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: