Risk Adjusted Performance Attribution

Comparing a fund or any portfolio's performance to a benchmark usually involves risk analysis and attribution analysis. Risk analysis considers measures such as beta and Jensen's alpha to determine if the portfolio is riskier than the benchmark. Attribution analysis decomposes the spread between the portfolio and the benchmark returns into differences due to allocating the portfolio sector weights differently than the benchmark versus selecting individual assets that perform well compared to the benchmark. These two types of analysis are typically done independently with attribution analysis essentially assuming that there are no differences in risk between the portfolio and the benchmark. As a result, selection and allocation are applied to what is sometimes referred to as “simple alpha” that is just the difference between the portfolio and benchmark return ignoring risk. Some attempts have been made to combine the two, but as explained in this article, none of them have done this in a way that is based on having attribution analysis apply to either Jensen's alpha using beta as a risk adjustment or using what has been referred to as Fama's beta to also adjust for taking on unsystematic risk by having an allocation different from the benchmark. This article proposes a risk adjusted performance attribution analysis that integrates risk measures with the Brinson models of attribution which allows us to decompose the excess portfolio return into components of risk, allocation and net selection that is additive and consistent with financial theory. Risk adjusted performance attribution can give us a quite different interpretation of which sectors contributed to better or worse performance relative to the benchmark. Traditional attribution analysis could result in a manager appearing to have done well in a sector where the higher return relative to the benchmark was just due to taking on more risk. Or the manager could appear to have underperformed in a sector that was a less risky sector