注:本文作者因居留海外,邮寄不便,顺请代为打印稿件. 多谢! 购买力平价，远期外汇升水，及选择性对冲交易风险：跨国界研究 Using PPP Puzzle and Forward Premium Anomaly to Selectively Hedge Transaction Exposure: A Multi-country Perspective (研究领域：金融学) 仇梅, John F. Pinfold， Lawrence C. Rose, 新西兰梅西大学商学院商科系Department of Commerce, Massey University - Albany, Auckland, New Zealand Contact Authors: Mei Qiu Lecturer & PhD Candidate Department of Commerce, Massey University Private Bag 102 904, North Shore MSC, Auckland, New Zealand Ph: 0064-9-414 0800 ext 9242 Fax 0064-9-441 8177 Email: @ John Pinfold Associate Professor, Department of Commerce, Massey University Private Bag 102 904, North Shore MSC, Auckland, New Zealand Ph: 0064-9-414 0800 ext 9463 Fax 0064-9-441 8177 Email: @ Lawrence C. Rose Professor, Department of Commerce, Massey University Private Bag 102 904, North Shore MSC, Auckland, New Zealand Ph: 0064-9-414 0800 ext 9243 Fax 0064-9-441 8177 Email: @
购买力平价，远期外汇升水，及选择性对冲交易风险：跨国界研究 仇梅, John F. Pinfold， Lawrence C. Rose, 新西兰梅西大学商学院商科系 内容提要 实验研究发现，外汇交易汇率经常在短期内偏离购买力平价理论值并随后在比较长的时期内纠正这一偏离，表明币值与理论值的偏差对于预测货币的长期走势具有参考意义。文献还揭示，汇率的实际变动方向经常与远期外汇市场交易汇率的升贴水方向相反。基于以上两个货币市场规律，本文推荐使用远期货币合同对跨国贸易中发生的多头外汇头寸作选择性避险， 即在外汇价格超过购买力平价水平并且远期外汇合同升水交易时进行远期外汇头寸卖出， 以期在预期汇率下跌时提前锁定较好的卖出价。采用八种主要浮动货币在1986年1月31日至2004年8月31日之间的历史数据进行验证，与不避险策略相比，该选择性避险策略有效地提高了现金流回报率水平并降低了回报率的波动性。随机占优分析显示，在56组比较测试中，所倡导的选择性避险策略在44组测试中优于不避险策略。 关键词：外汇交易风险，远期合同避险，策略。
Using PPP Puzzle and Forward Premium Anomaly to Selectively Hedge Transaction Exposure: A Multi-country Perspective By Mei Qiu, John F. Pinfold and Lawrence C. Rose, Department of Commerce, Massey University-Albany, Auckland, New Zealand Abstract Empirical studies observe that currency exchange rates often deviate from PPP theoretical values. Previous literature recognizes that cumulative exchange rate deviations are often corrected over subsequent periods, indicating that cumulative PPP deviations can provide reliable information for predicting future directions of exchange rate movements. Also established in the literature is the exchange market regularity that exchange rates often move to the opposite directions as implied in forward rate premiums or discounts. Based on these empirical findings, a selective forward hedging strategy is proposed for managing transaction exposures of long foreign currency positions. Intuition of the strategy is to avoid predictable depreciations of over-valued currencies and capturing benefits of forward premiums. The strategy calls for hedging when a foreign currency is over-valued and the forward contract is trading at a premium. Exposures are left uncovered otherwise. Examined on daily data of eight free-floating currencies for the period between 1986 and 2004, the strategy has increased domestic cash flow returns and reduced return volatilities compared to unhedged strategy. Superior performance of the proposed strategy is confirmed by analysis of the second order stochastic dominance which finds 44 out of 56 dominance of the proposed strategy over un-hedged strategy. Both components of exchange rate corrections to PPP and the forward premiums contribute to the success of the strategy. The proposed strategy is applicable by international corporations facing long-term exposures to foreign currency transactions. Key Words: Transaction exposure, Forward hedge, Strategy
1. Introduction Desirability of hedging foreign exchange transaction exposure is a subject of considerable debate in international finance. At the time an international corporation enters into a contract of foreign currency denominated transaction in future, the actual amount of domestic cash flow to be paid or received on the payment day is unknown but subject to changes in exchange rate. Corporations may loss significant amount of money if exchange rates moved unfavourably before the transaction is made. There are basically three views on whether transaction exposures should be hedged or not. One view believes that never-hedging is optimal in order to avoid hedging costs that would not be rewarded in an efficient financial market. The second view believes that the exposures should always be hedged to reduce cash flow variability and, consequently, to reduce the cost of financial distresses. The third view is to hedge selectively based on exchange rate forecasts. Under this view, corporations only hedge when they believe that exchange rates will move unfavourably and leave the exposures uncovered otherwise. Corporations taking this view believe that they can forecast the directions of exchange rate movements and profit from selective hedging activities. Empirical studies generally agree that passive hedging does lead to reduced cash flow volatilities，however, often at the cost of reduced cash flows. Some selective hedging strategies, however, have been developed in empirical studies showing ability to improve cash flow levels while reducing cash flow volatilities. These currency hedging strategies are developed upon different economic models, although often applied to the contexts of international portfolio management or currency trading activities. In this study, we introduce a conditional forward hedging strategy based on two robust observations of foreign exchange market regularities: the exchange rate deviations from PPP and the forward premium anomaly.
