Baran

 

39、The most important way in which the Monte Carlo approach to estimating operational VAR differs from the historical method and variance-covariance method is:

A) its heavy dependence on historical data.

B) it involves repeatedly shocking a model of risk data to produce a range of potential losses.

C) its computational simplicity. 

D) its inability to account for non-linear risk structures. 

Baran

 

The correct answer is B

 

The Monte Carlo approach uses simulation techniques, repeatedly shocking a model of loss data in order to produce a range of potential losses. It is more computationally intensive than either the historical or variance-covariance approaches. The model used can account for nonlinear risk structures and need not be limited by historical data.

Baran

 

38、The relationship between a three month call option and its underlying stock are presented in the following table.

Volatility: σ            = 15.0% Risk-free rate        = 6.0% Exercise price (X) = 24 Time to maturity    = 3 months S                          = $25.00 C                          = $1.60
Stock Price, S	$21.00	$22.00	$23.00	$24.00	$24.75	$25.00
Value of Call, C	$0.04	$0.15	$0.42	$0.91	$1.41	$1.60
Percentage Decrease in S	–16.00%	–12.00%	–8.00%	–4.00%	–1.00%
Percentage Decrease in C	–97.46%	–90.39%	–73.55%	–43.37%	–11.92%
Delta (ΔC%/ΔS%)	6.09	7.53	9.19	10.84	11.92

Using the linear derivative VAR method and the information in the above table, what is a five percent VAR for the call option’s weekly return?

A) 10.8%.

B) 40.9%.

C) 15.8%.

D) 21.3%.

Baran

 

The correct answer is B

The weekly volatility is approximately equal to 2.08 percent a week (). The 5 percent VAR for the stock price is equivalent to a one standard deviation move, or 1.65 for the normal curve. The 5 percent VAR of the underlying stock is 0 – 2.08%(1.65)= –3.432%. A one percent change in the stock price results in a 11.92 percent change in the call option value, therefore, the delta = 0.1192/0.01 = 11.92. 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 =11.92(3.432%) = 0.409 or 40.9%. In words, the 5 percent VAR implies there is a 5 percent probability that the call option value will decline by 40.9% or more.

Baran

 

Using the linear derivative VAR method and the information in the table, and assuming 255 trading days in a year, what is a 1-percent VAR for the call option’s daily return?

A) 11.9%.

B) 15.8%.

C) 43.4%.

D) 26.1%.

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.

Baran

 

37、If a 1-day 95 percent VAR is $5 million, the 250-day 99 percent VAR level would be closest to:

A) $55.89 million.

B) $83.84 million.

C) $111.79 million.

D) $21.00 million.

Baran

 

The correct answer is C

 

First it is necessary to adjust for confidence levels (2.326/1.645), then by days (√250). In this case, ($5 million)(2.326/1.645)(√250) = $111.79 million.

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.