R^2

D

dividend

Can someone explain what R^2 is in "lay man"'s terms? I understand it to be that if R^2=1.00 then that means the CAPM model can explain 100% of the real observed data.

If R^2 is .99 then 99% of the data fits into the capm model?

What about "adjusted" R^2...


Or better yet what would be a *GOOD* statistics 101 book that can explain these things like Feynman could in physics or Thompson in calculus....? Most textbooks are reference books and completely worthless/waste of time/ high risk:reward in terms of trying to learn from them in a short period of time.

Thanks.
 
R^2(X,Y) = Cov(X,Y) / (StdDev(X) x StdDev(Y))

In the case you refer, an R^2 of 1.0 means that you can fit a regression line through every point of excess returns mapped against MRP.

Note however that this does not exclude a +ve (or -ve) alpha (Y- intercept). This does not really go down too well with CAPM as in CAPM alpha is zero:

(Rp - rf) = beta(Rm - rf)
= beta x MRP

whereas

(Rp - rf) = beta(Rm - rf) + alpha

can also have an R^2 of 1.0 if every point is collinear (regression line goes through every point). It simply means that the model fits the observed data perfectly, even though it is in violation of pure CAPM for non-zero alpha (however pure CAPM is wrong - but lets not get started with that old chestnut...)

Note:
{
Rp = portfolio return
rf = risk free rate
Rm = Market return
MRP = market risk premium
}
 
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