3. Methodology
3.5 Constructing carry trade strategy
3.5.1.2 Short conclusion of the interview
國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
28
Different traders use various indicators or tools to determine when to implement carry trade. The following signals are frequently used by traders in practice.
1. When low-rate currency depreciates against high-rate currency, this may be an opportunity to implement carry trade. For example, U.S. dollar depreciates against Australia dollar, then the trader can borrow cheap U.S. dollar and invests in Australia dollar which has potential to appreciate in the future.
2. If central bank of high-rate country raises interest rate, this government action implies not only the increase in interest rate differential but also potential appreciation of the FX of high-rate country due to large capital inflow.
The two signals mentioned above also mean that the major return contributions of carry trade come from interest rate differential and FX favorable change.
Question 6: How do traders hedge the FX risk that investment currency depreciates abruptly?
Different institutional investors gauge different indicators to monitor FX positions and manage FX risk. FX traders pay closely attention on the announcement of central bank monetary policy and some macroeconomic factors such as nonfarm employment, unemployment rate, PMI index, consumer confidence index, and so on.
3.5.1.2 Short conclusion of the interview
1. Investment period is at least 6 months but no more than 12 months.
2. One-time trading amount equals to USD 50-100 million.
3. Investment currencies include AUD, NZD, MXN, REAL.
4. Both borrowing and investing rate are LIBOR.
5. The timing to implement carry trade includes:
(1) low-rate currency depreciates against high-rate currency
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
29
(2) Interest rate differential between two countries increases 6. Different institutions gauge different indicators to monitor FX risk
3.5.2 Determine the timing to implement and close out carry trade positions
This paper chooses two developed market currencies (AUD and NZD) and two developing market currencies (MXN and REAL) to act as investment currencies due to their high daily trading volume. So this paper uses these four currencies to examine the performance of carry trade strategies this paper constructs.
This paper divides the process of carry trade strategy construction into two parts.
The first part is the best timing to implement carry trade strategy. The second part is the timing to close out carry trade positions. Investors realize profit or stop losses when receiving trading signals.
3.5.2.1 The best timing to implement carry trade strategy
According to the practice of FX traders gained through an interview, this paper assumes the firms that implement carry trade strategy are large foreign financial institutional investors. We know that the LIBOR is the interest rate borrowed and lent in the London interbank. Only large financial institutions with great creditability can borrow funds at LIBOR rate. This paper further assumes that the firms that implement carry trade focus on interest rate differential. Therefore, the investment period is at least 6 months. This paper also assumes the one-time trading volume is 100 million, so this paper takes the transaction costs under normal and distressed conditions in to consideration. This paper constructs the carry trade strategy as followed:
If the following two conditions are met simultaneously, this paper implements the carry trade strategy.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
30
1. The Interest rate differential between two countries increases due to increase in the interest rate of investment currency
For example, if the interest rate differential between Australia and America increases and interest rate of Australia increases, this paper implements carry trade strategy.
2. Low-rate currency depreciates against high- rate currency
For example, if US dollar depreciates against Australia dollar, then it’s profitable to borrow cheap U.S dollar and invest in Australia dollar. This concept may seem simple and intuition. However, by what magnitude low-rate currency depreciates against high- rate currency could investors confirm that low-rate currency is in depreciating trend? This paper defines a threshold to verify that low-rate currency is in the trend of depreciation. In practice, FX traders usually use moving average to predict the trend of foreign exchange. So the decision rule is as follows:
Decision rule: if current spot FX rate is less than 20-day moving average FX rate, this situation satisfies condition 2.
3.5.2.2 The best timing to close out carry trade strategy
This paper constructs the following three strategies and compares their performance according to Sharpe ratio with the performance benchmark to determine which strategy performs best in different sample periods. This paper divides the sample period into in-sample period and out-of-sample period to confirm the robustness of the strategies.
Strategy 1―Buy-and-hold to maturity
1. The traders hold the carry trade positions for at least specific months and then close out the positions. Strategy 1 is passive strategy because traders don’t need to
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
31
make any tactical adjustment to reflect short-term changes in FX market. As this paper has mentioned in the section of interview with FX traders, the investment period of carry trade can be short-term (focus on short-term FX volatility) and long-term (focus on interest differential). Our major focus here is interest rate differential, so this paper requires the investment period of carry trade should at least 6 months but no longer than 1 year.
