Industry Perspective The Carry Trade and Volatility Vineer Bhansali, Managing Director | PIMCO
Overview The currency “carry trade”, in which an investor buys assets in a higher yielding currency by borrowing in a lower yielding currency, has been consistently exploited as a source of profits by investors. In this note, we explore the risk-return underpinnings of the carry trade and demonstrate that the carry trade is effectively a form of short volatility trade. We also explore a simple strategy that combines carry with options and present a heuristic statistic for the measurement of the economics of the carry trade. We test the strategy on actual historical carry and option price data and find that the hypothetical strategy allows for the presence of arbitrage opportunities between the forex option and carry markets. The recently unfolding crisis in the financial markets has been accompanied with rising volatility and unwinding of the carry trade.
Introduction The events surrounding the Federal Reserve’s FOMC meeting of Dec. 11, 2007 were interesting in many respects. Reflecting on the weakening credit and liquidity conditions that accompanied the subprime debacle of 2007, on that date the Fed cut both the FedFunds target rate and the discount rate by 25 basis points (bp). This was disappointing to market participants who were expecting more, and the stock market immediately sold off, credit spreads widened1, the Brazilian real and other emerging currencies sold off, and the Japanese yen strengthened close to a percentage point. In addition, volatility rose across markets2. Coming into the morning of Dec. 12, all of these moves were reversed as the Fed, ECB and all other central banks announced that they would make special liquidity available to alleviate the short-term credit squeeze. The dollar rallied against lower yielding currencies such as the yen. This two-day period was consistent with the expected performance of currency pairs in which one currency has a much higher interest rate (the carry currency) than the other currency (the funding currency) during periods of heightened and lowered risk. As recent market movements have shown, when volatility rises, the carry trade suffers, and when volatility falls, the carry trade does well. Can we explain this by leaning on finance principles? In the currency carry trade, an investor borrows in a lowyielding currency and invests in a high-yielding currency.
Anecdotally, it is observed that carry trades do well when currency volatility is low. This makes intuitive sense. To realize the carry in a carry trade, investors are required to hold the position for a while. If the foreign rate is and the domestic rate is , then the return to the carry trade is proportional, to leading order, to , where is the holding period. The risk to the carry trade is an adverse price movement in the level of the exchange rate. We can mitigate this risk by hedging in the currency options markets. If the spot FX market and the options markets price risk differently, then one could have potential arbitrage opportunities. To illustrate this, consider the following strategy: suppose we invest in the higheryielding currency, and hedge the exposure by purchasing an at-the-money forward (atmf) put on the higher-yielding currency. Then, since the delta of the out-of-the-money option is approximately one-half, at inception we would be immune to the movements of the exchange rate. If we adjust the notionals correctly, then by put-call parity, this portfolio is the same as an outright atmf call on the higher yielding currency. Details of the calculus to arrive at this conclusion are available in a recent article the author wrote in the Journal of Fixed Income (Bhansali [2007]). Putting the carry relationship together with the leading behavior of an atmf call option, we conclude that in equilibrium, a carry trade hedged with options obeys ~ Suppose the actual level of volatility in the market is expected to be lower, i.e. . Then the fair carry is not , but a quantity . If , then . In the extreme case where (e.g. when carry trades use the yen as the funding currency), this implies that , and the carry trade will drive investors to hold bond instruments in the domestic currency by financing them in the lower-yielding currency as a direct bet on lower volatility. In other words, the carry-volatility equilibrium dictates the availability of profits to investors who are willing to take interest rate risk as foreign exchange volatility falls. Similarly, if we expect volatility to rise, investors will shed bonds in the higher-yielding currency. We will see that the simple math shown above is borne out by actual data, especially for EM currencies such as the Mexican peso and the Brazilian real (see Figures 1 and 2).
As measured by the widely traded CDX index, credit spreads were about 7 basis points wider when compared to pre-FOMC levels. VIX, a measure of short-term equity volatility rose by 3%. MOVE, a measure of short-term interest rate volatility, rose from 126 bp/year to 141 bp/year.
1
2
6 | CFI Bulletin 2008, No. I
UCLA Anderson School of Management
Empirical Results We collected data for a number of major developed market currencies that have been the main beneficiaries of the carry trade3. The Japanese yen (JPY) and Swiss franc (CHF) have typically been used as funding currencies in the past, while the Australian dollar (AUD), New Zealand dollar (NZD) and U.S. dollar (USD) have been the higher yielding carry currencies. More recently, the improving fundamentals of the Mexican peso (MXN) and the Brazilian real (BRL) have enabled them to enter the toolkit of carry traders. Most pairs other than the dollar/yen show a relationship between carry and volatility, which seems to point to an anomaly that is driven by the special relationship between the dollar and the yen. The U.S. has historically been a large debtor of Japan, who now with the Chinese, are the largest creditors of the world. To a large degree, anecdotal evidence suggests that the recycling of surplus by the Japanese and Chinese creates an effective peg of the yen and RMB to the dollar4, muting the exchange rate volatility of these two countries vs. the USD. Thus, we see that even though carry of the dollar vs. the yen has varied a fair bit (from 6% high in 2000 to 1% low in 2004), the level of implied volatility has remained on a downward trend.
