.

D) $487,698.

Baran

 

The correct answer is B

The VAR is calculated as the daily earnings at risk times the square root of days desired, which is 10. The calculation generates ($203,918)(√10) = $644,845.