2. Buy-and-hold strategy usually acts as performance benchmark. As this paper will mention later, Strategy 2 and Strategy 3 hold the positions at least 6 months but no longer than 12 months. So, the investment periods of these two strategies are within 6 to 12 months. So, this paper chooses Buy-and-hold strategy for 6 months and 12 months to act as performance benchmarks.
Decision rules: Buy and hold the carry trade positions for 6 and 12 months .Then until maturity, this paper closes out carry trade positions.
Strategy 2―Using FX implied volatility
This paper has examined in the previous OLS regressions that FX implied volatility can explain the future change in FX rate. Furthermore, FX implied volatility is a forward-looking measure that reflects both the market consensus of participants, including informed traders, and contains all relevant information.
This paper uses at-the-money (ATM) FX implied volatility to gauge the current FX market volatility. Some people may argue that why you choose ATM implied volatility rather than out-of-the-money (OTM) implied volatility.
If short-term FX implied volatility breaches long-term FX implied volatility, this may provide a signal that FX market shifts from low-volatility state to high-volatility state. This paper chooses 20-trading-day FX implied volatility to stand for short-term
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
32
FX implied volatility and selects 240-trading-day FX implied volatility to act as long-term FX implied volatility.
Decision rule: if short-term implied volatility (20-day) breaches longer-term implied volatility (240-day), this paper closes out the carry trade positions.
Strategy 3―Using FX implied volatility and the results of Markov switching model (Combination strategy)
Strategy 3 includes not only the decision rule in Strategy 2 but also the empirical results this paper gained in Markov-switching model.
The two-stage Markov-switching model divides the whole sample into low-volatility state (state 1) and high-volatility state (state 2). The results of Markov-switching model show that the coefficients of implied volatility in AUD/USD, NZD/USD and USD/MXN under state 2 are higher than that under state 1.
The coefficient of FX implied volatility in USD/REAL under state 1 is higher than under state 2. This means that when the FX implied volatility under state 2 (or state 1) is high, the high-interest-rate currency tends to depreciate against low-interest-rate currency. If FX traders observe this situation, they could quickly close out the carry trade positions to hedge the FX risk.
Decision rules:
(1) Based on the results showed in Markov-switching model, FX implied volatility of AUD, NZD and MXN is higher in State 2 than in State 1 and FX implied volatility of REAL is higher is State 1 than in State 2.
(2) When current market is in State 1 (for AUD, NZD and MXN) or State 2 (REAL) and 20-day implied volatility breaches 240-day implied volatility, this paper closes out the carry trade positions.
‧
3.5.2.3 Determine the future state of Markov-switching model
The following methods refer to Young (2013). In order to determine whether the three carry trade strategies are valid, this paper uses in-sample and out-of-sample periods to test their performances. This paper defines the period between Jan 2000 to Dec 2012 as the in-sample period and the period between Jan 2013 to Dec 2013 as the out-of-sample period for eight currencies except NZD and AUD.
Due to data unavailability, this paper defines the period between Jan 2000 and June 2012 as the in-sample period and set the period between Jul 2012 and June 2013 as the out-of-sample period for AUD. this paper defines the period between Jul 2003 and Feb 2012 as the in-sample period and set the period between Mar 2012 and Feb 2013 to be out-of-sample period for NZD.
This paper provides the in-sample-period and out-of-sample period among eight currencies in Table 2.
Table 2
In-sample-period and out-of-sample period for four currencies
Currency In-sample period Out-of-sample period
AUD Jan 2000 – Jun 2012 Jul 2012 – Jun 2013
NZD Jul 2003 – Feb 2012 Mar 2012 – Feb 2013
MXN Jan 2000 – Dec 2012 Jan 2013 – Dec 2013
REAL Jan 2000 – Dec 2012 Jan 2013 – Dec 2013
This paper uses the expected probability to determine which state is more likely in the future. The equation for expected probability is as followed:
Expected probability = Prob(𝑠𝑡+1= 𝑦|𝐼𝑡, 𝜃) = ∑ Prob(𝑠𝑡= 𝑥|𝐼𝑡, 𝜃)
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
34
For example, filter probability of time t under State 1 and State 2 are (0.985, 0.015). Transition probability is [0.996 0
0.004 1 ].
Multiplying filter probability by transition probability obtains expected probability which equals (0.98525 0.01475). Based on expected probability, this paper expects that State 1 is more likely to occur in time t+1 due to high expected probability.
