qingshu

 

The correct answer is D

For a 24-hour period, there are 6 hours that overlap for the NYSE and London Stock Exchange. If we assume information is constant, we need to inflate the covariance by multiplying it by 1.33, calculated as follows:

 

 

 

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[2008] Topic 10: Quantifying Volatility in VAR Models 相关习题

2009-6-27 11:30

qingshu

 

AIM 6: Compare and contrast the use of historic simulation, multivariate density estimation, and hybrid methods for volatility forecasting.

l =	0.96
K =	100
Rank	Ten Lowest Returns	Number of Past Periods	Hybrid Weight
1	-4.30%	7	0.0318
2	-3.90%	10	0.0282
3	-3.70%	15	0.0230
4	-3.50%	20	0.0187
5	-3.00%	17	0.0212
6	-2.90%	28	0.0135
7	-2.60%	32	0.0115
8	-2.50%	18	0.0203
9	-2.40%	55	0.0045
10	-2.30%	62	0.0034

The value at risk measure for the fifth percentile using the hybrid approach is closest to:

A)  –3.90%.

B)  –4.30%.

C)  –4.04%.

D)  –4.10%.

qingshu

 

The correct answer is C

The lowest and second lowest returns have cumulative weights of 3.18% and 6.00%, respectively. The point halfway between the two lowest returns is interpolated as –4.10% with a cumulative weight of 4.59% calculated as follows: –4.10% = (–4.30%+ –3.90%)/2; 4.59% = (3.18%+6.00%)/2. Further interpolation is required to find the fifth percentile VAR level with a return somewhere between –3.90% and –4.10%. The 5% VAR using the hybrid approach is calculated as: 4.10% – (4.10% – 3.90%)[(0.05 – 0.0459)/(0.06 – 0.0459)] = 4.10% – 0.20%[0.2908] = 4.04%.

l =	0.96
K =	100
Rank	Ten Lowest Returns	Number of Past Periods	Hybrid Weight	Hybrid Cumulative Weight
1	-4.30%	7	0.0318	0.0318
2	-3.90%	10	0.0282	0.0600
3	-3.70%	15	0.0230	0.0830
4	-3.50%	20	0.0187	0.1017
5	-3.00%	17	0.0212	0.1229
6	-2.90%	28	0.0135	0.1364
7	-2.60%	32	0.0115	0.1479
8	-2.50%	18	0.0203	0.1682
9	-2.40%	55	0.0045	0.1727
10	-2.30%	62	0.0034	0.1761

 

qingshu

 

AIM 9: Explain the implications of mean reversion in returns and return volatility, respectively have on VAR forecasts over long time horizons.

Which of the following statements regarding mean reversion is FALSE?

A) The single period conditional variance of the rate of change is 2.

B) The 2-period variance is calculated as (1+b2)2, where b is the rate of change in mean reversion. 

C) The long horizon risk is smaller than the square root volatility if mean reversion exists.

D) If the rate of change of mean reversion, b, is greater than one, the process is mean reverting.

qingshu

 

The correct answer is D

Under the context of mean reversion the single-period conditional variance of the rate of change is σ2. The 2-period variance is (1 + b2)σ2. If b = 1, the typical variance would occur as this represents a random walk. If b < 1, the process is mean reverting.

qingshu

 

AIM 10: Discuss the effects non-synchronous data has on estimating correlation and describe approaches that mitigate the impact of non-synchronous data on risk estimates.

1、Assume that the flow of information is constant and that returns are independent of one another. By what amount should the covariance term be inflated to adjust for nonsynchronous data between the New York Stock Exchange and the London Stock Exchange if there is a 6-hour lag between the market closing times?

A) 2.66.

B) 3.00.

C) 6.00.

D) 1.33.

qingshu

 

AIM 7: Explain, in the context of volatility forecasting methods, the process of return aggregation.

All of the following are appropriate methods for addressing return aggregation in volatility forecasting methods EXCEPT:

A) the historical standard deviation approach creates a variance-covariance matrix that is estimated under the assumption that all asset returns are normally distributed.

B) the historical simulation approach weights returns based on market values today, regardless of the actual allocation of positions K days ago.

C) the RiskMetricsTM approach creates a variance-covariance matrix that is estimated under the assumption that volatility is constant over time.

D) for well-diversified portfolios, the strong law of large numbers is required to estimate the volatility of the vector of aggregated returns.

qingshu

 

The correct answer is C

Both the RiskMetricsTM and the historical standard deviation approach create variance-covariance matrices that are estimated under the assumption that all asset returns are normally distributed. A major disadvantage of this approach is the number of calculations required to estimate VAR.

qingshu

 

AIM 8: Explain how implied volatility can predict future volatility and discuss its advantages and disadvantages.

Approaches for estimating value-at-risk (VAR) can be based on the history of past returns or on current market data. The approach that focuses exclusively on current market data is:

A) the parametric approach.

B) the implied-volatility-based approach.

C) the hybrid approach.

D) the nonparametric approach. 

qingshu

 

The correct answer is B

The implied-volatility-based approach uses a derivatives pricing model such as the Black-Scholes option pricing model to estimate implied volatility based on current market data rather than historical data.