Portfolio Based Performance Analysis

AIM 73.5: Describe the portfolio-based performance analysis, including the use of performance attribution and performance analysis.

Returns-based analysis decomposes the realized returns into systematic (market) and specific (residual) components. Specific returns are taken as evidence of the managers skill. Unlike return-based analysis, portfolio-based performance analysis can attribute returns to multiple factors. Also, after isolating skill based returns, it can further dissect those returns and attribute them to various sources. Thus, not only can one determine whether the portfolio manager produced superior returns, but also one can find the source of skill based superior returns. Portfolio-based performance analysis can help answer questions such as: Did the manager produce superior returns? What are the sources of those returns? Were the superior returns due to stock and/or sector selection skill beyond the factor returns? Were the superior returns due to skill or style?

There are two components of portfolio-based performance analysis: performance attribution and performance analysis. Performance attribution analyzes one period (a month, for example), while performance analysis examines a time series of returns (for example, a 5-year analysis might include 60 monthly observations).

Performance Attribution

Portfolio returns over a single period are attributed to multiple factors. (Although it is not denoted in each equation to follow, it is assumed that all calculations are for only one period). There is no universally established scheme for classification of common factors. However, returns are generally classified into two sets of factors: risk control and return sources. Risk control factors are usually attributed to market and industry factors, while return factors are attributed to investment style, such as value, growth, or small or large capitalization.

Each factor is composed of several individual holdings. For example, the banking industry factor might contain holdings from Bank of America, Wells Fargo, etc. The total number of holdings in the portfolio is the sum of the number of holdings in each factor.

1 Fama, Eugene F, and Kenneth R. French. "Common Risk Factors in the Returns on Stocks and Bonds." Journal of Financial Economics, Vol. 33, No. 1. 1993. p. 3-56.

The return of an individual holding, d, can be decomposed into two components: one involving the return of the overall factor k to which holding d is a part, and a specific component that describes how the return of holding ┬┐┬┐differs from that of the overall factor k.

where:

Rhd = the return of holding d

RfK = the return of factor k

Sy = the specific return of holding d

Once the multiple factors have been selected, the portfolio returns attributed to each factor can be calculated. The portfolio return from factor k can be defined as:

where:

Rpk = the portfolio return from factor k Xpk = the portfolio exposure to factor k Rfk = the return of factor k

The specific return to the portfolio is that which cannot be explained by the selected factors. This is the sum of all of the specific returns from each holding (from all factors).

d where:

Sp = the specific return to the portfolio hpj = the portfolio exposure to holding d Sy = the specific return of holding d

Portfolio returns are composed of returns from the multiple factor returns and specific returns. A portfolio manager is credited for achieving the specific portfolio return, which is the component of the total returns remaining after controlling for common factor returns. These specific returns exhibit the managers asset selection or market timing skill.

Portfolio returns can be defined as:

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