wanganjie

 

AIM 3: Compute the standard deviation and VAR of an equally weighted portfolio, with equal standard deviations and correlations.

A manager has a portfolio of 25 positions. The returns of the 25 positions have the same standard deviation and the correlations between positions are all equal. The standard deviation of each position is 40% and the correlations are 0.3. If the portfolio’s value is $2 million, using a Z-value of 1.65 the VAR of the portfolio is closest to:

A) $755,981. 

B) $396,000. 

C) $87,636. 

D) $79,200. 

wanganjie

 

The correct answer is A

Using the formula for the standard deviation of the portfolio:

 

[attach]13955[/attach]

σ = 22.91%

VAR = 1.65 × 0.2291 × $2,000,000 = $755,981

wanganjie

 

AIM 6: Compute component VAR in a portfolio with a large number of positions and use it to decompose VAR.

1、For a portfolio with a large number of relatively small positions, the component VAR of a given position would probably be closest to:

A) the position’s marginal VAR divided by the value invested in the position. 

B) the position’s marginal VAR multiplied by the value invested in the position. 

C) the position’s marginal VAR multiplied by the beta of the position with the overall portfolio. 

D) the position’s marginal VAR divided by the beta of the position with the overall portfolio. 

wanganjie

 

The correct answer is B

In a large portfolio with many positions, the approximation is simply the marginal VAR multiplied by the dollar weight in position “i”: CVARi = (MVARi) × (wi × P) where P is the value of the portfolio, wi is the weight in the portfolio.

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2、In a portfolio of three currencies, the relationship between the component VAR and the individual VAR for each currency is likely to be what?

A) The individual VAR is likely to be equal to the component VAR.

B) The individual VAR is likely to be less than the component VAR.

C) There is no relationship between the component VAR and the individual VAR.

D) The component VAR is likely to be less than the individual VAR.

wanganjie

 

The correct answer is D

Unless assets are perfectly correlated, component VAR will be less than individual VAR.

wanganjie

 

3、The amount of risk a particular fund contributes by its position in the portfolio of funds is called:

A) liquidity VaR. 

B) marginal VaR. 

C) stress VaR.

D) component VaR.

wanganjie

 

The correct answer is D

This is the definition of component VaR. It will generally be less than the VaR of the fund by itself because of the diversification of some of the fund’s risk at the portfolio level.

wanganjie

 

AIM 7: Describe ways we can compute component VARs for a distribution of returns that is not normal or elliptical.

Computing component VAR for a position using the position’s beta with respect to the entire portfolio is appropriate for returns that follow:

A) an elliptical distribution but not a normal distribution. 

B) both an elliptical distribution and a normal distribution. 

C) a normal distribution but not an elliptical distribution. 

D) neither an elliptical distribution nor a normal distribution. 

wanganjie

 

The correct answer is B

It is appropriate for elliptical distributions, and normal distributions are a subset of elliptical distributions.