Deck 23: Estimating Volatilities and Correlations

Question 1

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.The current estimate of the volatility level is 1% per day.If we observe a change in the value of the variable equal to 2%,how does the estimate of the volatility change

A) 1.26%
B) 1.16%
C) 1.06%
D) 1.03%

Answer 1

C
The new variance rate is 0.000002+0.04×0.02²+0.95×0.01² = 0.000113.The new volatility is the square root of this or 1.06%

Question 2

Which of the following is true of maximum likelihood methods

A) They calculate the maximum possible values for parameters
B) They calculate parameters that give the highest probability of past data occurring
C) They calculate values for key variables that are most likely to occur in the future
D) They involve a multivariate regression analysis

Answer 2

B
Maximum likelihood methods are concerned with estimating parameter values by searching for the values that maximize the chance of observed data occurring.

Question 3

Which of the following is true

A) EWMA is a particular case of GARCH (1,1) where the reversion rate is zero
B) EWMA has a lower reversion rate than GARCH (1,1), but it is not zero
C) EWMA has a higher reversion rate than GARCH (1,1)
D) Sometimes EWMA has a higher reversion rate than GARCH (1,1) and sometimes it has a lower reversion rate than GARCH (1,1).

Answer 3

A
The reversion rate is 1− in GARCH (1,1).EWMA is a particular case of the GARCH (1,1)model where =0,and   .This means that the reversion rate is zero.

Question 4

At the end of Thursday,the estimated volatility of asset B is 1% per day.During Friday asset B produces a return of zero.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the volatility of asset B at the end of Friday?

A) 0.98%
B) 0.95%
C) 0.92%
D) 0.90%

Question 5

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.Which of the following is the closest to the long run average volatility?

A) 1.1%
B) 1.2%
C) 1.3%
D) 1.4%

Question 6

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.What is the reversion rate for the variance rate implied by the model

A) 0.5% per day
B) 1.0% per day
C) 1.5% per day
D) 2.0% per day

Question 7

Which of the following is true

A) GARCH models incorporate mean reversion; EWMA models do not
B) EWMA models incorporate mean reversion; GARCH models do not
C) Both GARCH and EWMA models incorporate mean reversion
D) Neither GARCH nor EWMA models incorporate mean reversion

Question 8

Which of the following is true

A) All option implied volatilities tend to move by the same amount from one day to the next
B) The implied volatilities of long-dated options tend to move by more than the implied volatilities of short-dated options
C) The implied volatilities of short-dated options tend to move by more than the implied volatilities of long-dated options
D) Sometimes B is true and sometimes C is true

Question 9

Which of the following is true

A) GARCH (1,1) will always give a maximum likelihood at least as high as EWMA
B) EWMA will always give a maximum likelihood at least as high as GARCH (1,1)
C) The maximum likelihood is the same for GARCH (1,1) and EWMA
D) Sometimes A is true and sometimes B is true.

Question 10

What does EWMA stand for?

A) Equally weighted moving average
B) Equally weighted median approximation
C) Exponentially weighted moving average
D) Exponentially weighted median average

Question 11

At the end of Thursday,the estimated volatility of asset A is 2% per day.During Friday asset A produces a return of 3%.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the volatility of asset A at the end of Friday?

A) 2.08%
B) 2.10%
C) 2.12%
D) 2.14%

Question 12

At the end of Thursday,the estimated covariance between assets A and B is 0.0001.During Friday asset A produces a return of 3% and asset B produces a return of zero.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the covariance at the end of Friday?

A) 0.000090
B) 0.000081
C) 0.000100
D) 0.000095

Question 13

The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.The current estimate of the volatility level is 1% per day.What is the expected volatility in 20 days?

A) 1.09%
B) 1.10%
C) 1.11%
D) 1.12%

Question 14

How many parameters are necessary to define an EWMA model

A) 1
B) 2
C) 3
D) 4

Question 15

If the volatility for a portfolio is 20% per year,what is the volatility per quarter?

A) 20%
B) 10%
C) 5%
D) 2%

Question 16

How many parameters are necessary to define a GARCH (1,1)model

A) 1
B) 2
C) 3
D) 4

Question 17

Which of the following is true when the parameter lambda equals 0.95?

A) The weight given to the most recent observation is 0.95
B) The weight given to the observation one day ago is 95% of the weight given to the observation two days ago
C) The weights given to observations add up to 0.95
D) The weights given to the observation two days ago is 95% of the weight given to the observation one day ago

Question 18

Which of the following is a definition of the covariance between X and Y?

A) Correlation between X and Y times variance of X times variance of Y
B) Variance of X times the variance of Y
C) Correlation between X and Y divided by the product of the standard deviation of X and the standard deviation of Y
D) Correlation between X and Y times standard deviation of X times standard deviation of Y

Question 19

Which of the following is true

A) Volatilities and correlations decreased in the second half of 2008
B) Volatilities and correlations increased in the second half of 2008
C) Volatilities decreased and correlations increased in the second half of 2008
D) Volatilities increased and correlations decreased in the second half of 2008

Question 20

Which of the following is true of a positive semi-definite variance-covariance matrix

A) All elements of the matrix are positive
B) The determinant of the matrix is positive
C) The matrix has ones on the diagonal
D) The matrix is internally consistent