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Setting Currency Weights in a Black–Litterman Benchmark Portfolio

Article Quant Q&A · Author: Ahmet İnal
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Summary

The document discusses how to include cash currencies in the market-capitalization benchmark used to initialize a Black–Litterman portfolio. One response says weights depend on the investor’s risk-free reference currency: domestic cash may serve as risk-free, while foreign cash carries exchange-rate risk. It cautions against using narrow money supply alone and points to international CAPM and universal hedging as methods discussed in the Black–Litterman literature.

A second response proposes scaling each currency’s money supply by its exchange rate, making the measure analogous to shares multiplied by price. Purchasing-power parity is offered as another possible proxy. These suggestions aim to temper the influence of currencies with large nominal supplies while recognizing the value of smaller monetary bases. The discussion does not establish a definitive standard or compare the proposed proxies empirically. It also notes that benchmark weights depend on the chosen investor perspective, so currency allocations should be interpreted within that reference framework.

Key ideas

  • The choice of risk-free currency affects how an investor views foreign cash and determines benchmark weights.
  • Money supply alone may not be a suitable proxy for a currency’s market value in an equilibrium portfolio.
  • Scaling money supply by an exchange rate is proposed as a currency weighting proxy analogous to market capitalization.
  • Purchasing-power parity is suggested as an alternative proxy, though no empirical comparison is provided.
  • The discussion points to international CAPM and universal hedging as approaches for deriving currency weights.

Tags

Multi-assetPortfolio constructionForex
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# How to find an initial equilibrium benchmark portfolio that includes currencies for Black-Litterman model


# How to find an initial equilibrium benchmark portfolio that includes currencies for Black-Litterman model












We're working on a term project to adjust B-L model to yield robust results. From our readings, we resulted in that initial benchmark portfolio is constructed by using market capitalization weight. However, we want to include different currencies to our portfolio (U.S. dollar, Euro etc.) and we are clueless about how to determine market caps of currencies. Using total money supply for currencies didn't seem intuitive to us since, in that case, it would outweigh currencies unreasonably. Is there a correct way to determine this?

## Answer by Sebapi (score 2)

https://quant.stackexchange.com/a/42780

We first need to define the risk-free asset. One may assume that for a US investor, the riskfree asset is the USD, whereas, for a Japanese investor, it is JPY.

This is important because the perceived volatility of USD to a Japanese will cause him to require a higher return on a USD asset than on a JPY asset, thereby causing some home bias.

While the market weights for a US investor are a linear combination of USD cash and an efficient market portfolio including some JPY cash seen as a foreign asset. The converse is true for a JPY cash investor.

Cash is always subject to inflation, arguably, an eternal investor such as an endowment might use the world stock market cap as its riskfree asset, in which case any currency holding is seen as a risky asset.

The point is that the weights depend on the risk-free reference, so that market weights reflecting expected returns and covariance should not be based on narrow monetary mass such as M0.

On the topic of equilibrium weights and fx cash holdings, BL (Black Litterman) refer in their article to an ICAPM (international capital asset pricing model) and Universal Hedging methodology to derive the weights they use.

Ironically the BL (Black Litterman) model advocated against home bias at the worst point of history for US investors: it was published and marketed in the late 80s/early 90s just as the Japanese market had overtaken the US market. It would help embolden US investors and justify that they jump ship from the home-biased investment to buy Japanese stocks.

The investors who followed this strategy must have fared very badly: they would enter the Japanese market at the height of its overvaluation, at the beginning of a 30-year bear market and missed 2 decades of bull market in the US.

## Answer by David Addison (score 0)

https://quant.stackexchange.com/a/38520

I think you have to use money supply in some regard, but I also agree with you that it is not a good proxy for total market value of that money.

Why not multiply money supply by exchange rate. You could also consider using purchasing power parity as a proxy for the value of money. The result of this operation is highly analogous to market capitalization (i.e., shares $\times$ price $\to$ M0 $\times$ FxRate).

For example, a country which has printed a lot of worthless money won't exert nearly as much effect on the initial equilibrium model. Likewise, a country with small, but valuable monetary reserves won't fall off the allocation scale.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.