Due to the computational complexity and some technical problems, this paper smooth the variables required to calculate filter probability and transition probability using 5-day the moving average of the preceding 5 days of related variables, include change in log of foreign exchange rate, interest rate differential, and FX implied volatility.
3.5.2.4 Transaction costs
Due to imperfect market, this paper takes transaction costs into account as implementing carry trade. This paper divides transaction costs into three parts.
1. Brokerage commissions.
2. Bid-ask spread.
3. Market impact due to one-time large trading volumes.
According to previous literatures, almost all papers assume perfect market. That is, they assume there are no taxes, transaction costs and related constraints. However, in practice, transaction costs could significantly affect carry trade returns. In our paper, this paper assumes imperfect market and takes transaction costs into account.
According to interview with FX trader, this paper assumes the one-time trading amount is 100 million. This paper ignores the brokerage commissions (only account for 1 to 2 basis points). This paper uses the daily FX data during period of Jan 2000 to
‧
Transaction cost - bid-ask spread ratio (bps)
Currency JPYUSD CHFUSD USDNZD USDAUD
Bid-ask spread ratio 4.77 4.88 10.28 6.71
Currency MXNUSD REALUSD ZARUSD INDUSD
Bid-ask spread ratio 21.67 98.77 42.90 49.69
Table 3 calculates the bid-ask spread ratio for eight currencies. This paper observes that the bid-ask spread ratios of developing markets under normal condition are five to ten times more than those of developed countries.
With respect to transaction costs due to one-time large trading volume, market impact needs to be taken into account. Because it’s difficult to measure transaction costs due to market impact precisely, this paper implements sensitivity analysis. This paper doubles and triples bid-ask spread ratio in normal condition to account for this effect.
Another issue is that institutions enjoy favorable bid-ask spread ratio relative to individuals. The investors in this paper focus on institutions.
3.5.2.5 Income tax and capital gain tax
The returns of carry trade come from two parts. One comes from interest income.
Another comes from capital gain due to FX change. This paper assumes that the head-quarters of institutional investors are based in America and taxed according to U.S tax rules.
According to U.S tax rules, corporate tax rate is 35%. With respect to capital
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
36
gain, the tax rate depends on the holding periods. If investors close out carry trade position for one year or less, this profit is considered a short-term capital gain and is taxed at the ordinary income tax rate (35% for U.S corporates).
This paper assumes that both interest incomes and capital gain income are taxed at a rate of 35%.
4. Data description
This paper collects daily foreign exchange rate against U.S. dollar (USD) and 1-month, 3-month, 6-month and 12-month interbank interest rates and FX implied volatility from Datastream during 2000 to 2013 for four developed markets and four developing markets: Japan (JPY), Switzerland (CHF), Australia (AUD), New Zealand (NZD), Mexico (MXN), Brazil (REAL), South Africa (ZAR) and India (RUBEE).
This paper presents the descriptive statistics in Table 4. Some data, emerging countries in particular, aren’t available for certain periods. So the observations may not be equal among eight countries. Basically, the time periods of eight currencies include major financial events such as subprime crisis, financial crisis and European debt crisis. In Table 5, this paper provides the descriptive statistics, both expected value and standard deviation, of these three variables for eight currencies. In Figure 2, this paper provides the time series of foreign spot rate and interest rate differential for eight currencies
‧
Mean and standard deviation of FX spot rate among eight foreign currencies, include JPY, CHF, AUD, ZND, MXN, REAL, ZAR, and RUBEE from January 3, 2000, to
Descriptive statistics of interest rate of eight foreign currencies, include JPY, CHF, AUD, ZND, MXN, REAL, ZAR, and RUBEE from January 3, 2000, to December 2, 2013 (percentage)
‧
Descriptive statistics of FX implied volatility of eight foreign currencies, include JPY, CHF, AUD, ZND, MXN, REAL, ZAR, and RUBEE from January 3, 2000, to
December 2, 2013
‧
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
40
Figure 2 the time series of FX spot rate and interest rate differential (against USD)
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
41
5. Empirical Results
5.1 The forward premium puzzle
This paper examines the forward premium puzzle among eight currencies in different investment periods (1-month, 3-month, 6-month, and 12-month) by using Fama regressions. In Table 7, the results show that all currencies in different periods reject the null hypothesis that alpha equal to zero and beta equal to one. This paper concludes that all eight currencies reject the UIP theory during the sample periods this paper specified.
