Issue 63, Winter/Spring 2006

Section I: Introduction

Given that buying an out-of-the-money option is a highly leveraged view (and used by both speculators and hedgers), risk reversals may be considered a valuable market sentiment indicator. Sections I & II will introduce and explain the concept of risk reversals.

In technical analysis literature, market sentiment is the term used to describe cumulative market expectations. Market practitioners employed sentiment indicators such as risk reversals data to quantify the levels of optimism or pessimism in the Foreign Exchange (FX) market. For example, a higher call to put premium ratio for a specific currency suggests that the majority of option traders expect the currency to rally. Conversely, a higher put to call premium point to higher expectation of currency depreciation.

To answer the question; Can risk reversals be used to identify buy and sell signals; this research paper will first determine if there is any correlation between risk reversals and currencies. If so, this raises the possibility that risk reversal is a potentially valuable forecasting tool. From a statistical perspective, measuring how well the regression model predicts movement in the dependent variable will help determine whether or not risk reversals can be considered a leading indicator for currency forecasts and can therefore be used to identify buy and sell signals. Section III summarizes the results from the regression analysis.

Section IV will provide some empirical evidence under very volatile conditions in the currency market and will investigate further the concept of market sentiment used in technical analysis. Particular attention is paid to extreme levels of risk reversals to determine if such occurrences would signal market turns. Section V will explore the use of some technical analysis tools. The focus will be on Bollinger Bands analysis on the assumption that risk reversals fluctuations may be contained within a statistical confidence band. The objective of this exercise is therefore to determine if risk reversals can provide reliable turning points in the currency markets.

1.1 – What are Risk Reversals?

Risk reversals are commonly used in the FX option markets to describe the strategy of buying and selling the same amount of out-of-the-money currency calls and puts (at the same exercise price). The standard and most common risk reversal contract is the 25-delta[1] option. A risk reversal is made up of two transactions that together take into consideration the implied volatility[2] of both put and call options. For example, the combination of a 25-delta currency call together with the same delta put is known as the risk reversal.

Risk reversals are calculated by taking the difference between the implied volatility on the 25-delta currency call and the same delta put, with the exact maturity date. This difference generates the risk reversal value. For example, if the one-month implied volatility on the 25-delta U.S. dollar- Japanese yen (JPY) call is 8.25%, and the one-month implied volatility on the 25-delta JPY put is 8.75%, the one-month 25-delta risk reversal on (JPY) is referred to as the 0.50 JPY put (8.75%-8.25%).

What does a one-month risk reversal of 0.50 JPY put mean? If the risk of JPY depreciation is deemed higher than an appreciation in the future, it will be highlighted in the implied volatility curve[3]. Based on this example, the implied volatility is higher for a JPY put than it is for a JPY call. The risk reversal quotation, therefore, communicates the market’s bias. In this example, a 0.50 JPY put reveals a bearish inclination toward the Japanese yen.

Risk reversals can therefore bring skew information about the market expectations of future currency rate changes.

Section II: Concept

2.1 – Why use Risk Reversals? 

Underlying Assumptions

The Black-Scholes[4] theory is the primary model for calculating option prices on stocks, commodities, interest rates, and foreign exchange instruments. However, not all of the underlying assumptions of the Black-Scholes theory are applicable in the FX markets. For example, it assumes that returns in the FX markets are subject to “normal distributions.” In other words, if returns are distributed normally, then according to Chebyshev’s theorem, 68% of the currency returns will fall within +/- 1 standard deviation of the mean, and 95% of the returns will fall within +/- 2 standard deviations of the mean. In practice, however, returns in the FX markets tend to have much more frequent occurrences of extreme values. Indeed, less than 68% of currency returns fall within one standard deviation and less than 95% of them will fall within two standard deviations of the mean currency return.

