Betting the Business

In our previous post in this series, we highlighted a line of research by Burnside et al. that explains the profitability of the carry trade as a “peso” problem. That is, the historical data doesn’t completely reflect all of the bad outcomes that may arise. The as yet unobserved bad outcomes are known as “peso events”. The historical profitability of the carry trade, isn’t the complete story. It’s a biased sample. The few bad outcomes not yet observed resolve the puzzle. Investors are worried about these “peso events” and price the currencies accordingly.

In this post we want to delve a bit more into this issue of how investors may be pricing “peso events.”

There are two different aspects to pricing “peso events.” First, we must assess the probability of an extreme negative event. Second, we must assess the discount we want to apply to that negative event. This second aspect is what we want to focus on.

In finance all dollars are not created equal. Cash received in states when the investor otherwise has plenty cash is not worth as much as cash received in states when the investor otherwise is short cash.

The standard models for pricing risk – such as the CAPM, the Fama-French and the Carhart factor models, among others – are based on what is called a linear stochastic discount factor across all states. They assume a linear relationship between the discount factor and some underlying risk factor. In the CAPM, that would mean a linear relationship between the discount factor and the payoff on the market portfolio. But there isn’t any natural presumption in favor of linearity in the discount factor.

The argument made by Burnside et al. is that the discount factor is not linear. Instead, a very high discount factor is applied to the as yet unobserved “peso events.” And this very high discount factor is essential in making sense of the historic profitability of the carry trade strategy.

In order to make the argument more accessible, we have constructed a simple numerical example:

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Holding cash is a key risk management tool, and corporations are holding more cash than ever. Where should the corporate treasury park that cash? In which currency should these balances be held–US dollars, Euros, Yen, Swiss Francs, Australian Dollars or what? The choice of the currency denomination of cash investments is the flip side of the problem of selecting the currency denomination of debt. Modern capital markets confront corporate treasury with a broad array of opportunities for borrowing and investing in various currencies.

Assuming the expected returns in all currencies are fairly priced for risk (i.e., Uncovered Interest Rate Parity holds), the answer will depend on the multinational structure of the company’s business and its exposure to fluctuations in the different currencies. Some companies will be better off stashing cash in dollar denominated securities because they anticipate future net cash outflows denominated in dollars, while others will be better off stashing cash in Euro denominated securities and others in Yen, and so on. Many companies will have an optimal mix of cash stashed in a variety of currencies. We’ll call the company’s optimal mix under the assumption of Uncovered Interest Rate Parity the company’s Benchmark currency portfolio.

Other factors will matter, too, such as international tax rules, concerns about capital controls and so on.

But what about that big assumption we made up front? What if expected returns in all currencies are not fairly priced for risk, so that Uncovered Interest Rate Parity does not hold? What if investments in certain currencies are generating big profits, while investments in other currencies are generating losses?

It is well documented that a speculative portfolio built by purchasing high interest rate currencies and selling low interest rates currencies—the carry trade portfolio—has been very profitable over many years.The figure below, taken from a recently published paper by Burnside, Eichenbaum, Kleschelski and Rebelo (here is the free working paper version), shows the cumulative return to an investment in the carry trade portfolio between 1976 and 2009 as compared against the cumulative return to an investment in US stocks and the return to an investment in US Treasury Bills.

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