Kyle Murphy

quant finance, econometrics, regression.

[Kyle Murphy @kmurphy1]

@0xFaust12 Thanks, will unlock (hadn’t realized)

I plan to continue, such a powerful learning tool. Cheers

[Kyle Murphy @kmurphy1]

An optimizer that wants low risk piles into calm-looking directions, where the sample understates risk the most, relative to what it reports.

RMT gives us the size of that spread. Take N independent assets with variance 1, so every true eigenvalue is 1. With T observations, the sample eigenvalues still spread from (1 − √(N/T))² to (1 + √(N/T))².

For any matrix and any sample size, the smallest sample eigenvalue sits below the smallest true eigenvalue on average.

(3.1/n)

[Kyle Murphy @kmurphy1]

I find it useful to rebuild major derivations, recompute examples and keep a ledger of things proven vs things cited. A thread with some takeaways
(1/n)

[Kyle Murphy @kmurphy1]

I am starting the fifth editition of Bernd Scherer's "Portfolio Construction and Risk Budgeting". So far I can say that the publishing quality is excellent.

[Kyle Murphy @kmurphy1]

Michaud (1989) says the optimizer is an error maximizer. Scherer states this problem - the optimizer picks assets with high return and low risk or correlation, "exactly the cases where estimation error is likely to be highest".

Every covariance matrix has directions: unit-length mixes of assets from riskiest to calmest. The eigenvalues are the variances along those directions. Estimate the matrix from a sample and the eigenvalues spread out, the riskiest-looking direction looks riskier than it is. The calmest-looking direction looks calmer than it is.
(3/n)

[Kyle Murphy @kmurphy1]

The hard part moves with the seat too, no?

Stock seat (Barra): specific-risk floors the spectrum and noise ratio ~0.05, what hurts is alpha outside the factor span.

Allocator seat: 20-40 sleeves higher noise ratio, no specific-risk floor, near-twin sleeves are real small eigenvalues and the precision matrix levers them the hardest

[Kyle Murphy @kmurphy1]

Another (well-known) reminder... risk models are used for estimating volatility of non-optimized portfolios, they are also used for portfolio optimization.

Most techniques for estimating covar matrices work well for one use case or the other, typically not both.

- Menchero, Wang, and Orr (2012)
- Menchero and Ji (2019)
- Shepard (2007/2008)

:D

[Kyle Murphy @kmurphy1]

There is a partial fix: eigenfactor adjustment. (Menchero, Wang & Orr 2012)

[Kyle Murphy @kmurphy1]

Shrinkage helps narrow the gap (moves reported eigenvalues back toward the truth) but it doesnt remove the selection. The optimizer still picks the directions where the remaining error is most favorable. Of course, real books have constraints, long-only & caps act like shrinkage and limit how far the optimizer can chase noise. (Jagannathan & Ma 2003)

[Kyle Murphy @kmurphy1]

Shrinkage helps narrow the gap (moves reported eigenvalues back toward the truth) but it doesnt remove the selection. The optimizer still picks the directions where the remaining error is most favorable. Of course, real books have constraints, long-only & caps act like shrinkage and limit how far the optimizer can chase noise. (Jagannathan & Ma 2003)

[Kyle Murphy @kmurphy1]

We have two questions: "how risky is this portfolio?" and "which portfolio is least risky?"

The first question holds weights fixed and measures one return series, and that estimate is right on average. (its error shrinks like one over the root of the number of observations)

The second question lets the estimate choose the weights, and because every estimate has errors, some mixes of assets look calmer than they are just by luck. The optimizer cannot distinguish betwen what is "real calm" from "lucky calm". It goes to "lucky calm" because the estimate says thats where the cheapest risk is.

as such - the chosen book looks safer than it actually is.

[Gappy (Giuseppe Paleologo) @__paleologo]

@kmurphy1 portfolio optimization is much harder.

[Kyle Murphy @kmurphy1]

On the first day of this new quarter let us recall that BL was built "not at all" (Litterman p.76) from a belief that equilibrium forecasts returns. The case for π is about making MVO more well-behaved.

It's a shrinkage case: a sensible center beats raw sample means inside an optimizer.

[Kyle Murphy @kmurphy1]

In the future all work will be done by frontier labs and all other companies will provide meat robots to service the flesh-and-blood relay network that enables it.

[Kyle Murphy @kmurphy1]

@0xfdf @macrocephalopod Related:
https://t.co/lLf2wmItFN

[Kyle Murphy @kmurphy1]

Selling a service (e.g. liquidity provision) or bearing priced risk address the first question.

Having information other dollar-weighted average market participants do not (or superior processing of contested data) and having structural advantages (colocation) address the second.

You don’t necessarily have to be smarter than your counterparty or have them be making a mistake - you may be willing to do something they can’t/won’t do.

[Kyle Murphy @kmurphy1]

Waiting in the airport. Some thoughts on investment strategies…

There must be an economic reason that a strategy earns a return, not just a statistical relationship that predicts one.

So we ask ourselves:

1. Why does an opportunity exist?
2. Why is your strategy in particular well positioned to capture it?

[Kyle Murphy @kmurphy1]

@anon597260576 @__paleologo Depends on a person’s marginal utility

[Kyle Murphy @kmurphy1]

Not sure the exact quote but recall it like “the market evolves to screw the largest amount of participants, at the worst possible time against their greatest levels of hubris”

I suppose ‘dollar-weighted’ is prefixed on each item…

[Nassim Nicholas Taleb @nntaleb]

Markets go from squeeze to squeeze, from sucker to sucker, from trap to trap.