Rather than following a normal probability distribution, currency returns in the FX markets follow a “leptokurtosis distribution,” which means that the kurtosis[5] of the distribution is greater than zero. From a statistical perspective, this indicates that it is more probable that FX returns will be extreme. One way to visualize this trend is to imagine that the tail end of a “bell curve” would be thicker than it would in a normal distribution (see Charts 1, 2 and 3). For example, the distribution of one-day returns on the U.S. dollar-Canadian dollar (USD-CAD) exchange rate from the end of Bretton Woods[6] (August 1971) until recently has an abnormal distribution with a kurtosis of almost six (note: the end of Bretton Woods marked the beginning of a floating exchange rate regime). This implies that the risk probability assigned for a catastrophe (or an unanticipated pleasant event), such as an extreme negative return (or positive return), is higher under a leptokurtosis distribution than it is in a normal distribution. This also implies that the application of the Black-Scholes model would systematically misprice and underestimate option prices. The risk reversal, however, avoids this problem because it uses the implied volatility of put and call options, rather than their prices.

The charts below illustrate the shape of a normal distribution as compared to that of a leptokurtosis distribution. (Note that the latter has a thicker tail distribution.)

The leptokurtosis distribution graph above implies that risk reversals may be an important variable used in a forecasting currency model.

Chart 3 below from the RiskMetrics Technical document by J.P. Morgan and Reuters (reference document, fourth edition 1996) illustrates this point. This graph shows the leptokurtosis distribution of log price changes in U.S. dollar-Deutsche mark (DEM) exchange rates for the period March 28 1996 through April 12 1996 compare to a normal distribution.

Section III: Risk Reversal Regression Model of Exchange Rates

3.1 – Regression Analysis

The regression analysis is restricted to a simple linear regression model. The dependent variable is the currency pair “Y.” The independent variable is the specific currency’s risk reversals (C2). Regression equation: Y = c1 + c2 * x.

Most financial time series are “random walks”, meaning that often the best predictors of their future values are today’s values. From a statistical perspective, this means that there could be a spurious regression problem in the regression equation. Spurious regressions occur when two or more variables do not influence each other, but whose R-squared and t-values indicate a significant relationship. Variables whose value contains a trend are said to be non-stationary. That is, the mean and variance of the variables are not constant over time. If the variables were non-stationary, then it would not be correct to use Ordinary Least Squares (OLS) method to test our regression equation. The hypothesis is that variables are non-stationary. The null hypothesis is that variables are stationary. It is important to determine whether or not to accept or reject the null hypothesis. H0: β2 = β3, H1: β2 = β3

To test whether the regression variables are stationary or non-stationary, an Augmented Dickey-Fuller Unit Root Test (ADF) is carried out on both the dependent and independent variables.

The ADF results on both variables pass the 10% critical value mark. Therefore, the hypothesis is rejected and the null hypothesis is accepted. The results of this test indicate that the regression model does not have a spurious regression problem and the OLS method can be used to test the regression equation.

3.2 – Methodology

To test whether or not there is a strong correlation between risk reversals and currency pairs using OLS method, risk reversals are compared to closing spot rates.

3.3 – Data

The FX rates and risk reversals database are from the Bank of Canada, JP Morgan Chase, Standard & Poor’s MMS, Bloomberg and Reuters, and cover the period from 1996 to 2002. (Note that risk reversals data are diffi cult to obtain prior to 1996).

These major currency pairs were selected because they were among the most liquid currency pairs and data on their risk reversals are easy to obtain. In addition, if the daily quotes on the risk reversal are illiquid, the information content may not be very useful.

1. AUD-USD (Australia-US dollar exchange rate)
2. EUR-USD (Euro-US dollar exchange rate)
3. GBP-USD (British Pound-US dollar exchange rate)
4. USD-CAD (US dollar-Canadian dollar exchange rate)
5. USD-JPY (US dollar-Japanese Yen exchange rate)

To prove that risk reversals have a strong influence on currency rates the following test is used:

Test: If the cut-off F-statistic is <0.05, and the P-value is <0.05, then the risk reversal model is significant. In addition, the t-statistics and the R Square have to confirm that the independent variable (risk reversal) is a significant input in explaining movements in the dependent variable.

