Baran

 

41、Which of the following statements comparing Monte Carlo VaR and historical VaR is most accurate?

A) Both compute VaR from percentiles from a given set of observed returns, but Monte Carlo VaR uses realized returns and historical VaR uses hypothetical returns.

B) Both are parametric approaches, but historical VaR uses a regression on past data while Monte Carlo VaR uses Kalman filtering to create forward looking VaR estimates. 

C) Both are parametric approaches, but Monte Carlo VaR uses fewer inputs into the model than historical VaR.

D) Both compute VaR from percentiles from a given set of observed returns, but historical VaR uses realized returns and Monte Carlo VaR uses hypothetical returns.

Baran

 

The correct answer is D

Historical VaR uses historical realized returns, and Monte Carlo VaR uses returns generated from a hypothetical model, which requires a significant number of inputs. Neither historical nor Monte Carlo VaR is a parametric approach.

Baran

 

42、On December 31, 2006, Portfolio A had a market value of $2,520,000. The historical standard deviation of daily returns was 1.7%. Assuming that Portfolio A is normally distributed, calculate the daily VAR(2.5%) on a dollar basis and state its interpretation. Daily VAR(2.5%) is equal to:

A) $83,966, implying that daily portfolio losses will fall short of this amount 2.5% of the time.

B) $70,686, implying that daily portfolio losses will only exceed this amount 2.5% of the time.

C) $70,686, implying that daily portfolio losses will fall short of this amount 2.5% of the time.

D) $83,966, implying that daily portfolio losses will only exceed this amount 2.5% of the time.

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.

Baran

 

43、You wish to estimate VAR using a local valuation method. Which of the following are methods you might use?

Historical simulation.

The delta-normal valuation method.

Monte Carlo simulation.

The grid Monte Carlo approach.

A) II only.

B) I only.

C) I and II only.

D) III and IV only.

Baran

 

The correct answer is A

 

Local valuation methods measure portfolio risk by valuing the assets at one point in time, then making adjustments to relevant risk factors that are expected to cause changes in the overall portfolio value. The delta-normal valuation method is an example of a local valuation method.

Baran

 

44、

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	< >>

Suppose that the stock price is currently at $25.00 and the 3-month call option with an exercise price of $24.00 is $1.60. Using the linear derivative VAR method and the information in the above table, what is a 5% VAR for the call option’s weekly return?

 A) 50.7%.

B) 43.4%.

C) 21.6%.

D) 45.3%.

Baran

 

The correct answer is D

 The weekly volatility is approximately equal to 2.77% a week (0.20 / √52). The 5% VAR for the stock price is equivalent to a 1.65 standard deviation move for a normal curve. The 5% VAR of the underlying stock is 0 ? 2.77%(1.65) = ?4.57%. A ?1% change in the stock price results in a 9.91% change in the call option value, therefore, the delta = ?0.0991 / ?0.01 = 9.91. For small moves, delta can be used to estimate the change in the derivative given the VAR for the underlying asset as follows: VARCall = ΔVARStock = 9.91(4.57%) = 0.4529, or 45.29%. In words, the 5% VAR implies there is a 5% probability that the call option value will decline by 45.29% or more over one week.

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

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