Empirical studies find that exchange rates often deviate from their PPP equilibrium levels in short term. Cumulative deviations, however, are self-correcting in the long run. Abuaf & Jorion (1990) report that approximately half of the deviations from PPP cumulated over a five year period are reversed over the following three to five years. Given the fact that the exact timing and magnitude of exchange rate movements are extremely hard to predict, predictions on directional movements of future exchange rates are potentially valuable to help making hedging decisions selectively. An equally important observation in literature is the forward premium anomaly. First reported by Fama (1984), the observation is that actual spot rate changes often move to the opposite directions as implied in forward premiums or discounts. The finding is found to be a robust observation by following studies of Bekaert & Hodrick (1993), Froot & Thaler (1990) and Engel (1996). Taking the position of exporters expecting three-month foreign receivables, three conditional hedging strategies are developed in this study. The first strategy, PPP-hedging (PH) requires that corporations only hedge when the spot rate is overvalued 1against PPP. The second strategy, forward-at-premium-hedging (FH), calls for hedging only when forward contract is trading at a premium. The third strategy, PPP & forward-at-premium-hedging (PFH), requires to hedging only when forward rate is trading at a premium and the spot rate is over-valued against PPP. The proposed selective hedging strategies attempt to capture forward premium benefits and avoid predictable depreciation loss associated with over-valued currencies. The rationales are: to protect exposures to over-valued currencies which are likely to depreciate in future, and lock in a more favourable exchange rate when the forward rates are with the corporations. Effectiveness of the proposed hedging strategies are examined against the never-hedging strategy (NH) and the naive always-hedging strategy (AH), from the view points of corporations based in each of the eight free-floating currencies. Both single period cash flow returns and the end-of-period wealth effects are examined using 1 An “or” rule was also tested but the results are not reported here because it did no better job than the “and” rule.
daily data between 1st Jan. 1986 and 31st Aug. 2004. The results can be extended to applications in hedging foreign payable exposures faced by importers, by adjusting positions taken by base countries and foreign countries. All of the three conditional hedging strategies are proved to be beneficial in terms of reducing risk, increasing return and improving risk-adjusted returns. Among them, superior performance of the PFH strategy is the most consistent across the studies. Its improvements over return and risk are of both economical and statistical significance. Over the entire period under study, the proposed hedging strategy have generated excess returns over the never-hedging strategy as high as 45 percent for Switzerland based exporters, and varies between 4 percent and 33 percent for exporters based in other countries. Evaluated using the distribution-free performance measure, the second order stochastic dominance criteria, the results suggest that the proposed hedging strategy outperformed the un-hedged strategy in 44 out of the 56 cases under the study. Both exchange rate corrections to PPP component and the forward premium component contribute to the success of the strategy. The rest of the study is organised as follows: Section 2 provides a review on relevant literature. The three selective hedging strategies are developed in section 3. Section 4 introduced data and research methodology. Test results are reported and discussed in section 5 with conclusions presented in section 6. 2. Literature Review Allayannis & Ofek (2001) claim that hedging by currency derivatives have significantly reduced foreign exchange risk faced by S&P 500 non-financial companies. Hagelin (2003) and Hagelin & Pramborg (2003) report similar evidence observed from Swedish companies. Allayannis & Weston (2001) report that derivative hedging increased large . corporations’ values by an average of percent. Pramborg (2004) confirms that company values are positively related to transaction risk hedging activities.
Smith & Stultz (1985), Nance, Smith & Smithson (1993) and Pramborg (2004) claim that, in practice, most companies indeed hedge their currency exposures. Duangploy, Bakay & Belk (1997) and Prevost, Rose & Miller (2000) find that transaction exposures are often dealt with using money market hedges, among which, currency forward contract is the most popular instrument. The literature, however, provide little evidence on forward hedging efficiencies in terms of cash flow impact in the context of managing transaction exposures. An example is Moosa (2004), who claims that from perspectives of three major developed countries, hedging or not makes no significant difference on managing three-month . payables over a long term. The study shows that even selective hedging using perfect exchange rate forecasts (obtained ex post) can not lead to significant gain compared to the always hedging or never hedging strategy. In related areas of managing currency risk of currency trading and international portfolio diversifications, empirical studies find some positive evidence on efficiencies of hedging selectively using currency forward contracts. Most of the proposed selective hedging strategies are relate to two observations on foreign exchange market regularities: the PPP puzzle and forward premium anomaly. As a fundamental exchange rate determination theory, purchasing power parity has theoretical appeal but is often found to have failed in reality, especially in short terms. Macdonald (1995) literature review, however, claims that exchange rate deviations from PPP are “short lived”. The phenomenon of long term validity of PPP in presence of short-term failure is termed as PPP puzzle, according to Rogoff (1996). Abuaf & Jorion (1990) find that approximately half of the cumulative exchange rate deviations from PPP are corrected after three to five years. Coakley & Fuertes (1997) estimated that the half-lives of corrections to PPP deviations were shorter than three years. Froot & Rogoff’s (1995) reviewed the literature and found that consensus estimates on half-lives of corrections to PPP deviations was about four years for exchange rates among major industrialized countries. Frankel & Rose (1996), Sarno & Taylor (1998), Cheung & Lai (1993), Lothian (1997), Lothian & Taylor (2000) and Fleissig &
Strauss (2000) offer more supportive evidence that exchange rates do revert to PPP equilibrium in the long term. At the same time, validity of the expectations theory has been challenged by the empirical findings that forward rates are often biased in predicting future spot rates. Bekaert & Hodrick (1993) demonstrate that the unbiased forward rate hypothesis is strongly rejected by empirical tests. Hodrick’s (1987, p155) surveyed the 1970s and 1980s empirical studies and claimed that evidence against the unbiasedness hypothesis “appears to be very strong and consistent across currencies, maturities and time periods”. Levy & Lim (1994) observed that in short terms, forward rates tend to underestimate the magnitude of changes of future spot rate in both directions. Moreover, Bilson (1981) and Fama (1984) find that actual changes in spot rates are in opposite directions to what implied in forward premiums or discounts. This observation is termed the forward premium puzzle and is well documented in literature since then. Cumby & Obstfeld (1982) report that forward premiums have generally mis-predicted the directions of future spot rate movements for dollar rates of UK pound, German mark, Swiss franc and Japanese Yen, for the period between 1976 and 1981. Hai, Mark & Wu (1997) find negative coefficients between forward premiums and spot dollar rate changes in pound, franc and yen, using monthly data between 1976 and 1992. Boothe & Longworth (1986) literature review claims that “the empirical regularities are that the future spot rate will move in the direction opposite to that indicated by the forward premium”. Engel (1996) concludes that the unbiasedness of forward rate as predictors of future spot rate have been “”routinely rejected” and that “the forward discount is strongly (negatively) correlated with subsequent changes in the exchange rates”. Enormous evidence suggests that the forward premium anomaly is “a robust finding”, as summarised by Froot & Thaler (1990). The empirical observations of predictive power implied in PPP deviations and forward premiums have found some meaningful applications in currency trading and risk management of international portfolio diversifications.
Bilson (1984) constructed a currency trading strategy based on an exchange rate forecasting model incorporating information contents of exchange rate deviations from PPP and forward rate premiums. Although the model exhibited limited power in forecasting, the trading strategy was found to be profitable at risk-adjusted basis when applied to six major currencies for the period between 1973 and 1982. It seemed that both the forward premium component and the PPP deviation component contributed to the superior performance of the strategy. Eun & Resnick (1988), Eaker & Grant (1990), Glen & Jorion (1993) and Eun & Resnick (1997) assert that forward hedging strategies conditional on forward rate premiums can improve the performances of international equity portfolios. Moery & Simpson (2001a), in extension to Eaker & Grant (1990) study, claim that a hedging strategy conditional on large forward rate premiums can enhance hedging benefits. VanderLinden, Jiang & Hu (2002) and Thorp (2005) provide further evidence on selective hedging efficiencies. Simpson (2004) demonstrates that a conditional currency future contract hedging strategy based on large exchange rate deviations from PPP can outperform the hedging strategy based on future contract premiums. The finding indicates that disparities between exchange rates and their parity levels contain valuable information in making hedging decisions. Morey & Simpson (2001b) report that a selective hedging strategy based on large forward rate premiums have improved international stock portfolio performances. A hedging strategy that only calls for hedging when exchange rates exceed PPP equilibriums have performed well for . investors. These findings provided further evidence that forward premiums and PPP deviations can provide useful information in making hedging decisions. Eun & Resnick (1994), on the other hand, presented mixed evidence on forward hedging efficiencies. They argue that while . investors benefit from forward hedging on currency exposures, Japanese investors gain little. Levy & Lim (1994) provide conflicting evidence on forward hedging efficiencies during two periods of the 1980s, suggesting that benefits from naïve forward hedging strategy may not be
reliable. Soenen & Lindvall (1992), De Roon, Nijman & Werker (1999) and Tezel & McManus (1998), however, present neutral and negative evidence on currency hedging efficiencies. In summary, the literature recognises that exchange rate deviations from PPP provide useful indications on future directions of exchange rate movements. What’s more, empirical studies suggest that movements in exchange rates are often in opposite direction as implied in forward premiums or discounts. The two observations have found profitable applications in currency trading and international portfolio hedging practices. The literature, however, provides little evidence on forward hedging efficiencies in the context of managing transaction exposures. In addition, previous literature has largely ignored the potential values of incorporating information contained in forward premium and exchange deviations from PPP in making hedging decisions for managing transaction exposures. This area of application is interesting because managing transaction exposures has become a constant challenging faced by international corporations under the background of increasing international trading act ivies. This study intends to fill in this gap by providing a new approach to hedge foreign transaction risk, which is more efficient than conventional hedging strategies. 3. Development of Conditional Hedging Strategies Inspired by the two empirical regularities, forward premium anomaly and exchange rate corrections to PPP deviations, three conditional hedging strategies are developed to exploit temporary exchanger rate disparities and forward premium benefits. The strategies are proposed for managing three-month foreign currency receivables. Exchange rates are expressed in terms of units of domestic currency per unit of foreign currency. Conditional Hedging Strategy 1 – PPP-hedging (PH):
Rule 1: Hedge by selling forward a foreign currency when the current spot rate is above the PPP equilibrium rate. Stay unhedged if the current spot rate is lower than the PPP equilibrium rate. This is illustrated in figure 1. Fig. 1 Illustration on PPP-hedging Strategy AUD/NZDPPP Equilibrium RateA$/NZ$ Not Hedge Hedge Time 97 98 99000102 Conditional Hedging Strategy 2 – Forward-at-premium-hedging (FH): Rule 2: Hedge by selling forward a foreign currency if the forward rate is at a premium to the current spot rate. Stay un-hedged otherwise, as illustrated in figure 2. Fig. 2 Illustration on Forward-at-premium-hedging Strategy SF/DM ForwardSF/DMSF/DM Hedge Not Time 8687 Conditional Hedging Strategy 3 – PPP & forward-at-premium-hedging (PFH):
Hedge by selling a foreign currency at the prevailing forward rate if the spot rate is higher than PPP equilibrium and the forward rate is at premium to the spot rate, otherwise, remain un-hedged. Figure 3 explains this strategy by an example. Fig. 3 Illustration of PPP& forward-at-premium -hedging StrategySF/DM ForwardSF/DPPP M SF /DM Hedge Not Hedge 86 87 Effectiveness of the three conditional hedging strategies will be compared with that of the never-hedging strategy in four aspects: percentage change of cash flows to be received in domestic currencies (returns), fluctuations in returns (risk), percentage change of cash flows in domestic currencies relative to return fluctuations (risk-adjusted returns), and the terminal wealth effects accumulated over a long period. Comparisons with the performance of a passive always-hedging strategy will also be presented for reference. Detailed discussions, however, are based on comparisons with the never-hedging strategy as will be discussed, although the always-hedging strategy often reduces cash flow fluctuations, reductions in risk are achieved at costs of reduced cash flows. 4. Data and Methodology For eight developed countries, namely Australia, Canada, New Zealand, Germany, Japan, Switzerland, . and the , three types of data are applied in this study: spot exchange rates, three-month forward exchange rates, and CPI data. For the period
2stbetween 1st Jan., 1986 and 31 Aug., 2004, spot and forward dollar rates are downloaded at daily intervals from Datastream. Exchange rates for German mark after 1st Jan. 1999 are converted from euro rates by multiplying the conversion rate of as announced by the council of the European Union. Indices of dollar rates for the seven currencies are graphed in appendix 1. Cross rates between any two currencies are derived from their dollar rates. To allow for five-year estimation period required by PPP rate estimation, longer history of spot rates and CPI data for five currencies with longer histories of floating are required to cover the period between 1st Jan., 1981 and 31st Dec., 1985. The extra exchange rate data are collected from the database retrieval system provided on the website of the University Of British Columbia Sauder School Of Business Pacific Exchange Rate 3Services. ststCPI data for the extended period between 1 Jan., 1981 and 31 Aug., 2004 are obtained at monthly intervals from Datastream, except for Australia. Australian CPI 4data are collected from the website of the Reserve Bank of Australia. Data for New Zealand CPI are only available at the quarterly interval and the monthly data are acquired by interpolating the quarterly data linearly assuming that monthly CPI data remain the same throughout the month. At time t, exchange rate deviation from PPP equilibrium rate (DS) can be estimated tby equation (1). DS=S−SP (1) tttwhere S represents the actual exchange rate at time t and SP is the PPP equilibrium ttrate estimated over a five-year period using equation (2): 2 This starting date is chosen because forward exchange rate data are only available since this date from Datastream. 3 URL for the database is: 4 We acknowledge Roger Hall at the Reserve Bank of Australia for kindly directing us to this database.