3.4 – Regression Results

Both the t-statistics and the F-statistics on the USD-JPY regression model results above are significant (at the 99% level). Although the R-squared does not reveal a perfect fi t, the 0.237788 number indicate that JPY risk reversals may have some explanatory power in this regression model. The JPY risk reversals movement can explain 23.7788% of the total variation in USD-JPY between 1996 and 2002 (See appendix 1 for the results on other currency pairs). However, it is important to note that the Durban-Watson[7] statistics highlight a statistical problem in this model. The Durbin-Watson statistic for the risk reversal equation is 0.020838. The 5 percent critical values from the Savin-White tables[8] are 1.758 and 1.778. Since the sample value falls outside the inclusive region, there is autocorrelation problem in this regression equation. To solve for this problem, three other scenarios are chosen. These assume that a lag factor may influence the relationship between currency pairs and risk reversals and would therefore solve for the autocorrelation problem:

1. Change in risk reversal (1-day lag) compared to closing spot rates.
2. Risk reversal compared to change in closing spot rates (1-day lag)
3. Change in risk reversals (1-day lag) as compared to change in spot rates (1-day lag).

These test results are not encouraging and continue to indicate an autocorrelation problem. It is possible that under volatile market conditions, and in situations of market stress, risk reversals may provide good signals. But when testing this assumption using the OLS method, (referring to the Asian currency and the Russian rouble currency devaluation crisis in the 1990s as benchmark periods of highly stressful times in the currency market), the results also indicate an autocorrelation problem. A more rigorous test, which is outside this paper’s scope, may solve for the autocorrelation problem. Additional tests may include independent variables such as fluctuations in short-term interest rate differentials, inflation expectations, or flow of funds type data.

3.5 – Regression Conclusion

A significant regression conclusion would obviously imply that risk reversals have strong predictive powers. The goal then is to construct a model that would make a reliable forecast on currency movements. Because of the autocorrelation problem, further econometric test is required. A more rigorous econometric analysis should be conducted before developing a model that could accurately identify buy or sell signals in the currency market. Additional econometric analysis is beyond the scope of this paper as this would shift its focus away from a technical analysis perspective. The risk reversals data up to this point do not add value to the forecast of FX rates. Furthermore, they do support the underlying concepts of risk reversals. However, two observations are worth noting: 1. R-squares are fairly significant. 2. R-squares increase under extreme volatile conditions in the FX market.

Section IV: Empirical evidence and an overview of market sentiment

The empirical evidence in this section suggests a possible link between risk reversals and FX rates from a market sentiment perspective. The relationship between risk reversals and currency movements under volatile conditions in the FX markets seems particularly strong. The focus from hereon is on quantifying the level of optimism or pessimism of risk reversals. Based on the theoretical presentation of this paper, risk reversals can be considered a sentiment indicator used to gauge the level of bullish or bearish activity in the FX market. For example, what happens when risk reversals reach extreme levels? There are many ways to quantify market sentiment (see amongst others P. Kaufman, J. Murphy and M. Pring). The underlying idea is on the premise that the majority is usually wrong. The focus of sentiment indicators is therefore on investor expectations. Usually, highly optimistic (bullish) readings indicate market tops while highly pessimistic (bearish) readings indicate market bottoms.

The experiences of the Bank of Canada (section 4.1) and the US Federal Reserve (section 4.2) in the 1990s provide some insight on how risk reversals can be used to gauge market sentiment in the FX market.

The experiences of the Bank of Canada and the US Federal Reserve 

From a central bank’s perspective, there is sometimes a need to signal to the market place that its currency is undervalued or overvalued. Risk reversals may provide some insight as to the timing of when to conduct the appropriate intervention. An example of how a central bank examined the role of risk reversals as a measure of market expectation can be found on the July-September 1996 New York Fed’s operation report.

“The dollar’s largest one-day move occurred early in the period on July 16. On this day, the dollar traded in a 3.1 percent range against the mark, implied volatility on one-month dollar-mark options spiked higher, and prices of risk reversals indicated a rise in the perceived risk of a further significant dollar decline. As with other sharp dollar moves over the period, the dollar’s trading ranges over subsequent days fell back toward the period’s average, implied volatility on dollar-mark options reverted toward record-low levels, and risk reversal prices moved closer to neutral”.

Some portfolio managers and FX traders also look to risk reversals for vital information about market sentiment. Citigroup FX Weekly “Commentary and Ideas update on 30th November 2004 illustrates the usefulness of risk reversals as a measure of market sentiment:

“Gamma is higher in USD-JPY due to the premium for the US Payrolls, although we have started to see sellers as the cash market fails to break lower. The value still appears to be in the back-end of the curve and the 4-year 25-delta risk reversals got paid at 3.70% today, highlighting the structural problems in the market and continued demand for longer dated JPY Calls. The 1-week risk reversals have more than halved the skew in favour of JPY Calls this week and decreased from 1.25% to 0.50%.”

