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I am conducting PCA on several return series of funds and am finding that when I look at the first principal component the values are huge and this the volatility is also enormous relative to the funds I have used to construct the PCA.

The average return vol for the funds is 3.38% with the largest being roughly 5%. The volatility however for the first PC is 17%, I thought the first PC was most likely a market factor (although with funds instead of stocks I’m not sure). I think the first PC in this instance is most likely a healthcare factor as funds with large loadings in the first PC are heavy on healthcare stocks.

My question therefore is how can the first PC have such a large volatility and what might the first PC represent (not specifically)?

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    $\begingroup$ What % of the returns are explained by the first PC? It doesn't quite make sense that the first PC would be "huge" (i.e. > 70%...?) and it's Vol would be 17%, whilst the average Vol for the funds would be only 3.38%. Otherwise, what time series are you looking at? Does it include the past year (i.e. Covid-induced higher vol?) The healthcare sector stocts have been very volatile over the past year, which could explain the relatively higher vol for the Healthcare sector. $\endgroup$ – Jan Stuller Jan 11 at 10:26
  • $\begingroup$ Ok so I’m not mad that doesn’t really make sense does it! I am using the last three years so includes Covid yep but even so, I compared the returns against the S&P biotech select which is a very volatile biotech index and the returns are still way higher vol wise. 20% explained variance for the first PC $\endgroup$ – Simon Nicholls Jan 11 at 10:35
  • $\begingroup$ Note I am using a PCA on the transposed return series meaning the PCs themselves have a value for each date which I am comparing the vol of the PC to the funds $\endgroup$ – Simon Nicholls Jan 11 at 10:42
  • $\begingroup$ The key question is: what % of the variance of the returns are explained by your first PC? $\endgroup$ – Jan Stuller Jan 11 at 10:52
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    $\begingroup$ If the first PC only explains 20% of the variance of the returns, then your results are not that surprising: it could be that the first PC has 17% vol whist the remaining 80% of your PCs only have vol < 3%, which could then in total produce a vol of 3.38%. Also it is a bit odd that the first PC only explains 20% of your data variance: in my experience, the first PC usually explains between at least 50% to over 70% of the total variance in the data... $\endgroup$ – Jan Stuller Jan 11 at 11:09

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