qingshu

 

The correct answer is B

All three methods are parametric, use historical data, and apply weights to past squared returns. The historical standard deviation approach weighs all returns in the estimation window equally. The RiskMetricsTM and GARCH approaches are exponential smoothing approaches that place a higher weight on more recent data.

qingshu

 

The correct answer is

The lowest and second lowest returns have cumulative weights of 2.68% and 5.21%, respectively. The point halfway between the two lowest returns is interpolated as –3.95% with a cumulative weight of 3.945%, calculated as follows: (2.68% + 5.21%) / 2. Further interpolation is required to find the fifth percentile VAR level with a return somewhere between –3.80% and –3.95%. The 5 percent VAR using the hybrid approach is calculated as:

3.95% – (3.95% – 3.80%)[(0.05 – 0.03945) / (0.0521 – 0.03945)] = 3.95% – 0.15%[0.8340] = 3.8249%

Notice that the answer has to be between –3.8% and –3.95%, so –3.82 is the only possible answer.

qingshu

 

3、Which of the following approaches is the most restrictive regarding the underlying assumption of the asset return distribution?

A) nonparametric.

B) parametric.

C) hybrid.

D) multivariate density estimation.

qingshu

 

AIM 5: Compare and contrast parametric approaches for estimating conditional volatility, including the historical standard deviation approach, the RiskMetrics? approach and the GARCH approach, and discuss the advantages and disadvantages of nonparametric methods for volatility forecasting.

1、

λ = 0.97 K = 150
Rank	Ten Lowest Returns	Number of Past Periods	Hybrid Weight	Hybrid Cumulative Weight
1	–4.10%	5	0.0268	0.0268
2	–3.80%	7	0.0253	0.0521
3	–3.50%	21	0.0165	0.0686
4	–3.20%	13	0.0210	0.0896
5	–3.10%	28	0.0133	0.1029
6	–2.90%	55	0.0059	0.1088
7	–2.80%	28	0.0133	0.1221
8	–2.60%	28	0.0133	0.1354
9	–2.55%	28	0.0133	0.1487
10	–2.40%	55	0.0059	0.1546

The VAR measure for the fifth percentile using the historical simulation approach is closest to:

A)  –3.90%.

B)  –2.70%.

C)  –3.80%.

D)  –3.10%.

qingshu

 

The correct answer is B

Under the historical simulation approach, all returns in the estimation window are equally weighted. In this example, K = 150; therefore, each return has a weight of 1 / 150 = .666667%, as shown in the following table. The fifth percentile is somewhere between –2.80% and –2.60%. The midpoint –2.70% has a cumulative weight of 5.00% (5.00% = (4.67% + 5.33%) / 2). If the midpoint did not have a cumulative weight of exactly 5.00%, interpolation would be necessary to find the fifth percentile.

Ten Lowest Returns	Historical Simulation Weight	HS Cumulative Weight
–4.10%	0.00666667	0.0067
–3.80%	0.00666667	0.0133
–3.50%	0.00666667	0.0200
–3.20%	0.00666667	0.0267
–3.10%	0.00666667	0.0333
–2.90%	0.00666667	0.0400
–2.80%	0.00666667	0.0467
–2.60%	0.00666667	0.0533
–2.55%	0.00666667	0.0600
–2.40%	0.00666667	0.0667

 

qingshu

 

2、The VAR measure for the fifth percentile using the hybrid approach is closest to:

A) –3.82%.

B) –4.10%.

C) –3.80%.

D) –3.10%.

qingshu

 

The correct answer is B

The most likely explanation for “fat tails” is that the second moment or volatility is time-varying. For example, volatility changes in interest rates are observed prior to much anticipated Federal Reserve announcements. Examining a data sample at different points of time from the full sample could generate fat tails in the unconditional distribution even if the conditional distributions are normally distributed. The conditional mean is not expected to deviate over time. The first two moments (mean and variance) of the distributions are similar for the fat-tailed and normal distribution. However, fat-tailed distributions typically have less probability mass in the intermediate range, around +/–1 standard deviation, compared to the normal distribution. Fat-tailed distributions have greater mass in the tails and a greater probability mass around the mean than the normal distribution.

qingshu

 

4、Which of the following deviations from normality leads to underestimating the distribution variance?

?            Higher probability of high returns.

?            Higher probability of mean returns.

?            The mean of the distribution is conditional on the economic environment.

?            The variance of the distribution is conditional on the economic environment.

A) II only.

B) III only.

C) I, II, and IV only.

D) III and IV only.

qingshu

 

The correct answer is A

Statements I & III lead to overestimates of variance. Statement IV leads to over or under estimates of the variance.

qingshu

 

AIM 3: Discuss the implications regime switching has on quantifying volatility.

A regime-switching volatility model of interest rates would assume all of the following EXCEPT:

A) the regime determines whether the volatility of interest rates is high or low.

B) the unconditional distribution of interest rates is normally distributed.

C) the mean is constant.

D) interest rates are conditionally normally distributed.