These examples suggest that market participants may be able to elicit essential clues from risk reversals for the timing of currency sales and purchases. Against this backdrop, it may be useful to identify the stage where a market is entering an extreme speculative market condition. Indeed, it can be shown empirically that risk reversal analysis may sometimes be used as a contrarian indicator.

4.1 – The Bank of Canada

In 1998 the Bank of Canada aggressively defended the Canadian dollar from speculative attacks. That experience reveals some of the predictive powers of risk reversal.

In 1998, the Bank of Canada made 44 interventions in the FX market. Nearly half of those interventions occurred in August. Assuming that the Bank has a longer holding period and much larger war chest than any currency manager, one could argue that its intervention was a success. However, it came at an extraordinarily expensive. Between January and December 1998, the Bank of Canada spent US$10.7 billion to guard against CAD devaluation. The intervention in August was the most aggressive in the Bank’s history, when US$5.8 billion was spent. Only after August has USD-CAD declined from its peak at 1.5850 (August 27 1998) to its trough at 1.4452 (May 6 1999).

The risk reversals revealed that the Bank of Canada’s interventions were untimely until the last week of August 1998. The Bank was in the market 13 times in August, and made about 20 transactions to protect the Canadian dollar. Prior to the fi nal week of August, every Bank of Canada intervention occurred when the one-month 25-delta risk reversal was around 0.2 in favour of CAD puts. For Canadian dollar risk reversals during the period under consideration, the 0.2 risk reversal quotation is viewed as a neutral reading (average CAD risk reversals were around 0.1 favouring CAD puts). That is the risk reversals did not show a strong directional bias despite seeing USD-CAD climb from 1.5115 to 1.5850 from the beginning of August 1998 to August 27 1998. For the most part, the Bank’s costly intervention had zero influence in altering the market’s perceived value of the currency. Nevertheless, CAD risk reversals reached extreme levels towards the end of August (CAD risk reversals were around 0.8 favouring CAD puts). This in all likelihood sets the stage for the Bank of Canada to catch the markets off guard. Precisely when the markets were getting complacent with what were considered sure-win bets, the Bank struck again. The Bank of England also intervened by buying Canadian dollars on August 27 1998. This rare occurrence introduced fears that more co-ordinated central bank effort was forthcoming. On the same day, the Bank of Canada jolted market sentiment with a surprise 100 basis points rate hike. The timing was perfect and was finally effective in transforming a bearish market sentiment to a moderately bullish one.

The Bank of Canada’s experience reveal that when the consensus view on the Canadian dollar reached extreme pessimistic levels in August 1998, the market had already positioned on the short Canadian dollar side and there was little potential selling power left. In this situation, market bottom on the Canadian dollar was associated with a risk reversal bias toward puts of around 0.8 (the average CAD risk reversal reading was 0.1 favoring CAD puts). The Bank of Canada’s intervention in late August is an example of using risk reversal to gauge market sentiment. From a technical analysis perspective, the Bank of Canada’s experience showed that extreme levels in risk reversals could be used as a contrarian signal.

4.2 – The U.S. Federal Reserve

The Fed’s FX experience under the Clinton Administration illustrates a slightly different perspective on the use of risk reversals. In 1995 there was a determined effort to boost the value of the dollar and the Federal Reserve intervened heavily in the FX market–by buying US dollars against the Japanese yen. For the most part, the effort was to stabilise an extremely disorderly market place for the dollar.

However, on July 7 and August 2, 1995, the strategy shifted to what is called a “strong dollar policy”. Part of the objective was to establish two-way risk in the FX market and to stave off speculative attacks on the US dollar. The Fed’s FX intervention goal was to establish a floor on the dollar and to signal to the market place that the Treasury department wanted an orderly reversal of its decline. Note that prior to the Fed’s July 7 and August 2 1995 Fed FX intervention, the risk reversals had a skew of over 2.0 favouring Yen calls (an extreme quotation for Yen risk reversals during this time frame). On July 7, the Yen risk reversal was still in favour of a Yen call (0.9/1.3), but had been trading lower all week and was already well below the 2.0 level. By August 2, the Yen risk reversal had shifted to a bias favouring Yen puts.

