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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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    $\begingroup$ 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. $\endgroup$ – Tal Fishman Sep 23 '11 at 18:16
  • $\begingroup$ Thanks @Ram Ahluwalia, you have covered multiple issues here and I wonder what book/paper you recommend to learn those things in details. $\endgroup$ – Warren Sep 3 at 9:27
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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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  • $\begingroup$ 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. $\endgroup$ – Tal Fishman Sep 23 '11 at 18:27
  • $\begingroup$ Right on. Shrinkage methods are remarkably effective and very easy to implement $\endgroup$ – Ram Ahluwalia Sep 23 '11 at 18:34
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I can see the following main reasons to create custom risk-models:

  1. Universe/Vendor model mismatch: Your universe of assets does not align with those provided by the vendor. For example, Barra provides US and Global models but say your universe has a number of Canadian and US equities then you may need a custom risk model.
  2. You want to use a new/different methodology: Your favorite new method (e.g. Engle, Ledoit, and Wolf (2019)) is not yet implemented or you want to estimate the correlations separately from the vols.
  3. Factor crowding: everyone is using one these models so that may generate crowding as everyone is trying to hedge the same things.
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  • $\begingroup$ Regarding the first point, Barra does have a country specific models (e.g. Canada). The second point is valid. I wonder how the third point would be implemented though. $\endgroup$ – AK88 Nov 12 at 13:14
  • $\begingroup$ Barra do have country-specific model but if your universe spans countries then their risk models won't work. So if you have both Canadian and US stocks, you can't use either the US or Canada risk model. A more serious example would be a STOXX600 based universe. $\endgroup$ – Kruggles 2 days ago
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Without detracting from or disagreeing with the many great answers already given, this one is more of an "information systems management" than a "risk model" problem. It's a classic "should I bespoke, outsource, or off-the-shelf?" dilemma.

So then the question becomes whether and/or how the risk you want to model differs from that of the modal/median customer of the mainstream providers. If you were yet another mutual fund tracking the same benchmark as the other thousands of mutual funds, there's almost no discernible reason to measure your risk differently from them if you manage it the same way, in a simple competitive arena. Sure, you might have some house difference to the median that is your "secret sauce". But to measure the sauciness of that secret sauce, it helps to compare yourself to the competition in their/the-classic terms. That's how you're differentiating!

But if say you were an equity investor whose core focuses were say REITs and/or private equity investor, then it might be perfectly rational to say that the cookie-cutter models for the stock and sector jockeys were not fit for your purposes.

The grey area lies, eg, where you have a "growth" or a "value" investor who is a classic equity investor; but has a very different view about what those terms means to the canned logic of the off-the-shelf solutions. The models might tell them they have X style exposure; but the investor measures it themself in a very different way. Then they need their own risk model, suited to their method/prejudices, because they are not operating just to beat thousands of other lookalikes with the same frameworks (that validate the same models as the lowest cost solution).

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