Investment Strategy We back-tested a carry strategy that uses both information from the options markets and from the interest rate differentials between currencies. The basic idea is to purchase at-the-money forward calls on a higher-yielding currency, and hold it to maturity. If there is indeed a forward exchange rate bias in the market, then simple carry strategies should result in positive returns — implementing the strategy through options when volatility is low, would further improve the risk profile of the strategy. When we typically think of option purchases, we think of the daily time decay as the cost of truncating the possibility of negative outcomes. However, if we note that as time passes, the forward will “roll-up” towards the current spot level, we can reduce the cost of the option by the embedded carry since the atmf option is going “into-the-money” as time passes. The strategy we explore invests in the higher-yielding currency via one year at-the-money forward options, and
rolls them every month5. We include transactions costs explicitly by taking the average transactions costs over the previous year. Additionally, we refined the strategies by putting optional “filters” on both volatility and carry, i.e. only entering the trade if the carry is higher than a threshold and/or if volatility is lower than a threshold. For example, in Figure 3 (page 9) we show the statistics of this strategy for the Australian dollar vs. the Japanese yen from a variety of different perspectives. The first table on the top left shows the returns per month binned by the returns. The histogram immediately to the right and the statistics below the table show the positive skew of the option based implementation, along with Sharpe ratios and annualized expected returns. We also display at the bottom left the carry and vol filters (if any) used in the back test. The charts below the histogram show the monthly performance time series of the strategy. The three charts on the right show the option based carry strategy return vs. spot levels for the pair, returns vs. the carry for the pair, and returns vs. the implied volatility for the pair. The AUDJPY pair shows high return per unit of risk. No wonder that the pair attracts carry investors and has been the first one to suffer in recent episodes of credit driven risk unwinds.
Conclusion One possible reason why the carry trade responds to central bankers’ actions and statements is that the currency markets, which are more macro in nature, have discounted the desire of central bankers to keep exchange (Continued on page 8) Dr. Bhansali is a managing director, firm-wide head of analytics for portfolio management, and a senior member of PIMCO’s portfolio management group. Bhansali joined PIMCO in 2000, previously having been associated with Credit Suisse First Boston as a vice president in proprietary fixedincome trading. Prior to that, he was a proprietary trader for Salomon Brothers in New York and worked in the global derivatives group at Citibank. He is the author of numerous scientific and financial papers and of the book Pricing and Managing Exotic and Hybrid Options (McGraw Hill, 1998). He currently serves as an associate editor for the International Journal of Theoretical and Applied Finance. Bhansali has 15 years of investment experience and holds a bachelor’s degree and a master’s degree in physics from the California Institute of Technology, and a Ph.D. in theoretical particle physics from Harvard University.
Data was provided by Citibank from January 1992 to October 2007. For the RMB, the peg is actual. 5 The results are largely similar for both shorter dated and longer dated options. 3 4
UCLA Anderson School of Management
CFI Bulletin 2008, No. I | 7
(The Carry Trade and Volatility, contd.)
rate volatilities low, while the rate markets respond more to the borrowing and lending needs of participants within their own countries. Whether this is the correct story or not remains to be seen, but it does seem that there are no obvious instruments to exploit the differential risk-premium pricing between the rate and forex markets. However, currency options do provide a mechanism to weakly arbitrage gross mispricing of risk in these markets. Indeed there is evidence that when option volatilities become cheap, levered hedge funds implement carry trades through options. Just the presence of cheap options might drive the carry
trade to be a good risk-reward opportunity in most states of the world, and when done through options, create artificial directional biases. We leave it to further research to explore why such arbitrage opportunities occasionally present themselves in today’s markets.
USDMXN –12m
USDBRL –12m
Figure 1: Relationship between implied volatility and carry for USD vs. Mexican peso (MXN)
8 | CFI Bulletin 2008, No. I
REFERENCES Vineer Bhansali (2007) “Volatility and the Carry Trade” Journal of Fixed Income, Winter, 2007.
Figure 2: Relationship between implied volatility and carry for USD and Brazilian real (BRL)
UCLA Anderson School of Management
(Evaluating the Carry Trade as a Trading and Investment Strategy, contd.)
return by 195 basis points on average. The first portfolio’s return increases on average by 50 basis points, while the last portfolio’s return declines on average by 145 basis points. In addition, during these episodes of high volatility, the HML return becomes highly correlated with the U.S. stock market return. To illustrate this point, we take a closer look at the last 12 months in currency markets. In February and in July of 2007, U.S. stock markets were subject to large and sudden increases in volatility because of developments in U.S. mortgage markets.
avg (annl) std ev (annl) IR min (mthly) max (mthly) skew kurt (exc)
1.02 1.27 0.80 -0.79 1.41 0.35 0.60
Carry Filter Vol Filter
1.50% ----
AUDJPY – 12m
Figure 2 plots the one-month correlation of daily changes in the exchange rate for two low interest rate currencies, the Japanese yen and the Swiss franc, and two high interest rate currencies, the NZD and the AUSD, with the returns on the S&P 500. None of these currencies were highly correlated with stock market returns until February 2007, the start of the subprime crisis. The sharp increase in the VIX index coincided with a sharp decrease in the correlation for the low interest rate currencies and a sharp increase in the correlation for the high interest rate currencies. The same scenario unfolds at the start of the summer in 2007. Figure 3 shows exactly how much market risk carry trade investors have exposed themselves to. It plots the VIX index against the market beta of a levered currency HML strategy in these four currencies (long in AUD and NZD, short in yen and Swiss franc). The leverage is 2.2. In the first instance, the market beta of levered HML dramatically increases from 0 to 2.25 in a matter of days. At the start of the summer, the increase is from .5 to 2.
Conclusion A carry trade investment strategy with the same volatility as the U.S. stock market consistently outperforms a buyand-hold in the U.S. stock market over the last three and a half decades. However, a currency’s interest rate conveys information about its riskiness, just like a book-to-market ratio does for stocks. This becomes most apparent in bad times for U.S. investors.
Figure 3: Stastistics of AUD JPY carry trade with options
Figure 3: Rolling market beta of currency HML with the VIX index UCLA Anderson School of Management
CFI Bulletin 2008, No. I | 9