That is, the options market was turning bullish on the dollar when the Fed intervened. In addition to the bullish risk reversal reading on the dollar, the Treasury issued a clear statement about its dollar policy. On August 2, the Treasury indicated that the Fed’s FX intervention was consistent with the April and June G7 FX communiqués, calling for an orderly reversal of the dollar’s decline during the previous two years.

The strategy worked. The Fed intervened when the market was already turning and the dollar strengthened considerably from 1995 to early 2003.

The US Federal Reserves experience is an example of how a policy maker took advantage of shifting market sentiment. In the situation described in section 4.2, the market psychology was already starting to shift from outright pessimism on the US dollar to one of growing confidence in the dollar’s future prospects. Between July 7 and August 2 1995, the Yen risk reversals had fallen rapidly from a relatively extreme reading of 2.0 (favouring Yen calls) to a risk reversal reading of 0.2 favouring Yen puts. The speed in which the Yen risk reversals reading shifted from extreme pessimistic to neutral reading was unusual. The Fed’s FX intervention in August 1995 is an example of using risk reversals as a sentiment indicator to alert that an important move may be in the offing. From a technical analysis perspective, sudden shift in risk reversals should prompt a closer than normal examination of market condition.

4.3 – How reliable is the Risk Reversal as a Directional Indicator?

The Bank of Canada’s and the Fed’s experiences above suggest that an oscillator type indicator may help in the analysis of market sentiment. The charts below represent a typical oscillator used in technical analysis. In this analysis, the oscillator calculation is based on risk reversals movements. The two standard deviation[9] shows risk reversals movement from one extreme to another, which is from –2 (extreme pessimism) to +2 (extreme optimism). When the risk reversals oscillator reaches the extreme pessimism or the extreme optimism lines, the probability favor that the prevailing currency trend reverses direction. 

Note however that not every signal results in a significant reversal. There are instances when the USD-CAD and USD-JPY trend continues much further when the CAD and Yen risk reversals oscillator touches the lower or upper bands. Sometimes the risk reversal oscillator is on the mark, and sometimes it gives premature signals.

Table 4 captures the CAD risk reversals oscillator’s turning points. The table is a summary of the oscillator impact on the USD-CAD rate one week later. The turning point is defined as when the CAD risk reversals oscillator reaches either the lower or upper boundaries of the two standard deviation bands.

Between 1996 and 2003, the CAD risk reversals oscillator generated 11 signals of which 6 were correct in its direction prediction. The currency movements were wider than usual one week after the risk reversal oscillator signal (an average of 147 points vs. the mean weekly USD-CAD movement of 93 points between 1996 and 2003). The most profitable signal occurred on August 27 1998 in which USD-CAD moved 400 points one week after the signal was generated. This coincides with the most extreme CAD risk reversal quotation at that time.

The Yen risk reversal oscillator generated 21 signals, of which 14 accurately predicted the direction of the currency movement. The EUR risk reversals had the best success rate on currency directions (nine out of ten signals). Both the AUD and GBP risk reversal oscillator had the lowest success rate on currency directions (four out of thirteen signals for the AUD-USD and three out of eleven for the GBP-USD).

The main drawback in interpreting the risk reversal oscillator results are that they do not provide reliable exit points once a trading position is taken after the oscillator touches their extreme points. This flaw demonstrates the necessity of using the risk reversals oscillator with other technical analysis tools. Another drawback is that the risk reversals data are available only after 1996, which is a very short time, compared to other sentiment indicators.

Overall, this paper finds the risk reversal oscillator to be a valuable tool to have when assessing market sentiment in the FX market. The use of one standard deviation risk reversal oscillator should generate more signals. However, the results will be more erratic than the two standard deviation risk reversal oscillator. There may be more signals with the one standard deviation measure, but the results may not be as useful for identifying intermediate term currency trend.

