Jay's Asset Allocation Blog

Blog about my off-hours work on the problem of Asset Allocation including but not limited to Portfolio Optimization algorithms, algorithms and approaches for improved estimation of Asset Allocation inputs and other potentially related items.

Monday, March 23, 2009

Shrinkage Methods

The akutan open source project includes code that implements a few shrinkage methods. Spherical shrinkage is the latest one. It comes from Attilio Meucci's book. I've also revisited and finally found and fixed the bugs in the Ledoit-Wolf shrinkage code. I haven't updated the applet, but CVS has been updated.

It is interesting to compare the efficient frontier drawn for these two methods, the Ledoit-Wolf shrinkage frontier is very close and just to the right of the "standard" efficient frontier. When you look at the portfolios you see they are more diversified than those on the "standard" efficient frontier. When you consider spherical shrinkage, the efficient frontier can be far to the right in parts and then for the example I was considering, was actually to the left of the "standard" efficient frontier. This is because the spherical shrinkage also shrinks the means, so the efficient frontier can move both in the risk direction and the return direction.

Thursday, March 12, 2009

Do we need to use constrained optimization with Idzorek's method

Another reader has asked me whether they need to use constraints during the process of backing the uncertainty in a view out of a confidence when using Idzorek's method.

The thrust of their argument was that their view at 100% certainty was too extreme, and thus they would not consider holding the portfolio generated at 100% certainty.

Idzorek's method provides a simple and clean way to determine the variance of the view by backing it out from a confidence and the change in the weights based on an individual view. You don't need to use a constrained reverse optimization process, and in fact that would change the problem from a simple linear one to a much more complex one. If your views are too extreme, you can shrink the size of the return (Q vector) for that view, however what is important is the impact of the views at the confidence level you hold in them (what you do with the variance backed out from Idzorek's method) rather than the 100% confidence portfolio.

So even if you will use a constrained optimization with the final posterior returns, you do not need to use any type of constraints when computing the 100% confidence posterior as part of Idzorek's method. In fact if you use the formulas included in my paper, you don't really even see the 100% confidence portfolio.

Wednesday, March 11, 2009

Currency as an Asset Class and Black-Litterman

I was recently asked a question regarding how to integrate currency as an Asset Class into the Black-Litterman model. This raises several interesting questions. I am hoping this post answers a few, rather than making it more murky.

I am of the opinion that currency is not an asset class. Here are some ideas in that direction.

I do not believe that institutional investors consider currency as a separate asset class. They do often seem to segregate hedge fund investments as if they are a separate asset class, and may place currency managers there. Check out the asset allocations of major endowments for example, I don't recall seeing one with currency called out as a separate asset class.

Within the initial Black-Litterman papers, they considered a global equilibrium that was partially hedged and thus considered currency in this light. It was not considered a separately investable asset class. You essentially hold currency along with the assets denominated in them.

When using a model like Black-Litterman and the CAPM market model, an asset class market capitalization does not include derivatives, only what we might call the cash market. In F/X, as an asset class this might mean holding a basket of currencies as an asset, but you would want to at least earn a deposit rate on the currency which means rather than a currency investment, we could look at it as a basket of short term bonds.

Finally, the criteria for identifying something as an asset class is that they should be homogenous, mutually exclusive, diversifying, contribute to a the market cap and capable of absorbing liquidity. Currency meets most of those criteria, except for being mutually exclusive. If we desire foreign equities to be an asset class, and currency as well then we need to use the hedged foreign equities as our asset class, but that is really just a long position in foreign equity and a short position in the currency. The CAPM equilibrium model in the original Black-Litterman paper deals with this type of model where currency hedging is included in the model, but currency is not an asset class.

For further information, there are some papers linked to from the site which consider issues of whether commodities are an asset class and how to compute their market cap, and also a similar paper dealing with real estate.

I have not found any similar papers discussing currency as an asset class on the internet as of this time, but I haven't searched exhaustively.