Forecasting Volatility | cfa level 3 notes

LOS-discuss methods of forecasting volatility

1.Sample statistics, use history return data to forcast
Advantages: unbiased and consistent
Disadvantages: sample data limited, sample error, not consider the cross-sectional consistency

2.Multi-factor model
Advantages: able to deal with large data(the number of assets can be large relative to the observations), less sample error, improve the cross-sectional consistency
Disadvantages: biased and inconsistent

3.Shrinkage estimation model
the weighted average of the sample VCV and the factor-based VCV, it increase the efficiency of estimates.

4.estimating from smoothed return data
for private assets or real estate. usually understate the risks and overstate the diversifications.

One of the simplest and most widely used models implies that the current observed return, Rt, is a weighted average of the current true return, rt, and the previous observed return:

Rt=(1λ)rt+λRt1


where 0 < λ < 1. From this equation, it can be shown that

var(r)=(1+λ1λ)var(R)>var(R)

As an example, if λ = 0.8, then the true variance, var(r), of the asset is 9 times the variance of the observed data. Equivalently, the standard deviation is 3 times larger.

5.ARCH model
the current volatility depends on its own recent volatility history.

σt2=γ+ασt12+βηt2=γ+(α+β)σt12+β(ηt2σt12)

where α, β, and γ are non-negative parameters such that (α + β) < 1. The term ηt is the unexpected component of return in period t;

21 Jul 2023 - Original by toptradeready.com