Suppose we have a basket of stocks in our portfolio.
We'd expect that when the Market goes UP
(or DOWN), our portfolio will go UP (or DOWN).
>You're talking about my portfolio, eh? I always noted that ...
Pay attention. This correlation with the Market seems inevitable. Normally, we can't avoid it.
For example, here's the relation between the monthly S&P 500 returns and GE returns
However, if the Market goes UP by 5% we'd expect, of course, that our portfolio would go UP
... but maybe we can arrange that it go UP by 8%. If the Market goes DOWN by 10%,
maybe, by judicial choice of assets, our portfolio will ...
>Go DOWN by 12%!
 Figure 1

Yes, maybe. We might be able to exaggerate (or diminish) the Market swings.
That exaggeration is measured by
beta,
which compares stock returns with Market returns.
Anyway, here's what we'll do:
 We find the average monthly (daily? yearly?) returns of a collection of stocks over, say, 1980  2000 (or, better,
riskadjusted returns: see Notes)
 We also find the returns for "the Market"
 We calculate the beta
for each stock return
(that's the slope of the regression line)
 We plot the stock returns versus the corresponding beta.
For example, using a bunch of DOW stocks and the S&P 500 as a proxy for "the Market",
we get Figure 2.
 Figure 2

>What's the red line?
That's the "Best Fit" line to the fifteen data points, namely (Beta, StockReturn).
>A regression line?
Yes, and its equation is shown on the chart: y = 0.0104 x + 0.0005
>What's this got to do with Capital Asset Pricing ...?
Noting that there seems to be a relationship/correlation between Returns and Beta,
we consider the following CAPM prescription:
E[R] = R_{f} + Beta(E[R_{m}]  R_{f})
>Beg pardon?
Here, R_{f} is a riskfree return (say 4%)
and E[R_{m}] is
the Expected Market return (say 9%)
and E[R] is the Expected return of the asset
whose Beta is ... uh, Beta.
Note that, should Beta = 1, the Expected asset return is the same as the Market return.
But see the Appendix
>Example?
Okay, suppose the Expected Market return is 10% and we assume a riskfree return of 4% and
we're considering a stock with a Beta of 1.2 so that ...
>So we calculate 4% + 1.2(10%  4%) = 11.2% which is ...
The Expected return for this asset.
>Are we talking monthly returns?
In this example, we're talking annual returns.
>Do you believe it?
I refuse to comment on the grounds that it ...
>Forget I asked. How about a calculator?
 Figure 3

Notes:
As Beta increases, the CAPM for the asset increases beyond the Market return.
On the other hand, for smaller Beta, you'd expect a smaller return than the Market.
On the other hand, for large Beta, when the Market goes DOWN big time, so does the Expected asset return.
On the other hand, in CAPM, one uses riskadjusted returns: a stock's return less some Riskfree return (like money market or Tbills).
On the other hand ...
>Forget the hands. Tell me, how did all this start? I mean ...
Check out
an interview with Sharpe.
