Market Benchmark

Beta-adjusted market benchmark

• We estimate the market (CAPM) beta by regressing

Alpha and the information ratio

• The return \(r - [\beta r_m + (1-\beta)r_f]\) is called the active return.
• Its mean is \(\alpha\). Hence, “seeking alpha.”
• Its risk is the risk of the regression residual \(\varepsilon\).
• The ratio \(\alpha / \text{stdev}(\varepsilon)\) is the Sharpe ratio of the active return.
• It is called the information ratio.

Compounding active and market returns

• To see visually how much the active return is adding to performance, compound
  • the benchmark return \(\beta r_m + (1-\beta)r_f\)
  • the active return \(\alpha + \varepsilon\)
  • and the total return \(r\).

Example