Risk-Adjusted Attribution Analysis of Real Estate Portfolios

Abstract

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 components that are due to allocating the portfolio sector weights and selecting individual assets differently than 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 or nominal alpha, which is just the difference between the portfolio and benchmark return, ignoring risk. Some attempts have been made to combine the two, but none 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 Fama’s beta, which relies only on relative standard deviations and adjusts for any additional risk resulting from not having a well-diversified portfolio. 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, selection, and net selectivity 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 due to taking on more risk. Alternatively, the manager could appear to have underperformed in a sector that was a less risky sector. This is demonstrated using actual but masked open-end fund data as the manager portfolio compared to the NCREIF Property Index as the benchmark portfolio.

TOPICS: Real estate, statistical methods, risk management

Key Findings

• • A manager’s portfolio returns must first be adjusted to the same risk as the benchmark before using Brinson attribution analysis to evaluate performance.

• • Using risk adjusted returns results in a better understanding of which sectors contributed to over or under performance.

• • The model proposed herein allows adjustment for both market risk (beta) and non-diversification risk (standard deviation) consistent with the CAPM and Fama’s concept of net selectivity.