*CPI∗CPItt−1 PS=S∗ (2) tt−1*CPI∗CPIt−1tWhere PS represent the estimated PPP equilibrium value and S is the spot rate in tt-1the last term, expressed in terms of units of domestic currency per unit of foreign currency ; i and i* are the inflation rates of the home and foreign countries, respectively. We use daily data to mitigate potential bias of test results induced by small sample problem and extraordinary influence of unusual end-of-month or end-of-quarter fluctuations in foreign exchange market. Total samples include 1,899 contracts for Australian and New Zealand related contracts and 4,566 contracts otherwise. To simplify discussions, positions are taken as domestic exporters expecting transaction of three-month receivables denominated in foreign currencies. It is assumed that each strategy starts with 1,000 units of domestic currency. Where decisions are made to hedge, hedge ratios are set to unity. Cash flows from the previous terms are assumed to roll forward to the next in full amount. Three-month single period percentage changes in cash flows are also obtained for comparing single period returns of the strategies. Risk-adjusted returns are measured by reward-to-risk ratios (RTR), as calculated by equation (3): RTR=R/SD (3) Where R is an average return and SD stand for standard deviations of return distributions. End-of-period wealth effects of the strategies are evaluated for cumulative hedging effects. In calculating end-of-period wealth, daily cash flows happened within the quarter are averaged to alleviate influence of extraordinary data points. The path of quarterly cash flows are presented as well to show strategy effects accumulating over time. For corporations based in each of the eight nations, hedging positions are taken across seven foreign currencies; provide a total number of 56 studies for each
comparison. Taking a multi-country perspective is expected to be able to avoid reaching conclusions subject to base currency biases. Transaction costs and tax 5implications are ignored. Efficacy of a hedging strategy is evaluated in terms of average return, risk and risk-adjusted return, compared with each other as well as against the unhedged strategy and a passive-hedging strategy. Analysis based on the second order stochastic dominance criteria is provided to complement the mean-variance analysis. It is argued that although combination of mean and variance can provide complete description on return series with normal distribution, it may not be true for series with undesired distributions. For skewed data distribution (as evident in this study), results derived from mean and variance analysis may be misleading. The second order stochastic dominance (SSD), on the other hand, calls no restrictions on return distributions and only makes assumptions on non-satiation and risk-aversion. The stochastic dominance approach to risky decisions is developed by, among the others, Hadar & Russell (1969) and Hanoch & Levy (1969), and has seen significant theoretical developments in recent years by, among the others, Barrett & Donald (2003). In financial studies, the SD framework has been applied in selecting investment strategies and evaluating portfolio performances, as demonstrated by Bawa, Bodurtha Jr., James, Rao & Suri (1985) and Post (2003). The most appealing feature of the framework is its nonparametric property due to the fact that investment preference is assessed on entire distribution of economic outcomes. This feature makes the SD assessments an appropriate complement to mean-variance analysis in this study. The SSD criteria are briefly introduced as follows. For more detailed information, Levy (1998) provides an excellent comprehensive reference. 5 Morey and Simpson (2001b) estimated that one-half of the average bid-ask spread on monthly 3-month forward contracts for five major US dollar exchange rates between Jan 1991 and Dec 1998 ranged between and . Jorion & Khoury (1996, pp 186) stated that the spread between bid and ask quotations from the roward dealers was around percent for large transactions above $1 million.
For an empirical return sample with size N, assume equal opportunity; define P(x) as the probability of having a return of x, P(X) is the cumulative probability of having returns no greater than x, then: P(x) = 1/N (4) P(X) = P(X ≤ x) = P(x) (5) ∑X≤xSince each return has an opportunity of (1/N), P(X) is effectively the proportion of returns that have values no greater than x in the sample. For two empirical return series A & B, with cumulative distribution functions F(x) and G(x), F dominates G by the second order stochastic dominance (denoted as (A) SSD (B)) if and only if the following two conditions are satisfied: Condition 1 [G(x)−F(x)]≥0 (6) ∑X≤xCondition 2: There is at least one x value that (6) function is strictly greater than zero. Figure 4 provides a graphical illustration on the SSD concept. Fig. 4 Illustrations on Second Order Stochastic Dominance BAReturn 40 30 20 10 0 -10 Cumulative Probability -20 -30
For discrete empirical return data series A & B with the same length of N, condition (6) is equivalent to the following condition: kk(x)−(x)≥0 (7) ∑Ai∑Bii=1i=1Where i & k can take any value between 1 and N and the return series of A & B are sorted in ascending order. The intuition is that one is more likely to get a higher return from A than from B, if (A)SSD(B). Although calculations and discussions of this study are based on the assumption of exporters managing foreign receivables, the conclusions can be equally applied to importers managing foreign payables. To illustrate this, think about company A which is an Australian base exporter expecting receivables in Canadian dollars in three months’ time; and company B which is a Canada based importer planning to pay Australian dollar bills in three months’ time. Under both of the scenarios, the businesses need to exchange Canadian dollar cash for Australian dollars, therefore, company A and B have essentially the same positions. 5. Findings and Discussions Research findings are presented and discussed in three parts: (1) single-period return analysis, including mean-variance analysis and stochastic dominance analysis; (2) cumulative long-term cash flow effect evaluations; and (3) long-term end-of-period wealth effect analysis. Mean-variance Single-period Return Analysis Annualised single period returns of five hedging strategies are presented in appendix 2, tables - , together with return volatilities and reward-to-risk (RTR) ratios, the overall measurements on strategy performances. Appendix 3 reports statistics on return distributions.
