A RISK ANALYST IS ESTIMATING THE VARIANCE OF STOCK RETURNS ON DAY N...

4.

A risk analyst is estimating the variance of stock returns on day n, given by , using the equation

where and

represent the return and volatility on day n-1, respectively.

If the values of

α

and

β

are as indicated below, which combination of values indicates that the variance

follows a stable GARCH (1,1) process?

a.

α

= 0.084427 and

β

= 0.909073

b.

α

= 0.084427 and

β

= 0.925573

c.

α

= 0.084427 and

β

= 0.925573

d.

α

= 0.090927 and

β

= 0.925573

Correct Answer: a

Rationale:

For a GARCH (1,1) process to be stable, the sum of parameters

α

and

β

need to be below 1.0.

Section:

Quantitative Analysis

Reference: John Hull, Options, Futures, and Other Derivatives, 9th Edition (New York: Pearson Prentice Hall, 2014),

chapter 23, “Estimating Volatilities and Correlations for Risk Management.”

Learning Objective:

Describe the generalized auto regressive conditional heteroskedasticity (GARCH(p,q)) model

for estimating volatility and its properties:

•

Calculate volatility using the GARCH(1,1) model

•

Explain mean reversion and how it is captured in the GARCH (1,1) model

24

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2015 Financial Risk Manager (FRM®) Practice Exam

The following information applies to questions 5 and 6.

A portfolio manager holds three bonds in one of his portfolios and each bond has a 1-year default probability of

15%. The event of default for each of the bonds is independent.