Skewness Risk Premia and the Cross Section of Currency Returns

Centre for Endowment Asset Management (CEAM)
Centre for Endowment Asset Management (CEAM)

Overview

This project explores how fears of rare, severe currency crashes are reflected in foreign exchange (FX) markets, and how investors are rewarded for bearing this risk.

Pointing at an laptop screen showing financial graphs.

Authors

Junye Li

Gabriele Zinna

Lucio Sarno

Cambridge Judge Business School, University of Cambridge

About the research

Investors are not only worried about day‑to‑day currency volatility, but also about big, sudden crashes, such as sharp depreciations during financial crises. These concerns show up in the prices of FX options, which can be used to insure against extreme downside moves. This research focuses on skewness risk, which captures how tilted currency returns are towards large negative moves. They construct a skewness risk premium (SRP) by comparing: 

  • what option prices imply about the likelihood of extreme negative moves, and 
  • what is expected based on actual currency returns. 

A high SRP means markets are paying a lot to insure against crash risk in that currency. 

Using monthly data from 1998–2021 for up to 28 currencies against the US dollar, including both major and emerging market currencies, the researchers combine spot and forward exchange rates with over‑the‑counter FX option data to build a model‑free measure of SRP for each currency. For each month they sort currencies into portfolios from low SRP to high SRP, and study the performance of a strategy that buys high‑SRP currencies and sells low‑SRP currencies. 

Findings

  • The high‑minus‑low SRP strategy earns strong average returns with a high risk‑adjusted performance. 
  • Most of these returns come from interest rate differentials, similar to the classic carry trade, but with a clearer link to crash risk. 
  • Returns are negatively skewed and suffer during crises such as the Global Financial Crisis and Covid‑19, consistent with investors being paid to bear downside risk. 
  • The effect is especially strong for emerging market currencies, which are more vulnerable to sudden stops and devaluations. 

When they test many different currency strategies together, a factor based on SRP helps explain why some strategies earn higher returns than others, and it adds more pricing power than the traditional carry factor. The project shows that investors care about the shape of the distribution of currency returns, not just their volatility. Skewness risk – the risk of large crashes – is systematically priced in FX markets. Understanding and measuring this risk can improve how we model currency returns and how we design trading strategies. 

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