Historical Simulation with uneven time series

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mrpmkt
Posts: 11
Joined: Thu Aug 06, 2009 6:06 pm

Historical Simulation with uneven time series

Postby mrpmkt » Thu Jan 21, 2010 10:23 pm

Hello,

For historical simulation with uneven time series how do we handle the missing returns? e.g. if i want to go back 5 years but some securities in the portfolio have history only for the last 2 years.
Do I somehow backfill the returns for the shorter history to go back to 5 years or do we have to consider the period where all history is available?

Thanks a lot.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Historical Simulation with uneven time series

Postby coalexander » Fri Jan 22, 2010 9:28 am

Hiya

Here are the options:

1. Use only 2 years of data, and use a kernel or aparametric distribution fuit to estimate VaR at extreme quantiles
2. Map the stock returns with missing data to some factors, based on the data you do have. If you get a very good fit in the factor model (on both in-sample diagnostics and out-of-sample forecsting - see Vol II for methds) then you can use the data on the factors over the whole historical data period, to re-create artifical returns for the missing stocks

Comment: Do not feel obliged to use a very long histroical period - indeed, two years should be fine for most VaR measurment. Using a very long period with [u:1n4lzx7o]equal[/u:1n4lzx7o] wrighting of the data makes the VaR model much too insensitive to current market conditions. Thats why a volatility adjustment should be used, if you use a long sample period. But you can use only 2 years, and fit a kernel (or another distribution) - and that will be more response to current condions than an equally weitghed histroical VaR.

Carol

mrpmkt
Posts: 11
Joined: Thu Aug 06, 2009 6:06 pm

Re: Historical Simulation with uneven time series

Postby mrpmkt » Fri Jan 22, 2010 1:07 pm

Thank you for the information.
In general if there are some securities in a portfolio with very little history (few months) whereas all the other securities have 2 year history, how do we handle such a situation for Historical Simulation.

Thanks again.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Historical Simulation with uneven time series

Postby coalexander » Fri Jan 22, 2010 1:22 pm

How many data points do you have? Is the data daily? How many securities in total and how many with sparse data?

Carol

mrpmkt
Posts: 11
Joined: Thu Aug 06, 2009 6:06 pm

Re: Historical Simulation with uneven time series

Postby mrpmkt » Fri Jan 22, 2010 2:43 pm

This is daily data. There are 70 securities out of which 5 have
histories ranging from 20 days to 7 months. The others have the
full 2 years of data.

Thanks a lot.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: Historical Simulation with uneven time series

Postby coalexander » Fri Jan 22, 2010 5:05 pm

OK, use PCA. For each of the 5 securities, take n similar securities (where n depends on the one you take, maybe for security 1 then are only 10, for security 2 there are a lot more similar ones, etc). n should be large, if you can.

With the data available for security 1, do a PCA on it and its similar securities, and save the matrix of eigenvectors (the factor weights). Use all the PCs. Each PC is a linear combination of security returns, with fixed factor weights. Recreate each PC by omitting the security with only a bit of data...call these PC* ... how similar are they to PCs? Not changed much? Good. Because the PC*s can be reconstructed over the whole 2 years!

Each return is a linear combination of the PC*s, with fixed factor weights. Use the factor weights to reconstruct your security return data.

I'll done this before and it worked really well. See Market Models (C. Alexander, 2001) Wileys.

mrpmkt
Posts: 11
Joined: Thu Aug 06, 2009 6:06 pm

Re: Historical Simulation with uneven time series

Postby mrpmkt » Fri Jan 22, 2010 5:15 pm

Awesome.

Thanks a lot!


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