Return, risk and risk-adjusted return on cash flows obtained under the three conditional hedging strategies are compared to those from the never-hedging strategy. Table 1 reports percentage rate of a conditional hedging strategy achieved higher average single period returns than the unhedged strategy. Table 2 reports excess returns each conditional hedging strategy obtained on top of that of the unhedged strategy. Table 1 Performances of Conditional Hedging Strategies against Unhedged Strategy The chance that a conditional hedging strategy beat the never-hedging strategy is reported in percentage form. Total number of comparisons is 56. . “NH” stands for the never-hedging strategy, “PH” refers to the PPP-hedging strategy, “FH” denotes for the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. The 66 percent success rate obtained for the PH strategy means that 66 percent of 56 performance comparisons suggest the PH strategy outperformed the NH strategy in terms of higher returns. StrategyPHFHPFHPercentage chance of return improvement 66% 52% 84% Percentage chance of statistically significant return 55% 38% 57% improvement (at the 5% level) Percentage chance of risk-reduction 100% 100% 100% Percentage chance of improvement in risk-adjusted returns 77% 56% 89% Table 2 Hedging strategy Excess Returns over the Never-hedging Strategy Excess return (ER) is calculated by subtracting average return fo the never-hedging strategy from the average return of a conditional hedging strategy, expressed in terms of percentage annualized returns. For each base currency, excess returns from hedging each of seven foreign currencies are averaged and reported. “PH” refers to the PPP-hedging strategy, “FH” denotes for the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. Strategy PHFH PFH ER ER ER A$ Based C$ Based DM Based NZ$ Based SF Based UK£ Based Yen Based US$ Based
Results presented in tables – of appendix 2 indicate that, compared with the never-hedging strategy, the always-hedging strategy always successful in reducing return volatilities, however, often at the cost of reduced returns. This finding agrees with Morey & Simpson (2001b). Refer to table 1, the three conditional hedging strategies can improve single period returns of the never-hedging strategy. Returns obtained from the PPP & forward-at-premium-hedging (PFH) strategy are higher than that from the never-hedging strategy 84 percent of the cases under study, or for 47 out of the 56 cases under this study. The PPP-hedging (PH) strategy improved returns 66 percent of the cases studied and the forward-at-premium-hedging (FH) strategy obtained higher returns 52 percent of the cases under study. The results indicate that both the FH strategy and the PH strategy can improve cash flow returns, however, not as consistent as the PFH strategy when viewed across the samples. The above findings are in sharp contrast to that of Moosa (2004b), which claims irrelevancy of forward hedging even with perfect predictions of exchange rates. We replicated Moosa tests and find that although the cash flows from hedged and unhedged strategies exhibit no significant difference; percentage differences between the two strategy proceeds average to is as high as percent, which is statistically significantly different from zero. We argue that since our study covers a much broader sample over a much longer period, the results of this study should be more reliable. In terms of risk reduction effects, all of the three conditional hedging strategies have reduced the risk associated with single period return fluctuations, as compared to the never-hedging strategy. Evaluated by risk-adjusted returns, the PFH strategy has outperformed the never-hedging strategy 89 percent of the cases under study. In other words, it only failed in 6 out of the 56 comparisons. The PH strategy and FH strategy have reduced return volatilities 77 percent and 56 percent, respectively, of the comparisons.
