Quant analytics: Paper for the Black Litterman Model: BLACK, F. (1989): “Universal Hedging: …”
For the people involved in the Black-Litterman model, I think the paper written by Black in 1989 is very interesting, talking about equilibrium (applied to forex) one year before the 1990 internal paper in Goldman Sachs. I’d add it to the bibliografy regarding the BLM.
BLACK, F. (1989): “Universal Hedging: Optimizing Currency Risk and Reward in International Equity Portfolios”, Financial Analysts Journal, pages 16-22, July-August 1989.
The interesting paper on universal hedging recommended by Carloshttp://www2.mccombs.utexas.edu/faculty/keith.brown/chilematerial/black%20faj89.pdf
is by Black, but it is not specifically on Black-Litterman.
Black was fascinated by the concept of equilibrium, and he used this concept in many of his articles, including in the above paper on universal hedging and in the Black-Litterman paperhttp://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Black_Litterman_Global_Portfolio_Optimization_1992.pdf
In the Black-Litterman paper, equilibrium is used to set the prior, but the main contribution of Black-Litterman is a methodology to mix the prior, which need not stem necessarily from equilibrium arguments, with a set of subjective views.
In the paper by Black on universal hedging, equilibrium assumptions are made to derive the universal hedge ratios. The formal proofs are contained in yet another paper by Black, “Equilibrium exchange rate hedging”, Journal of Finance 43, 899-908, which I could not find on the web.
However, you can find interesting comments on the subject in this other paper by Jorion and Glen http://merage.uci.edu/~jorion/papers/JorionGlen-1993-JF.pdf, such as “assumptions must be made to obtain the result [by Black]. In particular, the universality of the hedge ratio follows directly from the assumptions that impose homogeneity on world investors. Moreover, the assumptions require foreign investment to be in balance for all countries at all times.”
IMO The Black-Litterman model is an attractive way to mix priors with subjective views. Its most attractive properties seem to be that estimates of expected returns ( to which mean variance optimisation is notoriously sensitive ) are not required and that the optimal weights are consistent with the subjective views imposed via the extra-covariance matrix leading to more stable optimal weights through time*. The main weakness though seems to be the assumption that the Market portfolio is always in ‘equilibrium’ i.e. at ‘fair value’. Unfortunately one only has to look at the prices paid per dollar of dividends for the S&P500 over time to see that the consensus opinions as reflected by the market cap weights are not always perfectly rational and that ‘equilibrium’ if it exists at all is fleeting. Other estimation error avoidance methods like Ledoit-Wolf”s shrinkage and random matrix theory methods appear to give better out of sample results.
*See: He and Litterman http://papers.ssrn.com/sol3/papers.cfm?abstract_id=334304
Unfortunately, there can’t be a real equilibrium -in the sense of optimun- portfolio, but I guess that eventually, the equilibrium portfolio acts as a benchmark for those benchmark-linked managers. Some investment firms are using it that way: A small strategyc asset allocation group working on the starting point (equilibrium portfolio) and several managers linked to it.
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