4.4 – Market Sentiment Conclusion

The conclusion this paper draws from this section is that an option-based indicator such as the risk reversal do provide useful signals on market expectations. This finding is based on the Bank of Canada’s and the Fed’s FX intervention experiences in 1998 and 1995 respectively. The risk reversal oscillator tests conducted on currencies between 1996 and 2003 appears significant. At the minimum, risk reversals can be useful in analyzing the stability of the FX market. On its own, the risk reversal does not inform us of what the appropriate level will be for any particular currency, but its quotation often helps uncover periods of “systematic buying” or “systematic selling” of the currency in the option market. This will often shed light on the market’s perception of risk. At extreme levels, particularly at the two standard deviation bands, a contrarian view on the currency may be appropriate. The main drawback is that it is difficult to devise a timing filter for short-term trading purposes. It seems useful to combine the risk reversals oscillator with other technical analysis tools.

Section V: Volatility Studies & Technical Indicators

5.1 – Bollinger Bands

Bollinger Bands may have a place in the risk reversal analysis. The empirical evidence highlighted in Section IV implies that extreme risk reversal quotations may provide useful guidance to currency direction. Recall that currency returns in the FX markets follow what is statistically known as a “leptokurtosis distribution.” This means that it is highly likely that FX returns will be extreme and do not follow what statisticians’ term as a “normal bell curve.” Therefore under a leptokurtosis condition, it may be possible to associate extreme readings in risk reversals to the near term directional bias of the currency. For this research, Bollinger Bands can help identify periods of extreme conditions in the options market. The area of interest corresponds to those times when risk reversals approach the lower or upper boundary of the Bollinger Bands. The objective of the volatility analysis is to determine a consistent method to pinpoint when to liquidate or reverse existing FX positions.

Test: Can Bollinger Bands and Risk Reversals help identify points when to liquidate or reverse current positions in the FX market?

Assumption: Bollinger Bands properties can help identify extreme points in the FX market. Calculating a 2 standard deviation of risk reversals over a 20-day period implied that 95% of the times risk reversals will hover between the lower and upper Bollinger Band boundaries.

Proof: Using the Metastock software to help identify periods when risk reversals touch the lower or upper boundaries of Bollinger bands. The attached graphs on USD-CAD, USD-JPY and AUD-USD revealed that when risk reversal reach an extreme point[10] this often coincides with turning points in the FX market.

Bollinger Bands definition: Bollinger Bands consist of an upper and lower band, and a moving average. The upper and lower bands are standard deviations calculated from the moving average. The standard deviation represents a confidence level and our choice of 2 standard deviations equate to a 95% confidence band. These bands tend to alternate between expansion and contraction. In a period of rising price volatility, the distance between the upper and lower bands will widen. Conversely, in periods of low market volatility, the distance between the upper and lower bands will contract. When the upper and lower bands are unusually wide, the current trend is said to be ending. Times when the Bollinger Bands are unusually narrow often indicate that the market may be about to initiate a new trend.

5.2 – Bollinger Bands Results

The arrows on the Bollinger Bands risk reversals indicate when risk reversals touch the upper or lower boundaries of the trading bands. An example of the Bollinger Bands risk reversals impact is presented on Table 5.

The Bollinger Bands on Yen risk reversals appear wider than usual in October 2002 and again in August 2003. On both occasions, this corresponds to a shift in the USD-JPY trend. This is the expected reaction based on the Bollinger Bands definition. However, it is more difficult to obtain a precise timing filter for trading purpose. The key point is that Bollinger Bands highlight extreme market conditions. It makes sense to use Bollinger Bands as a complementary tool with other technical analysis tools.

The wider than usual Bollinger Bands on the CAD risk reversals in May 2000 was an alert to a possible trend change. But it took USD-CAD nearly two months to respond to the signal. This illustrates that Bollinger Bands do not necessary provide precise buy or sell signals. This also illustrates the drawback in using Bollinger Bands on risk reversals as a stand-alone timing tool.

The Bollinger Bands on the AUD risk reversals were unusually narrow between April and June 2003. This signaled the possibility that the AUD-USD rally in June 2003 may have peaked. Although this proved to be an accurate forecast, it took AUD-USD one month to react to the signal.

These examples indicate the difficulty in using Bollinger Bands as a precise timing indicator. Table 5 is the summary of the JPY risk reversal signals and the impact they had on the USD-JPY rate. The turning point is defined as when the risk reversals touch the upper or lower boundaries of the two standard deviation Bollinger Bands. 

Over the sample period 1998 to 2003, the Bollinger Bands on Yen risk reversals generated 15 signals. These signals indicate market tops and bottoms but the currency movement often took longer to respond. The average currency movement one week after the signals were generated was in line with the average seen over the sample period. As a stand-alone indicator, it is difficult to devise a trading strategy.

5.3 – Bollinger Bands Analysis Conclusion

The Bollinger Bands charts suggest that incorporating risk reversals with Bollinger Bands analysis can provide important insights into market perceptions of FX movements. It is a worth-while exercise to pay particular attention to situations when risk reversals get to the lower or upper boundaries of the Bollinger Bands.

5.4 – MACD[11] Analysis

Table 6 captures the MACD turning points of JPY risk reversals and summarizes the impact this had on the USD-JPY rate. The turning point of the risk reversals is defined as when the 9-day MACD line crosses over the 20-day MACD line.

The result generated from the MACD crossover was significant. USD-JPY movement one week after the signal was generated revealed average movement of 1.27 points, higher than the average of 1.05 points. The results were also signifi cant on the USD-CAD, GBP-USD, and AUD-USD but not on the EUR-USD.

5.5 – MACD Results

The Bloomberg graph below is an example showing MACD turning points on JPY risk reversals. The code is; USJYVRR <INDEX> GPO MACD.

5.6 – MACD Conclusion

The key highlight from Table 5 shows that on average, USD-JPY moved 1.27 points 1 week after the MACD lines generated a signal. This is above the median figure of 1.05 as calculated by the week over week USD-JPY change measured from 1998 to 2003. 

The implication drawn from this analysis is that the MACD indicator is a useful technical tool for risk reversals. The MACD signals can help determine the direction and give reasonable confi dence that the magnitude of the currency movements is generally greater than the norm.

5.7 – Moving Average Analysis

According to most technical analysis authors, the most commonly used Moving Average is the 7, 21, 50, 100 and 200 period averages. From an analytical perspective, there is no correct period. Usually, experience will determine which period is most appropriate for a given security. The 7-period Moving Average will be more sensitive than the 200-period Moving Average.

5.8 – Moving Average Results

Investors use the moving average indicator for a variety of reasons. This research paper examined the moving average indicator from a filter perspective. In the example below, a turning point is confi rmed whenever the 7-period moving average cuts below or above the 21-period moving average[12]. The graph below is an example of a USD-JPY risk reversal graph. The code on Bloomberg is USJYVRR <Index>.

5.9 – Moving Average Conclusion

The Moving Average is essentially a lagging indicator. It is therefore not prudent to conclude that using moving averages on its own will provide useful buy or sell signals in the FX market particularly when risk reversals have a high tendency to make abrupt movement away from its mean. This is clearly reflected in the sharp spike up, and sharp fall in the JPY risk reversal graph above. However, the key point here is that the Moving Average indicator can still be a useful filter. It is simple and intuitively easy to understand. Using the Moving Average indicator will help increase the confidence of spotting turning points and will in general confirm an emerging trend of the underlying security. Using an exponential moving average indicator is also useful but in this analysis, the indicator does not improve the results significantly.

Section VI: Research Conclusion

The regression results revealed an auto correlation problem, which means that a multi-variable model may be required to explain short-term currency movements. The regression results do not prove conclusively that risk reversals have strong predictive powers, but they do suggest that risk reversals may be a useful variable for inclusion in a more elaborate equation model.

The empirical evidence outline and the overview of market sentiment in section IV, and the Bollinger Band Analysis in section V suggests that risk reversals do provide good signals when they reach extreme points. Risk reversals, while straightforward, should at certain times be looked at in a different context. Notable shifts in the risk reversal reading are often associated with a sudden shift in market sentiment and therefore market expectation of future movement in the currency market. It appears that significant shifts in the risk reversals often precede big moves in the FX markets. The risk reversal oscillator and the Bollinger Bands analysis imply that it may be important to pay attention to extreme readings in the risk reversal quotation.

The primary purpose of analyzing risk reversals is to determine the directional bias and the turning points of a currency. On its own, risk reversals do not indicate what the appropriate level will be for any particular currency. This research paper finds that extreme levels of risk reversals provide valuable information on market sentiment. Sudden and big shifts in risk reversals often preceded big moves in the FX markets. Combining a risk reversals analysis with other technical analysis tools may prove useful in gauging market sentiment in the FX market.

Appendix 1: Regression Results

Appendix 2: Durbin-Watson Test

References

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Beams, Nick, “When the Bretton Woods Systems collapsed,” August 2001.

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Greene, William H, “Econometric Analysis,” Prentice Hall, 3rd edition, 1997.

Henderson, Callum, “Asia Falling—Making Sense of the Asian Crisis and Its Aftermath,” McGraw-Hill, 1998.

Kaufman, Perry J, “Trading Systems and Methods” Wiley, 3rd edition, 1998.

Murphy, John J, “Technical Analysis of the Financial Markets—A comprehensive guide to trading methods and applications,” NYIF 1999.

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Endnotes

1. In the options market, delta is defined as the first-order (derivative) measure of sensitivity to movement in the underlying security. In this research paper, the underlying security is the respective foreign exchange (FX) rate. The 25-delta is the out-of-the-money option quoted by dealers in the FX market. Market participants in the FX options market view the 25-delata options as the standard risk reversal quotation as opposed to other numeric deltas. Since changes in the underlying security are often the primary source of risk in the options market, noticeable changes in the delta may provide some useful directional clues in the FX rate.
2. FX options are quoted in terms of their implied volatility. The implied volatility represents the standard deviation of price movement. Implied volatility is based on an expectation as opposed to a posted value. The more uncertain the outcome of an event is, the more expensive the implied volatility of an option will be. As a result, the implied volatility of an option is usually associated with the riskiness of the underlying security. A high implied volatility rate therefore implies more volatile market conditions and as such, dealers will require a higher risk premium for the underlying security. The calculation of implied volatility is based on; (1) the risk less rate of return; (2) the exercise price of the underlying security; (3) the maturity date; and (4) the price of the option. These four variables go into the Black-Scholes Option Pricing Model (the most popular option pricing model). Movement in any of these variables will affect the price of the FX option. Most option pricing models use all of these four variables to calculate the implied volatility of the FX option. Inherent in any FX option pricing is an implicit estimate of the future volatility of the implied volatility. The implied volatility quotations can therefore provide some impression of which scenario the market is leaning toward. A high probability implies greater risk.
3. The slope of the implied volatility curve may reveal how complacent or nervous the market is concerning future events. For example, a downward sloping implied volatility curve would suggest that dealers are demanding a higher risk premium in the near future as opposed to further out in the future. Aside from demand and supply considerations, this could also indicate that the risk premium surrounding an upcoming event is particularly high. A downward sloping curve could also imply that current market conditions are extremely volatile and unpredictable, and as such, require a risk premium.
4. The factors that affect implied volatility are the riskless rate of return, the exercise price, maturity date and the price of the option. Implied volatility appears in several option pricing models, including the Black-Scholes Option Pricing Model.
5. Kurtosis is based on the size of a distribution’s tails. Distributions with relatively large tails are called “leptokurtic”; those with small tails are called “platykurtic.” A distribution with the same kurtosis as the normal distribution is called “mesokurtic.”
   The following formula can be used to calculate kurtosis:
6. On August 15, 1971, without prior warning to the leaders of the other major capitalist powers, US president Nixon announced in a Sunday evening televised address to the nation that the US was removing the gold backing from the dollar. The commitment by the US to redeem international dollar holdings at the rate of $35 per ounce had formed the central foundation of the post-war international financial system set in place at the Bretton Woods conference of 1944.
7. The Durbin-Watson test statistic is calculated from the OLS estimated residuals êt as:
8. Critical values for Durbin-Watson can be found in the Savin-White tables in the back of most econometrics texts (Savin & White, 1997).
9. Calculates how prices are dispersing around an average value. The two standard deviation ensures that 95% of the price data will fall within the two trading bands. The two standard deviation provides less erratic signals. The draw-back is that there will be considerable fewer signals of currency trend reversals.
10. Note however that this paper’s reference to extreme points cover the sample period after 1996. Risk reversals data are difficult to obtain prior to 1996.
11. Moving Average Convergence/Divergence. Technical analysis term for the crossing of two exponentially smoothed moving averages Source: Investorwords.com
12. The default parameters of 7 and 21 periods for the moving averages were chosen because they appear less erratic than a shorter sample period. A longer sample period would probably omit some valuable signals.