Analyzing Covid-19's impact on different sectors I would like to use sector indices. Can you use CAPM or similar to calculate abnormal returns of indices or does it only work with stock prices?
Sure. Your CAPM will tell you there's significant positive alpha in Tech and significant negative in Energy! Which makes total economic sense...
Except do the same for the last 5 years excluding 2020; and you might/will get largely the same result. Tech boomed; and Energy sucked for years before Covid ;-)
So if you're serious about measuring the Covid effect, put in a "dummy" (1 if after February this year) and a "slope dummy" variable into your analysis (ie market returns if post-Feb, 0 if before). These will tell you how Covid has changed the Tech-loving, Energy-hating behaviour of the markets in the Covid-period versus similar before ;-)