ForecastingStocks

Once you can measure risk and return, the next question is how much of a portfolio's result came from simply riding the market versus genuine skill. Beta and alpha split that apart.

Beta: sensitivity to the market

Beta measures how strongly an asset moves with the overall market.

beta = covariance(asset, market) / variance(market)

Beta of 1: the asset tends to move one-for-one with the market.
Beta of 1.5: it tends to amplify market moves by half — up 15 percent when the market is up 10 percent, and down harder too.
Beta of 0.5: it dampens market moves.
Negative beta: it tends to move against the market (rare; gold and some hedges).

Beta captures systematic risk — the part of an asset's risk that comes from the market and cannot be diversified away.

Alpha: the part the market does not explain

Alpha is the return a portfolio earned above what its beta would predict. If the market returned 10 percent, the risk-free rate is 2 percent, and your portfolio has a beta of 1.2, the expected return from market exposure alone is:

2 + 1.2 times (10 - 2) = 11.6 percent

If your portfolio actually returned 14 percent, your alpha is:

14 - 11.6 = +2.4 percent

That 2.4 percent is the value added beyond passive market exposure — the closest thing to a numerical measure of skill.

The interpretation trap

Positive alpha can be skill, or it can be luck, or it can be hidden risk the model does not capture (selling disaster insurance looks like steady alpha until disaster strikes). Alpha is also measured against a chosen benchmark and beta estimate; change either and the alpha changes. Treat a single period's alpha as suggestive, never as proof.