Okay, we found that, in Part I, picking the top four stocks from the DOW according to principal component vector gave a much better return compared to investing in just the DOW and ...

>Why's that?
Exactly!

>Exactly what?
We should investigate ... to see why picking stocks according to PCA should provide a better allocation than the thirty DOW stocks.

>If PCA picks out the four most volatile stocks then dramatic returns would be expected and ...
Yeah, that's what I thought so I plotted the Mean and Annualized Returns versus Volatility to see if there were a significant correlation, especially with the four stocks that PCA selected and ...

>And what did you get?
This:

>Is that a spreadsheet?
Yeah. Click on the picture to download the spreadsheet ... and play with it yourself to see what makes the top four PCA stocks such a good allocation of assets, compared to the DOW itself. Monthly returns over the past three years are downloaded, for all 30 stocks as well as the DOW, and a bunch of stuff is calculated.

>I'll do that!
Good! Let me know what you find.
In the meantime, you'll notice that the spreadsheet also has the correlation between each stock and the DOW as a whole, like so:

The question is this: Why would the top four components of the principal eigenvector provide such a good allocation, compared to the DOW?
After all, the principal eigenvector provides an allocation which attempts to maximize the volatility of your portfolio.
If you stare intently at the spreadsheet above, you'll see that larger volatility tends to produce smaller returns.

>For the DOW!
Yes, and for this particular time period and using monthly instead of daily or weekly returns and ...

>And for some other collection of stocks ... instead of the DOW? What then?
I have no idea, but you can stick any 30 stocks into the spreadsheet.
Try it ... and let me know what you discover.

>I have a suggestion that's better and simpler than principal eigenvectors and all that stuff.
What's that?
>Pick the single stock with the largest returns!
Very funny.

>So how come you don't have a spreadsheet that downloads the entire DOW and calculates the principal ...
The Principal Eigenvector? Yeah, I got me one of them, too.
It's much like the one above, but downloads 8 years of data ... and works harder (calculating a 30x30 covariance matrix, for example).
It looks like this:

>Do I have to type in the thirty DOW symbols?
Well, any 30 symbols will should work ... so long as Yahoo has eight years of monthly prices.
>Aha! The correlation chart don't agree with your previous chart, above!
Uh ... that earlier chart involved just three years of data, not eight.
>And what's that slider thing?
You move the slider and you get a different chart. Try it!
One of the charts is CAPM which needs some "risk-free" rate ... so you enter that.
In fact, there's an "Explain" sheet that looks like this
>And what's that button called see Distribution?
Oh, that. It's magic ... but gives pretty pictures like this
>And you believe that stuff?
Don't everybuddy?

Oh, I almost forgot. You can (if Yahoo has eight years of data), do the PCA thing for mutual funds.
For example, here's what you'd get with a bunch of Vanguard funds:

for Part III