## (solution) I want to get idea about answering part e of"Explain whether

I want to get idea about answering part e of?Explain whether the conclusion are consistent with what you expected.?

QUESTION 4

On 01/01/2015, a company invests of \$1 million in NAB stocks. Assume that this is

the only investment of the company. Also, assume that returns on the considered

stocks are independently and normally distributed with a daily mean return of zero. In this question, you are asked to use two tailed Kupiec test to conduct back test for

these models using NAB stock price data observed over period 01/01/2014 31/12/2014.

a) Create a spreadsheet to calculate the actual loss for the portfolio over period

01/01/2014 - 31/12/2014

The spreadsheet is done in the Excel sheet 4a

b) Estimate the volatility of NAB rate of return over period 01/01/2014 31/12/2014 using each of the above 3 models

We use observations in 2014 only to estimate the initial volatility value for EWMA

and GARCH (1, 1), we can get the following results:

MODEL CONSTANT (EWMA) GARCH(1,1) Daily Volatility 0.0132 0.0087 0.0086 Annualized Volatility 0.2089 0.1385 0.1363 c) Calculate Value at Risk for each day over period 01/01/2014 - 31/12/2014

using each of the above 3 models

We use observations in 2014 only to estimate the initial volatility value for EWMA

and GARCH (1, 1), we can get the following results: MODEL Working Process VaR Constant Volatility NORM . S . INV (95 )× 0.0132× 1000000 21647.58 EWMA NORM . S . INV ( 95 )× 0.0087 ×1000000 14355.80 GARCH (1,1) NORM . S . INV ( 95 )× 0.0086 ×1000000 14125.04 d) Calculate the number of exceptions for each of the 3 models

We use observations in 2014 only to estimate the initial volatility value for EWMA

and GARCH (1, 1), we can get the following results:

MODEL No. of Exceptions Constant Volatility 4 EWMA 11 GARCH (1,1) 11 e) Calculate the Kupiec test statistics for each model. What are the decisions

suggested by the tests? Explain whether the conclusion are consistent with

what you expected.

Kupiec test statistic: We use all observations in 2014 only to estimate the initial volatility value, we can get

the following results: MODEL Kupiec test statistic Value Constant

Volatility 4 261?4

4 4

1?

×

261

261

261?4

4

?2 ln [ ( 1?5 )

× 5 ] +2 ln ?¿ 8.97 EWMA 11 261?11

11 11

×

261

261

261?11

11

?2 ln [ ( 1?5 )

× 5 ]+ 2 ln ?¿ 0.36 ( ( 1? ) ) ( )

( ) GARCH

(1,1) 11 261?11

11 11

1?

×

261

261

261?11

11

?2 ln [ ( 1?5 )

× 5 ]+ 2 ln ?¿ ( ) ( ) 0.36 Conclusion:

We reject the constant volatility model but do not reject the EWMA and GARCH (1,

1) model if we use the 2014 data only to estimate the initial volatility for EWMA and

GARCH (1, 1) model because these Kupiec test statistic value is higher than 3.84 at

5% significance level for the constant volatility model and are less than 3.84 at 5%

significance level for EWMA and GARCH (1, 1) model.

Explanation:

The conclusion is consistent with what I expected. The reason could be that the stock

performance in 2014 is too good compare with historical average performance.

Therefore, for both the EWMA and GARCH (1, 1) model, the VaR based on initial

volatility estimated from observations in 2014 only is appropriate for the stock

performance in 2014.

Hence, according to the Kupiec Test statistic, we should use either EWMA or

GARCH (1, 1) model with initial volatility estimated by using 2014 data only.

However, this back test is not good enough to decide which method is good since the

market performance for NAB over period 01/01/2014 - 31/12/2014 is too good

compare with other periods, so it can be not very representative. Thus, the decision

about which model is good is heavily related to the periods of data chosen to decide

the initial volatility for EWMA and GARCH (1, 1) model.

Solution details:

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Sep 13, 2020

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