Refer to table 2, for exporters based in seven out of the eight countries under study; the PFH strategy has realized between to percent higher returns than the unhedged strategy. The strategy, however, has failed in the . based study. The PH strategy obtained between to percent excess returns over the never-hedging strategy for investors based in six of the eight countries studied, with two exceptions of Japan and . based studies. Finally, the FH strategy outperformed the unhedged strategy from the view points of five countries under study. Regarding the performance of the always-hedging strategy, although it greatly reduced risks of returns, the strategy has realized substantially lower returns as the price. In summary, the PPP & forward-at-premium-hedging strategy is proved to be able to generate higher single-period returns than the unhedged strategy. Further, this strategy has reduced return volatilities, resulting in superior performance at risk-adjusted level. Both PPP deviation component and forward premium component contribute to the superior performance of the PFH strategy, although the PPP deviation component seems to have contributed more. On superior performance of the PFH strategy, the most controversial evidence comes from . based study. As reported in table of appendix 2, the PFH strategy has realized significantly less returns than the never-hedging strategy in hedging Deutsche mark, Swiss franc and Japanese yen. The exceptions happen probably due to the fact that . dollar experienced continuous downward adjustments against all three currencies in 1980s and 1990s, as evident from the dollar rate graphs presented in appendix 1. Our finding on this point is consistent with Levy & Lim (1994), who claims that the unhedged strategy outperformed hedging strategies when the domestic currency of . was experiencing depreciation. The observation may be explained by Levy & Lim’s (1994) observation that forward rate generally underestimated domestic currency depreciations, under which circumstance; leaving foreign receivables uncovered would do the best in capturing benefits from depreciations of home currencies.
It is observed that, from appendix 3, most of the return series under the study are non-normally distributed. Nevertheless, the fact that return distributions of the never-hedging strategy are often more left-skewed than those obtained under the conditional hedging strategies indicates that our results discussed above are conservative and remains valid after taking account of data distribution characteristics. T-test results on equality between risk, returns and risk-adjusted returns of a conditional hedging strategy and the never-hedging strategy are presented in table 3. The tests have been carried out on two different samples: one sample including and the other excluding the . based hedging activities. Table 3 Summary Statistics on Single-period Risk / Return Comparisons Return, risk and reward-to-risk ratios are calculated by taking averages of hedging outcomes across currencies. Panel A reports the results for the . perspective inclusive study and panel B presents the results with the . view point excluded. Reported t-test statistics are p-values from t-tests on equalities of economic series between a particular strategy and the never-hedging strategy. Panel A – . Perspective Included NH AHPH FHPFH Returns t-test stat. deviations Mean t-teststat. -to-risk ratio Mean t-teststat. Panel B – . Perspective Excluded Returns NH AH PH FH PFH Mean -teststat. Standard deviations t-test stat. -to-risk ratio Mean t-teststat.
Risk-adjusted returns from the always-hedging strategy are not significantly different from that of the never-hedging strategy from the statistical point of view (at the 10 percent significance level). Among the three conditional-hedging strategies, the PFH strategy has generated higher return than the never-hedging strategy, with both economic and statistical significance (at the ten percent level). The . inclusive studies suggests that the strategy achieved percent average return, as opposed to the percent return of the unhedged strategy, indicating an average percent annual access return. For the . exclusive studies, the PFH strategy obtained percent average return, earning an extra over the percent average return realized by the unhedged strategy. Returns from the other two conditional hedging strategies, however, are not statistically significantly different from that of the never-hedging strategy. The two strategies, however, have significantly reduced return volatilities, resulting in superior performances in terms of higher risk-adjusted returns. The overall evidence of t-test results confirms that the PFH strategy significantly improved hedging efficiencies in terms of increased returns, reduced risks and improved risk-adjusted returns. Therefore, we recommend this strategy to be applied in managing foreign transaction currency risk. Both PPP component and forward premium component contribute to the superior performance of the PFH strategy, although the PPP component seems to be more informative, confirming the Bilson (1984) finding. Assessing Strategy Performances under Stochastic Dominance Rules Apply the second order stochastic dominance criteria to compare cash flow returns obtained from the conditional hedging strategies and the never-hedging strategy. Each comparison has paired samples of 56 return series, obtained from hedging activities
on seven currencies taking the view points of each of the eight countries. The numbers of comparisons that one strategy dominates the other are reported in table 4. From table 4, the conditional hedging strategies PH, FH and PFH are found to dominate the never-hedging strategy in 36, 29 and 44, respectively, out of the 56 series under study. On the other hand, the unhedged strategy never dominates any of the three conditional hedging strategies. The evidence clearly indicates that all of the three conditional hedging strategies have performed better than the never-hedging strategy. Table 4 Number of Comparisons Showing Stochastic Dominance Reported are the numbers of comparisons that one strategy stochastically dominates (in the second order) the other, following the criteria discussed in section 4. There are 56 comparisons for each pair of strategies. Reported numbers should be interpreted as: for 56 comparisons, X strategy stochastically dominates Y strategy in the second order sense. The names of X strategies are listed in the first column of the table while the first row gives Y strategy names. Total = 56 NH PH FH PFH NH-000PH 36 - 14 22 FH290-18PFH 44 0 1 - Compared with each other among the three conditional hedging strategies, the PFH strategy is sometimes dominated by the PH or the FH strategy, but the reverse dominance rarely happens. Nevertheless, the PFH strategy is recommended by us because it has outperformed the unhedged strategy most consistently across currencies from different countries’ perspectives. The dominance analysis results confirm that of the mean-variance analysis. Cumulative Long-term Performance Analysis For large multinational corporations dealing with ongoing foreign transactions over the long term, it would be interesting to see what influence that the conditional hedging strategies may make on the businesses’ wealth over time. In this section, we analyse cumulative wealth effects of the hedging strategies.
