wanganjie

 

AIM 2: For a two-asset portfolio, compute the portfolio VAR when the returns have no correlation and perfect correlation, respectively.

1、Simply adding the VARs for each security in a portfolio to compute the portfolio value at risk (VAR) implies the assumption of:

A) perfect and negative correlation.

B) imperfect and positive correlation.

C) imperfect and negative correlation.

D) perfect and positive correlation.

wanganjie

 

The correct answer is D

Simply adding the VARs of individual securities to compute the portfolio VAR assumes that there is a correlation of “1” between all the securities. A correlation value of “1”, is perfect and positive. This is called the undiversified VAR.

wanganjie

 

2、An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to:

σR = 34%

σS = 16%

rR,S = 0.67

WR = 80%

WS = 20%

A) 8.7%.

B) 2.1%.

C) 29.4%.

D) 7.8%.

wanganjie

 

The correct answer is C

The formula for the standard deviation of a 2-stock portfolio is:

s = [WA2sA2 + WB2sB2 + 2WAWBsAsBrA,B]1/2

s = [(0.82 × 0.342) + (0.22 × 0.162) + (2 × 0.8 × 0.2 × 0.34 × 0.16 × 0.67)]1/2 = [0.073984 + 0.001024 + 0.0116634]1/2 = 0.08667141/2 = 0.2944, or approximately 29.4%.

wanganjie

 

3、Which of the following is NOT a primary factor affecting the risk of a portfolio?

A) Total risk for a large portfolio of diversified assets. 

B) The degree to which assets within the portfolio move together.

C) A high degree of concentration in one asset within the portfolio.

D) The volatility of individual assets held within the portfolio.

wanganjie

 

The correct answer is A

In a diversified portfolio with a large number of assets, the most relevant risk is systematic risk since the unsystematic (i.e., firm-specific risk) gets diversified away. In other words, the unsystematic risks of the individual assets offset each other.

wanganjie

 

AIM 4: Compute incremental VAR, explain why calculating incremental VAR may be difficult, and give a useful approximation.

1、A portfolio consists of assets A and B. The volatilities are 10% and 20%, respectively. There are $10 million and $5 million invested in them, respectively. If we assume they are uncorrelated with each other, the VAR of the portfolio using Z = 1.65 would be closest to:

A) $2.475 million. 

B) $1.750 million. 

C) $3.500 million.

D) $2.333 million. 

wanganjie

 

The correct answer is D

We can use matrix notation to derive the dollar variance of the portfolio:

 

 [attach]13956[/attach]

This value is in ($ millions)2. VAR is then the square root of this value times 1.65: VAR = 1.65 × ($1,414,214) = $2,333,452.

wanganjie

 

2、A manager is considering adding a new position to a portfolio. The size of the position will be 1% of the portfolio. The manager computes the derivative of the portfolio’s VaR with respect to the change in the weight of the position. Multiplying the value of the derivative times 1% will yield:

A) marginal VaR.

B) incremental VaR.

C) component VaR. 

D) Monte Carlo VaR.

wanganjie

 

The correct answer is B

Incremental VaR, or IVaRi, is an estimate of the amount of risk a proposed new position in fund i will add to the total VaR of an existing portfolio.