Attilio Meucci starts praying

Attilio Meucci has written “The Prayer” which gives a ten-step process of quantitative analysis of the profit and loss stream.

The paper is nicely laid out.  Each step includes at least one “key concept” box.  These give a clear, concise statement of a main idea. These allow you to quickly get the thrust without needing to sort idea from mathematics.

Also there are “Pitfalls” sections that state views that are reasonably common that Attilio thinks are wrong.

Here are the steps:

P1: Quest for invariance

This step is the attempt to find the market patterns that repeat over time.

I think that recognizing this as a separate task is the most important thing in the paper.  A simple observation that is often buried.

One of the Pitfalls listed for this step is: “… The random walk is too crude an assumption …”  His response is that once risk drivers are taken into account the random walk is hard to beat in practice.  I agree — see “The tightrope of the random walk” and “Bear hunting”.

P2: Estimation

Estimate the distribution of the invariants found in the previous step.  His example is multivariate normal but he doesn’t necessarily believe in normal distributions.  He also emphasizes that estimation risk exists.  Even if we’ve found the true market mechanism, we don’t know the exact parameters for that mechanism.

P3: Projection

Predict the risk drivers at the investment time horizon.

P4: Pricing

Compute the price distribution of individual assets at the investment horizon given the state of the risk drivers.

P5: Aggregation

Compute the price distribution at the investment horizon on the portfolio level.

P6: Attribution

Decompose the predicted profit and loss into effects of a set of risk drivers.

P7: Evaluation

Create summary statistics for predictions on hypothetical portfolios.  Examples are expected return, tracking error, information ratio.

P8: Optimization

Maximize predicted satisfaction given the portfolio obeys the given constraints.

He states that mean-variance optimization can be done using a variation of quadratic programming.  I think it is better to go farther afield than that for the optimization algorithm.  But I would, wouldn’t I?

He doesn’t intimate that there are other optimization procedures other than mean-variance, even though his examples include options and bonds.  Scenario optimization is the natural choice for these assets.

Pitfall: “… Mean-variance assumes normality …”  Attilio states that is not true.  As I’ve previously explained normality means that mean-variance is your only option, but mean-variance can be sensible for non-normal distributions.

P9: Execution

Perform the trade (probably in steps over some time interval) suggested by the optimization.

P10: Ex-post analysis

Identify contributions to the realized profit or loss.


I highlighted the first step, identifying invariants, as the key insight in the paper.  That is indeed what quant is all about.  The fault I find in the paper is that it assumes that invariants can be found.

The market isn’t a clock, it’s a cat. It’s going to do what it wants when it wants.

Quantitative methods depend on the past repeating in some fashion.  And it does — sort of, sometimes.  The paper allows for estimation risk, it doesn’t allow for the meta-estimation risk of the market being dynamic.

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