［2008］Topic 32: VAR Methods相关习题

Baran

 

AIM 2: Explain how the full valuation is supported by the Monte Carlo and historical simulation approach, respectively.

 

1、Local-valuation methods used to determine changes in portfolio value are appropriate when the portfolio:

A) has substantial option-like exposures.

B) has numerous complex risk factors.

C) has few option-like exposures.

D) changes are expected to occur over a long-term horizon.

gdwwiaxo

这个贴子要顶~~~~~~~~~~~~~~

yulestoic

怎么这么多广告……= =

Baran

 

The correct answer is D

The weekly VAR is 2 million × 1.65 × 0.0065 × √5 = $47,964.

Baran

 

46、A portfolio manager is constructing a portfolio of stocks and corporate bonds. The portfolio manager has estimated that stocks and corporate bond returns have daily standard deviations of 1.8% and 1.1%, respectively, and estimates a correlation coefficient of returns of 0.43. If the portfolio manager plans to allocate 35% of the portfolio to corporate bonds and the rest to stocks, what is the daily portfolio VAR (2.5%) on a percentage basis?

A) 2.71%.

B) 3.05%.

C) 2.27%.

D) 2.57%.

Baran

 

The correct answer is A

First, calculate the daily percentage VAR for stocks and corporate bonds:

Stocks: VAR(2.5%)Percentage basis = z2.5% × σ = 1.96(0.018) = 0.0353 = 3.53%

Bonds: VAR(2.5%)Percentage basis = z2.5% × σ = 1.96(0.011) = 0.0216 = 2.16%

Next calculate the portfolio VAR using weights of 35% for bonds and 65% for stocks:

[0.652(0.03532) + 0.352(0.02162) + 2(0.35)(0.65)(0.0353)(0.0216)(0.43)]0.5 = 0.0271 = 2.71%

Baran

 

47、An insurance company currently has a security portfolio with a market value of $243 million. The daily returns on the company’s portfolio are normally distributed with a standard deviation of 1.4%. Using the table below, determine which of the following statements are TRUE.

< >>	zcritical
Alpha	One-tailed	Two-tailed
10%	1.28	1.65
2%	2.06	2.32

1. One-day VAR(1%) for the portfolio on a percentage basis is equal to 3.25%.
2. One-day VAR(10%) for the portfolio on a dollar basis is equal to $5.61 million.
3. One-day VAR(6%) > one-day VAR(10%).

 A) II and III only.

B) I and III only.

C) I only.

D) I, II, and III.

Baran

 

The correct answer is B

To find the appropriate zcritical value for the VAR(1%), use the two-tailed value from the table correspondnig to an alpha level of 2%. Under a two-tailed test, half the alpha probability lies in the left tail and half in the right tail. Thus the zcritical 2.32 is appropriate for VAR(1%). For VAR(10%), the table gives the one-tail zcritical value of 1.28. Calculate the percent and dollar VAR measures as follows:

VAR(1%)

 = z1% × σ

 = 2.32 × 0.014

 = 0.03248 ≈ 3.25%

VAR(10%)

 = z10% × σ × portfolio value

 = 1.28 × 0.014 × $243 million

 = $4.35 million

Thus, Statement I is correct and Statement II is incorrect. For Statement III, recall that as the probability in the lower tail decreases (i.e., from 10% to 6%), the VAR measure increases. Thus, Statement III is correct.

Baran

 

45、

Annual volatility: σ = 20.0%
Annual risk-free rate = 6.0%
Exercise price (X) = 24
Time to maturity = 3 months
Stock price, S	$21.00	$22.00	$23.00	$24.00	$24.75	$25.00
Value of call, C	$0.13	$0.32	$0.64	$1.14	$1.62	$1.80
% Decrease in S	?16.00%	?12.00%	?8.00%	?4.00%	?1.00%	< >>
% Decrease in C	?92.83%	?82.48%	?64.15%	?36.56%	?9.91%	< >>
Delta (ΔC% / ΔS%)	5.80	6.87	8.02	9.14	9.91	< >>

Alton Richard is a risk manager for a financial services conglomerate. Richard generally calculates the VAR of the company’s equity portfolio on a daily basis, but has been asked to estimate the VAR on a weekly basis assuming five trading days in a week. If the equity portfolio has a daily standard deviation of returns equal to 0.65% and the portfolio value is $2 million, the weekly dollar VAR (5%) is closest to:

A) $29,100.

B) $21,450.

C) $107,250.

D) $47,964.

Baran

 

The correct answer is D

VAR(2.5%)Percentage Basis = z2.5% × σ = 1.96(0.017) = 0.03332 = 3.332%.

VAR(2.5%)Dollar Basis = VAR(2.5%)Percentage Basis × portfolio value = 0.03332 × $2,520,000 $83,966.

The appropriate interpretation is that on any given day, there is a 2.5% chance that the porfolio will experience a loss greater than $83,996. Alternatively, we can state that there is a 97.5% chance that on any given day, the observed loss will be less than $83,996.