In Table 8, this paper observes that almost all interest-rate slope coefficients of different currencies in different investment periods are statistically significant and their values are negative. These results are consistent with the previous literatures.
That is, the average coefficients of interest rate differential are different from zero and their values are negative. Froot (1990) summarizes the previous empirical results of UIP test and find that the average coefficient of interest rate differential is -0.88.
The failure of UIP theory implies that most of the time, low-interest-rate currencies tend to depreciate and high-interest-rate currencies tend to appreciate. This phenomenon results in the prevalence of carry trade. Many international institutions implement carry trade by borrowing low-rate currency and invest in high-rate currency. Could carry trade strategy make a profit on average over time? This paper will examine the return of carry trade in details in the next sections.
5.2 Using carry interest to predict future performance
According to previous literatures, empirical results show that carry trade strategy could earn an excess return on average over time. Although previous papers have confirmed carry trade can earn excess returns, this paper still wants to do some reality checks.
‧
Applying Fama regressions to test UIP theory for developed and developing countries
Horizon (months) JPY CHF AUD NZD
Slope coefficient of Fama regressions for developed and developing countries
Currency 1M 3M 6M 12M know that carry trade can divide into FX change focused and interest rate differential focused. This paper is focused on interest rate differential, so the investment period should be at least 6 months but no longer than 12 months. This is also the reason why this paper only forecast the returns on carry trade over next four quarters.
‧
Coefficients of interest rate differential among eight currencies
investment period JPY CHF AUD NZD differential among eight currencies in different period are positive and statistically significant. The results imply that if the interest rate differential is positive, the returns on carry trade over the next four quarters tend to positive. Due to the fact that interest rate differential is the stable source of return and also accounts for a large proportion of carry trade return, this paper concludes that interest rate differential contains certain predictive abilities in carry trade returns.
This paper also finds some interesting results that the coefficients of interest rate differential of five out of eight currencies except CHF, MXN, and RUBEE tend to decrease over time. Take AUD as an example, the slope coefficient in first quarter and four quarters are 0.9974 and 0.9903 respectively. This paper deduces the reason is that the uncertainty increases over time. The uncertainty may come from adverse change in FX.
5.3 Using OLS to find influential factors
Although carry trade can earn excess returns on average, the returns aren’t risk-free. Many people say carry trade strategy is an arbitrage strategy. However, theorists and practitioners have different definitions of arbitrage. In academia, an
‧
According to “Alternative Investments, risk management, and the application of derivatives, CFA institution”, they have some comments related to arbitrage. They say arbitrage is a strategy with low risk instead of no risk. In our view, this paper argues that carry trade cannot call “arbitrage” strategy because of potential high FX risk.
In order to control FX risk, which is the major risk of carry trade, this paper wants to find some influential factors that could explain the adverse FX change. This paper uses multiple regressions and choose interest rate differential and FX implied volatility as independent variables. In Table 10, the results show that almost all the coefficients of implied volatility are statistically significant among eight currencies in different investment periods. This paper concludes that FX implied volatility is a valid variable to explain adverse FX change. This paper has examined the relationship between FX change and interest rate differential in UIP test and confirms interest rate differential is a valid variable. To prevent redundancy, this paper doesn’t show the coefficients of interest rate differential in this section.
Table 10
The coefficients of FX implied volatility among eight currencies using multiple regressions for different investment periods
1M 3M 6M 12M
‧
5.4 The results of two-stage Markov switching model
The two-stage Markov-switching model divides the whole sample into two parts
─ State 1 and State 2. State 1 is low-volatility regime and State 2 is high-volatility regime. This paper then discusses the relationship between interest rate differential, FX implied volatility and FX change. The FX quotation is units of high-interest-rate currency per low-interest-rate currency per. In our paper, JPY and CHF, USD are considered high-interest-rate currencies. AUD, NZD, MXN, REAL, ZAR, RUBEE, USD are considered low-interest-rate currencies. Due to the limited space, this paper only provides one example for developed market and one for developing market. This
─ State 1 and State 2. State 1 is low-volatility regime and State 2 is high-volatility regime. This paper then discusses the relationship between interest rate differential, FX implied volatility and FX change. The FX quotation is units of high-interest-rate currency per low-interest-rate currency per. In our paper, JPY and CHF, USD are considered high-interest-rate currencies. AUD, NZD, MXN, REAL, ZAR, RUBEE, USD are considered low-interest-rate currencies. Due to the limited space, this paper only provides one example for developed market and one for developing market. This