P1 T4 Allen Pg7 Notes

[INDRAJIT]

Hi David,

Have got a few basic questions.

1. Conditional distribution(time varying). Suppose we cosider a time series of returns over a 10yr period. Say the distribution is changing as assumed and to keep it simple lets say the dbn is changing every 6 month period. In that case when we consider the whole time series of data then the resultant dbn we get is a mixture and/or addition of the 6 onthly distributions? This resultant distribution obtained from the 10yr time series is negatively skewed and fat tailed? Is that what we are saying?
2. When we say volatility of the distribution is changing, are we saying every 6 months the volatility is changing for that specific 6 monthly period i.e. it remains constant for 6 month and then in the next 6 months it is changing? We are assuming the simple 6 monthly time varying distribution as above for the 10yr period.

Notes excerpt below:

"How can outliers be indications that the volatility varies with time?

We observe that actual financial returns tend to exhibit fat-tails. Jorion (like Allen et al) offers
two possible explanations:

1.
The true distribution is stationary. Therefore, fat-tails reflect the true distribution but

the normal distribution is not appropriate

2.
The true distribution changes over time (it is “time-varying”). In this case, outliers can

in reality reflect a time-varying volatility."


Thanks,
Indrajit