A summary of the high points of the day.

## Factor models and optimization

Three of the talks formed a theme: factor models of variance — especially as applied to portfolio optimization.

The basic problem is that variance matrices are created with error. A variance matrix is a key input to (some) portfolio optimizations. The optimizer dutifully magnifies some of the errors.

There are two types of error:

- model error
- estimation error

Model error is the fact that the model will miss or distort aspects of reality. Estimation error is the fact that even if the model fit reality exactly we don’t have exact knowledge all of the numbers that go into the model.

#### Jason MacQueen

Jason MacQueen of R-Squared Risk Management started off the day with quite a nice explanation of factor models in finance — more in-depth than my previous post explaining factor models.

Jason pointed out how estimation errors enter, and described a nice trick to reduce some error. A lot of factor models are fit using monthly data. This trick changes one month to four weeks. The data are updated every week and the last four (overlapping) models are averaged.

#### Jose Menchero

Jose Menchero of MSCI Barra talked about the bias of the *ex-ante* risk of an optimized portfolio relative to its realized risk. The job of the optimizer is to make the risk small. Because of error in the variance matrix, it will tend to think that the risk is smaller than it actually turns out to be.

The biases that he got were somewhat larger than a theoretical formula for bias that he showed us. The formula suggests that optimization with most statistical factor models would have only trivial bias. My rule of thumb with the statistical factor models I’m used to using is that the bias is about 10%. That is smaller than the biases Jose showed us.

But Jose did have a fix. It was essentially to shrink the eigenvalues of the factor covariance towards a central value. The key problem with bias is if the optimizer can find a trade that looks to have very little risk. This shrinkage makes sure that all trades have more than a trivial amount of risk.

#### Sebastian Ceria

Sebastian Ceria of Axioma finished the day. He focused on the model error of factor models. Factor models inherently assume that there are a lot of directions that have zero systematic risk (though they will have asset specific risk). That’s a little silly. And it gives the optimizer an opening to be silly with that silliness.

Sebastian described a clever approach to find — in each particular optimization — one additional direction that has the largest impact and give that some risk. A suggestion from the floor was to just give all directions some risk — problem solved without fancy tricks.

For me the most interesting part of Sebastian’s talk was his insight that the optimizer is not really using the expected returns that are the input to the optimizer, but the implied alpha of the resulting portfolio. However, as I write this I’m not so sure that is correct.

A key academic mistake is to think that what is being done is **portfolio **optimization. Not true. It is **trade **optimization. We are looking for the best trade to move away from where we are. In that light I’m not so sure that implied alpha is really right — needs more thought.

## Fund manager selection

Now for something completely different.

#### Dan di Bartolomeo

Dan di Bartolomeo of Northfield talked about a large plan sponsor — without mentioning a name — that has hired Northfield to completely revamp their selection procedure for fund managers.

They investigated their existing procedure (which is very much like everyone else’s). They knew they spent a lot of money doing it. They found that they received pretty much zero benefit.

They want to switch to a largely automatic process that quantitatively finds the best mix of fund managers. Dan’s analogy is of a sports team hiring players. The existing players that are performing well are safely on the team. The players who are most likely to get hired are ones that best complement the good existing players.

## Access to slides

The slides for at least some of the talks are supposed to be put on the London Quant Group website at some point. I think access might be restricted to members, but I’m not sure.