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Importance of PCA

Ken Abbott

Managing Director
From said former student:
"If you want to work in the rates space; that could be US treasury or emerging markets or end up there in risk, trading or quant area, knowing PCA is extremely helpful. The problem in these areas is the number of time series available. E.g The US treasury desk: There are 1,3,6,12M ,2,5,7,10,15,20,30Y time series whether treasuries or constant maturity yields. You will have position linked to each and you think or mentally monitor your pnl for each position. You have to reduce it to get a better idea of your PnL and in a scenario like that PCA is your best friend. It also helps with quick stress testing of extreme scenarios without re-pricing your whole portfolio.
Learning PCA and time series analysis can only help with jobs or keeping your job."
 
The impression I get is that it's taught mindlessly: the meaning of principal components analysis is rarely discussed. Ideally an instructor would want to start with two variables, followed by three variables, and work through some examples in detail, explaining the significance of PCA. Jackson does this in the first chapter of his A User's Guide to Principal Components. There's also some coverage in Krzanowski's Principles of Multivariate Analysis. From a pedagogical point of view neither is perfect. Do you know a better source?
 
From said former student:
"If you want to work in the rates space; that could be US treasury or emerging markets or end up there in risk, trading or quant area, knowing PCA is extremely helpful. The problem in these areas is the number of time series available. E.g The US treasury desk: There are 1,3,6,12M ,2,5,7,10,15,20,30Y time series whether treasuries or constant maturity yields. You will have position linked to each and you think or mentally monitor your pnl for each position. You have to reduce it to get a better idea of your PnL and in a scenario like that PCA is your best friend. It also helps with quick stress testing of extreme scenarios without re-pricing your whole portfolio.
Learning PCA and time series analysis can only help with jobs or keeping your job."
Hi Ken,
I didn't quite understood how can PCA be used in PnL positions in treasuries. Traditionally, I have done and seen, PCA being used to decompose yield curve or figure out weights for the curve/butterfly trades
 

Ken Abbott

Managing Director
You can use it as a very fast way of accurately estimating the p&L of a large, complex rates portfolio. It also informs the hedging process, e.g. if the 1st PC covers 95% of the total variance, a simple duration-weighted hedge should be fine.

BTW: People seem to like A Tutorial on Principal Components Analysis by Lindsay I Smith.
 
Thanks Ken. apart from finding weight for curve and butterfly trades and hedging (like the way you mentioned), what else can PCA be used for in rates (especially from trading perspective)?
 
I found PCA to be one of those things the profs tend to reference but nobody ever teaches. They just kind of assume you will learn it elsewhere. I like Avril Coghlan's booklets available for Multivariate Analysis and Time Series. Both focus on R and are more on the applied side than the theory.
 
Hi, I am a newbie here. What would be some of the "good" variables to use if I would to conduct a 2 to 3 dimension PCA for EM rate portfolio?
 
The application of PCA to level/slope/curvature of bond yield curves all stems from:

Litterman and Scheinkman, "Common Factors affecting Bond Returns",​


published in 1991 in the very first issue of Journal of Fixed Income.​

Although they never utter the term "Principal Components" in their paper, that's exactly what they are doing.
 
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