The Portfolio Optimization Problem

During the second half of 2014, the Russian ruble began a sharp correction that was caused by the rapid fall in the price of oil. For many investors holding Russian assets, the resulting losses were difficult to hold, and many sold ruble-denominated assets and fled to safer currencies. Imagine trying to model this situation at the beginning of 2014. Not only would you need a lot of information about the ruble, you'd also need to predict the price of oil and its path on a time horizon. So how would you categorize the development of a global-currency portfolio?

Clearly yes! It's a complex process that involves numerous variables that actually grow geometrically as you expand your analysis. So it's not easy to develop a global-currency portfolio, including the optimization process. Developing an optimal portfolio starts with analyzing the optimal foreign currency asset and foreign exchange exposures to select portfolio weights that place the portfolio on the efficient frontier of the trade-off between risk and expected return. But what currency should this risk and return trade-off be measured in?

No. The process definitely isn't straightforward.

No. Sometimes a country's currency is impacted by unforeseen correlations.

Not quite. The foreign currency is a part of the return measurement, but it's not the ultimate return currency.

That's it! The domestic currency is the currency used to measure the risk and reward trade-off within the optimization process. So basically, you're trying to build the most efficient domestic-currency portfolio. This portfolio construction process starts with expected returns and risks for each of the foreign-currency assets, along with expected returns and risks for each of the foreign-currency exposures.

No. That's not the currency that the investor can use the proceeds in.

That's why it's so difficult to accurately analyze all the variables that go into foreign asset and foreign exchange exposures. It's simply too many variables with too many correlations between them. In an ideal world with perfect efficiency and no cost of information, you could try to combine the optimization of all the portfolio's exposures simultaneously. But you don't live in a perfect world, and neither do asset managers. So there's a choice to be made on how to try to build the optimal portfolio, and really, it's best to start by utilizing the optimization process for what it develops best: the optimal portfolio without currency risk. So where's the best place to start the optimization process?

That's not it. Setting active currency exposures means that you'll be introducing currency risk into the portfolio.

Yes. By using a fully hedged portfolio, you'll remove currency risk from the initial step of the optimization process so that the optimal portfolio can be produced. Then you can overlay selections of active currency management, if desired. This overlay of active currency management can be achieved through securities that allow you to separate the price risk and exchange risk. What type of security allows you to separate out specific risks?

Not quite. Setting a range for currency movements would still involve too many variables and include currency risk.

No. Foreign equities will carry currency risk along with price risk.

Right! Price and currency risk can be separated using derivatives. So you can manage the price risk separately from the foreign exchange risk, and that allows you to develop an optimized portfolio that's completely hedged. Basically, it makes the optimization process much easier by allowing you to pick the set of portfolio weights that optimize the foreign-currency asset risk–return trade-off. Then, you can decide to relax the fully hedged portfolio and manage the currency risk on an active basis if you want to.

That's not it. Foreign bonds will carry price and currency risk together.

To sum it up: [[summary]]

Complex

Straightforward

Logically ordered

Foreign

Domestic

A third-party base currency

Selecting active currency exposures

Running the optimization with fully hedged returns

Setting expectations on the range of foreign currency movements

Equities

Derivatives

Fixed income

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