Separating Currency and Equity Risk in Portfolio Optimization
Summary
The document considers how to optimize a portfolio of foreign-currency equities when returns and risk are measured in an investor’s home currency. Its central suggestion is to model the investment as carrying both equity risk and currency risk, rather than treating the foreign stock weights as the only relevant exposures. Portfolio return and risk estimates should account for both sources before optimization.
It presents currency hedging as an alternative: remove the currency exposure and then optimize based on equity risk. The answer points to research on multi-currency and global portfolio optimization as further reading, but does not provide a mathematical formulation, constraints, or a worked example. The response also explicitly expresses uncertainty about the robustness of its proposed approaches. It therefore offers a useful framing for the problem, while leaving implementation details—such as how to represent currency positions and estimate joint covariance—unresolved.
Key ideas
- Foreign-currency equity holdings expose a portfolio to both stock-market and exchange-rate movements.
- Return and risk estimates should incorporate both equity and currency exposures.
- An investor can instead hedge currency exposure before optimizing equity allocations.
- The answer offers conceptual approaches but does not specify an optimization model or validate their robustness.
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# How to take into account currency risk when optimizing portfolio? # How to take into account currency risk when optimizing portfolio? I have a portfolio of foreign stocks. All stocks are denominated in foreign currency. I need to compute returns and risk metrics in national currency which is different from stocks currency. Stocks`s weights in the portfolio may change during optimization, but currency position always has the weight equal to one (no stocks from other exchanges). How to implement this in portfolio optimization procedure? Maybe I should add some constraint to my portfolio? How to deal with such a constraint as that the sum of all other assets weights must be equal to 1? ## Answer by AK88 (score 2, accepted) https://quant.stackexchange.com/a/31693 I think for multi currency portfolios you will have to seperate out equity risk and currency risk. For example, if you own Gazprom stocks with current value of 1M RUB, then you have company specific risk (equity risk) and Ruble risk (currency risk). Since your investment has two risk sources, you should calculate risk and return metrics both for equity and currency. Then you can optimize your portfolio accordingly. On the other hand, you could hedge out your currency exposure entirely, then move on optimizing your portfolio only considering equity risk.I am not completly sure if these are robust approaches. There are several research papers out there that discuss this subject: - Currency Hedging Optimization for Multi-Asset Portfolios (PIMCO, 2016) - Computing optimal multi-currency mean-variance portfolios (Rustem, 1994) - Global Portfolio Optimization (Balck & Litterman, 1992)
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