GARCH and EWMA Key Points

QUESTION:

If the current daily variance of some underlying asset is 1%, and its long term average is 1.5%, then which one of the following statements is most likely to be true:
(a) EWMA will predict a higher future daily variance than GARCH(1,1)
(b) EWMA will predict a similar future average variance to GARCH(1,1)
(c) EWMA will predict a lower future daily variance to GARCH(1,1)
(d) EWMA will predict a higher future average variance than GARCH(1,1)


Both EWMA and GARCH employ exponential smoothing!

Why named as GARCH?

Autoregressive (AR): tomorrow’s variance is a regressed function of today’s variance—it regresses on itself

Conditional (C): tomorrow’s variance depends—is conditional on—the most recent variance. An unconditional variance would not depend on today’s variance

Heteroskedastic (H): variances are not constant, they flux over time

GARCH regresses on “lagged” or historical terms. The lagged terms are either variance or squared returns. The generic GARCH (p, q) model regresses on (p) squared returns and (q) variances. Therefore, GARCH (1, 1) “lags” or regresses on last period’s squared return (i.e., just 1 return) and last period’s variance (i.e., just 1 variance).

Persistence of GARCH and EWMA

Persistence means how fast/slowly the volatility reverts/decays to long-term average. For GARCH, it is equal to alpha+beta(John Hull Notation). For EWMA, it equals to 1, which means there is no mean reverting effect at all.

So for the question above, according to GARCH, variance has a trend to revert to long term average, from 1% to 1.5%. but EWMA has a higher persistence, which means it has no this kind of trend. Therefore, EWMA will probably get a lower future daily variance than GARCH. C should be correct.

I found this graph is quite clear: