qingshu

 

15、Which of the following are true about the RiskMetrics, GARCH, and historical standard deviation approaches to estimate conditional volatility?

I.           RiskMetrics and historical standard deviation assume equal weights on all observations.

II.         RiskMetrics and GARCH are parametric models: historical standard deviation is not.

III.        Increasing λ suggests a higher relative weight on the most recent data for exponential smoothing models.

IV.      The most recent weight for GARCH exceeds the most recent weight for historical standard deviation, assuming the same high number of observations.

A) II, III, and IV only.

B) III and IV only.

C) II and III only.

D) I, II, and IV only.

qingshu

 

The correct answer is B

RiskMetrics does not assign equal weights across observations. Historical standard deviation is a parametric model.

qingshu

 

16、Using both RiskMetrics and historical standard deviation, calculate the K-value that equates the most recent weight between the two models. Assume λ is 0.98.

A) K = 30.

B) K = 50.

C) K = 51.

D) K = 98.

qingshu

 

The correct answer is B

(1 ? λ) λt = (1 ? 0.98)(0.98)0 = 0.02; 1/K = 0.02, K = 50.

qingshu

 

17、How many of the following statements about VAR methodologies is (are) TRUE?

I.           The parametric approach is typically defined by the calculation of the distribution mean and variance.

II.         The nonparametric approach has the advantage of no required asset distribution.

III.        The implied-volatility based approach estimates volatility using current market prices.

IV.      The GARCH approach is a parametric model that uses time varying weights on historic returns to calculate distribution parameters.

A) Three statements are true.

B) Two statements are true.

C) One statment is true.

D) All statements are true.

qingshu

 

The correct answer is D

All of the statements are true.

qingshu

 

18、Consider the following EWMA models that are used to estimate daily return volatility. Which model’s volatility estimates will have the most day-to-day volatility, and which model will be the slowest to respond to new data, respectively?

Model 1: σ_n² = 0.04μ_{n ? 1}² + 0.96σ_{n ? 1}²

Model 2: σ_n² = 0.02μ_{n ? 1}² + 0.98σ_{n ? 1}²

Model 3: σ_n² = 0.20μ_{n ? 1}² + 0.80σ_{n ? 1}²

Model 4: σ_n² = 0.10μ_{n ? 1}² + 0.90σ_{n ? 1}²

       Greatest day-to-day volatility    Slowest to respond to new data

 

A)        Model 2                     Model 2

B)        Model 3                                  Model 2

C)        Model 2                                 Model 3

D)        Model 1                                 Model 4

qingshu

 

The correct answer is B

The form of the basic EWMA model is σn2 = (λ ? 1)μn ? 12 + λσn ? 12, where λ is the weight on the previous volatility estimate. EWMA models with a low value for λ (Model 3) will put more weight on the previous day's return and will lead to volatility estimates that in themselves are highly volatile from day to day. EWMA models with a high value for λ (close to 1, such as Model 2) will put less weight on the previous day's return, and the model will respond more slowly to new data.

 

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.