# When should you build your own equity risk model?

Commercial risk models (e.g., Barra, Axioma, Barclays, Northfield) have evolved to a very high level of sophistication. However, all of these models attempt to solve a very broad set of problems. The optimal risk model for, say, risk attribution in a fundamental portfolio may differ substantially from the optimal risk model for downside risk estimation of an optimized quantitative strategy or for hedging unwanted exposures in a pure relative value play.

Suppose that one already subscribes to a decent risk model provider, so that cost is not an issue. For what applications is it most appropriate to build your own equity risk model? What are the main benefits of a customized risk model? When is it worth the time and effort to replicate the increasingly sophisticated data cleaning/analysis and statistical methods to reap these benefits?

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Great question. We would expect 3rd party risk providers to have specialized expertise (robust regression techniques, factor research, data cleansing etc.). We might grant them these advantages but still find weakness in the product design.

Let's start off with the different uses of risk models and the procedure or metric which is maximized to solve for that use case. What we will see is that solving for a particular objective diminishes our ability to achieve other objectives.

1. Portfolio construction = If you want to construct a minimum variance portfolio, for example, then the key here is developing a covariance matrix (of factor returns) that is invertible and stable. So we could use procedures that develop well-conditioned cleansed covariance matrices. This conflicts with #3

2. Estimate beta for the purposes of hedging = here you care about the yet-to-be-realized return on a security you wish to hedge, and yet-to-be-realized returns on a basket which you will use to hedge. So if you wanted to create a market-neutral constraint, then you would want to use betas from a time-series regression so that the estimation error for each particular beta can be diversified away. You would also want to maximize accuracy (at the expense of interpretation) perhaps using statistical factor methods such as asymptotic PCA.

3. Performance reporting (risk and return decomposition) = here you have some contemporaneous regression specification (i.e. the time-index is the same on the left and right-hand side of the regression). Your concern is interpretability of factor exposures at the expense of accuracy.

4. Estimate marginal factor returns = use a cross-sectional regression to explain the returns accruing to a factor after controlling for all other factors. The technique is quite popular and used to explain the cross-section of returns or measuring the risk premiums for various factors. However, there is a substantial errors-in-variables problem. The errors in the estimated betas for such a security cannot be diversified away, unlike a time-series regression so it is risky to apply this model to other use cases. This conflicts with #2.

5. Risk forecasting = here you have a forecasting specification (left-hand side time index is $t+1$, right-hand side time index is $t$). This conflicts with #3.

6. Some people use risk models to make systematic factor bets. It can be difficult to develop a variant perception if you are using the same risk framework as everyone else.

7. Predict volatility. At shorter-horizons a stochastic volatility model would be appropriate, whereas at longer horizons a factor-model makes more sense.

Any risk model that excels at one of these objectives will have severe weaknesses in some other areas.

You could have multiple risk models (indeed Axioma has one for fundamentals that is easily interpretable, and another based on statistical methods for accuracy) but this can be confusing to clients.

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Great answer! I see that essentially your answer is to be sure to use the right risk model for the task at hand. Thus my question may actually be six separate questions of which is better, build or buy, for the six use cases you outlined. I wonder, though, if there are any general principles for whether to build or buy, assuming that you would buy the appropriate risk model. –  Tal Fishman Sep 23 '11 at 18:16

Danielsson and Macrae suggest that portfolio optimization should be based on simple models. I interpret that to mean using something like Ledoit-Wolf (as opposed to most commercial models). In that case doing it yourself is not at all laborious assuming you have return data.

A link to Danielsson and Macrae (worth reading if you haven't seen it) is in http://www.portfolioprobe.com/2011/08/15/appropriate-risk-modeling/

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Thanks for the reference, but Danielsson and Macrae are referring to a different kind of risk model, so what you write is not really relevant to my question. –  Tal Fishman Sep 23 '11 at 18:27
Right on. Shrinkage methods are remarkably effective and very easy to implement –  Quant Guy Sep 23 '11 at 18:34