I am trying to test the statistical significance of the alphas in my trading strategy.
However, I do not understand the difference between the alphas generated in R.
To test the statistical significance you run the regression
$$ R_{pt} - r_f= \alpha_P + \beta_P (R_{Mt}-r_f)+e_{Pt} $$
I interpret this as running the excess returns of the strategy on the l.h.s, and the returns predicted by the CAPM/market on the r.h.s., which is:
lm(strategy - rf ~ alpha + beta*(market-rf)
(lm()
is the regression function in R)
I use the package PerformanceAnalytics
and function CAPM.alpha()
which get the same alpha as when I do summary((lm(strategy -rf ~ market - rf))
, where market
is simply the historical returns from the market.
So, which is the right method to test for the statistical significance (t-test, p-value etc.) of the alpha?
lm(strategy - rf ~ alpha + beta*(market-rf)
(CAPM on rhs), orlm(strategy - rf ~ market - rf)
I. $R_{pt} - r_f= \alpha_P + \beta_P (R_{Mt}-r_f)+e_{Pt}$
II. $R_{pt} - r_f = R_{Mt} - r_f$
The former method is statistically significant, while the latter is not.