My Finance

There are three S&P indices: Large-Cap 500, Mid-Cap 400, Small-Cap 600. These have exchange-traded funds (ETFs) by iShares. We use their monthly data to study equity premia: Total returns (including dividends) minus risk-free returns (measured by 3-month Treasury bill). As suggested previously, we divide these by monthly average volatility (measured by VIX) and get . Regress the last two upon the large to do Capital Asset Pricing Model: and . We get: are not significantly different from zero, so let us ignore them. But .

Thus investing in mid-cap and especially small-cap stocks creates a slightly larger market exposure than the benchmark S&P 500 but does not have extra return on top of the one predicted by this extra risk assumed.

The residuals are independent and identically distributed, judging by the autocorrelation function plot, and Gaussian for mid-cap but not for small-cap stocks. For the latter, they seem to be well-described by the Laplace distribution.