Alphas in disguise: A new approach to uncovering them

Four-factor Carhart alphas of passive indices should be zero, but recent empirical evidence shows otherwise. We propose an optimization algorithm that makes small (fixed) adjustments to the time series of the market, size, value, and momentum factors, which ensures a zero alpha for any (single) self-designated benchmark index of a mutual fund. Our "adjusted factors" can then be used to estimate a mutual fund's "adjusted alpha." We test this methodology on a sample of 1,281 active and 102 tracker U.S. equity mutual funds (reporting S&P 500 index as their prospectus benchmark). Our time series adjustment of the Carhart 4 factors leads to an increase (decrease) in a fund's "adjusted alpha" in periods of fund-benchmark underperformance (outperformance). On the whole, our "adjusted alphas" of both active and tracker funds are statistically significantly negative. This is particularly pronounced for tracker funds.