Performance Analysis Notes

Outline

All portfolio performance updates should contain the following:

• A header page, with strategy name, authors, and date.

• An executive summary page that summarizes the most important aspects.

• The contents:
  • the overall compound portfolio rates of return
  • clear and prominent identification of the benchmark (upfront)
  • basic univariate performance statistics
    • average and standard deviation of rates of return, annualized (Y/T, sqrt(Y/T))
    • Sharpe ratio (perhaps more, e.g., gain-loss ratio).
    • tracking error analysis: as above, but subtract benchmark from returns first (for SR, subtract benchmark instead of rf)
    • equivalent numbers on the overall stock market in the same sample
  • benchmarking analyses of portfolio returns
    • simple difference (non-beta adjusted) to benchmark
    • exposure-benchmark-adjusted portfolio returns (i.e., same but with a beta coefficient to your benchmark). Identify clearly whether beta is ex-ante or ex-post. We need both, and we need to be clear which is which (and where the betas are from). (The ex-post beta version is from a time-series regression jointly estimated with alpha.)
    • exposure-market-adjusted portfolio returns (like the above, but with the market, such as SP500 or vwretd), as always with ex-ante and ex-post betas (latter from "Fama-French-style time-series regression" again).
    • a 5- or 6-factor model-adjusted portfolio return (where betas are ex-post jointly estimated with alpha)
    • if you obtain beta loadings, also a textual description of what your portfolio is loading up on (market? value? size? momentum? etc.)
• The same analysis for the portfolio constituents, especially standout ones (extreme winners and losers)
  • what was caused by stark events and what was more generic drift?
  • contribution of individual components to portfolio risk and reward
    • like a market-model regression, but with the own portfolio rate of return as index. alphas should add to zero. own betas should add to 1.0.
  • possibly also an industry component analysis

• Perhaps an analysis and conclusion of what you got right and what you got wrong...and what you think now you could and should have done differently and better. I.e., what you have learned.

• An appendix that re-describes the strategy choices, and the benchmark choices.

• In addition, if you traded within the sample period, more information about why, what, how, etc. What is your strategy turnover?

Writing and Contents

• Brevity rules. Imagine readers have ADD.

• Start with template examples (i.e., reading earlier reports). Then improve.

• It must never be unclear whether you are working with capital gains or rates of return (including dividends). Never! And you must never get this wrong. (Note that the moronic SP500 gets this wrong, primarily because it was started in the days before computers.)

• Every (data) source should be explained. The reader should never have to guess where you got the betas from (web-site, calculated [how?], or where you got risk-free rates from. The reader should never have to guess what data period the data covers. And so on.

• Tables should be readable from afar. No more than 60 characters across, and 20 lines high...if that. Ideally, half this.

• Every exhibit should be annotated to be comprehensible. The reader should not have to guess what a column heading might mean.

• Every exhibit should have at least one sentence telling the reader what the important take-aways from the exhibit are.

• Don't give silly digits. A beta or percent rate of return is no more accurate than to the second digit. So, b=1.2, not b=1.217130283. An alpha is 0.3%, not 0.2825912%.

• Be clear about units. By 0.2, did you mean twenty percent or 0.2 percent?

• The sample period is so important that it is not a bad idea to mention it below each exhibit.

• Be careful: don't make mistakes with subtracting out the risk-free rate in the wrong spots.

• Don't use "Confidential" on non-confidential material. Read the story about the boy who cried wolf too often. (You are not a lawyer. Lawyers are in the business of not doing anything to avoid liability. You are not.)

Performance Analysis and Attribution

Let's say that your (overall) portfolio had a net-of-risk-free rate of return of -2% and exposures of 0.6 to xmkt, 1.3 to hml, 1.4 to smb, -0.5 to rmw, -0.6 to cma, and -0.2 to umd (momentum factor). [PS: As you know, you must measure exposures with daily-frequency returns.] PS: I prefer the term "net-of-riskfree rate of return" to "excess rate of return," because the latter could mean different things to different people.]

Let's say that the factor rates of return were 4%, 3%, -5%, 2%, 3%, and 6%. Then

It follows that your portfolio's alpha was 2.7% (-2%-(-4.7%)). Your portfolio performed so poorly in absolute terms primarily because you had carried a positive 1.4 exposure on smb. Smb did really poorly (-5%) in your measurement period, and your portfolio exposure of 1.4 exposed you badly to this lousy performance. Fortunately, you somehow escaped some of it, ending up with a rate of return that was not as bad as the exposures and factor returns would have suggested---this is exactly what your alpha with respect to this model has told you.

You further can learn from this that your portfolio is about half-equity like (b-xmkt=0.6), tilted heavily towards value and small firms, modestly tilted towards weak and aggressive firms, and not very momentum oriented.

Overall Analysis

We need at least one good analysis for our overall portfolio.

PS: Others

Ken French updates the factors about mid-month. Thus, as of 3/30, I see the 2/28 rate of return in the file.