End-of-period wealth obtained from each hedging strategies are obtained by taking average of daily cash flows occurred in the last quarter. Results are shown in table 5. Table 5 End-of-period Wealth of Different Hedging Strategies For each hedging strategy, average cash flows received in the last quarter are reported in terms of domestic values. The strategies start with 1,000 units of domestic currencies and roll forward 30 quarters for Australia and New Zealand related transactions or roll forward 72 quarters for other currencies. In comparing strategy performances, the highest end-of-period wealth are highlighted with “*”. Where cash flows obtained under PFH strategy are no less than that from the unhedged strategy, the values are highlighted with bold characters. Base Foreign A$ C$ DM NZ$ SF UKP Yen US$ Country Currency NH 1113 1109 1014 1228 1208 1186 1084 AH 1089 1141 942 1311 983 1432 1085 Australia PH 1265 1453*1135*1646*1128 1563 1016 FH 1136 1191 1018 1282 1267 1466 1599*PFH 1309*1427 1071 1617 1324* 1596* 1497 NH 899 1398 912 1499 1212 1659 967 AH 919 1275 865 1629 785 2002 1207 Canada PH 1044* 1820 1030*2146 1031 2836* 1017 FH 939 1829*992 1995 1410* 2016 1482*PFH 906 1828 935 2274*1378 2835 1246 NH 902 716 914 1073 868 1186 692 AH 876 787 825 1282 617 1575 950 Germany PH 1149* 1022 1068*1382*905 2070 773 FH 942 1027* 890 1277 1007* 1725 1445*PFH 958 1023 917 1333 975 2124* 1040 NH 1018 1097 1094 1211 1192 1170 1070 AH 1062 1156 1213 1392 1044 1521 1152 New PH 1172* 1305 1416* 1715*1260 1727 1261 Zealand FH 1083 1257 1180 1366 1131 1496 1351 PFH 1139 1384*1375 1689 1284* 1732* 1456* NH 815 667 932 826 809 1106 645 AH 763 615 783 718 482 1230 742 Switzerland PH 1023* 880* 1007*1017* 775 1749 744 FH 796 818 930 810 816* 1567 819* PFH 811 773 964 822 810 2013* 761 NH 828 825 1153 839 1237 1369 798 AH 1018 1275 1624 958 2076 2552* 1539 . PH 949 1080 1700 1013*1981 2194 1353 FH 1066* 1482*1881*909 2092* 2528 1655*PFH 908 1107 1754 891 1993 2194 1400
Table 5 (cont’) End-of-period Wealth of Different Hedging Strategies For each hedging strategy, average cash flows received in the last quarter are reported in terms of domestic values. The strategies start with 1,000 units of domestic currencies and roll forward 30 quarters for Australia and New Zealand related transactions or roll forward 72 quarters for other currencies. In comparing strategy performances, the highest end-of-period wealth are highlighted with “*”. Where cash flows obtained under PFH strategy are no less than that from the unhedged strategy, the values are highlighted with bold characters. Base Foreign A$ C$ DM NZ$ SF UKP Yen US$ Country Currency NH 843 604 844 855 906 733* 585 AH 699 500 637 658 814 392 603 Japan PH 921* 854* 1111* 971* 1286* 632 604 FH 863 609 927 841 1153 726 734* PFH 841 609 898 838 1007 726 664 NH 923 1034 1446 935 1551 1254 1717 AH 922 829 1056 868 1349 650 1659 . PH 865 871 1180 1023 1556 1102 1717 FH 1360* 1270* 2194* 1097* 1711* 1349* 2067* PFH 923 1036 1624 950 1674 1298 1881 Refer to table 5, the end-of-period cash flows obtained from the unhedged strategy are higher than that from the PFH strategy in only five out of the 56 cases under study. Under most of the conditions, the selective hedging strategies of PH and FH have realized the greatest end-of-period wealth among the five strategies under study. Nevertheless, the PFH strategy seems to have outperformed the unhedged strategy most consistently. Special attention should be addressed to hedging effects on managing Japan and Switzerland based foreign transactions. The results show that while PFH strategy has ended up with greater wealth in managing some of the currencies, but failed to beat the unhedged strategy in other currencies. On the other hand, the strategy incorporating only PPP deviations has performed especially well under these scenarios. Note that currencies of both countries have appreciated significantly against the other currencies over the last two decades. The evidence indicates that exchange rate deviations from equilibriums are useful in predicting currency depreciations. For corporations expecting transactions equally spread among seven foreign currencies, cash flows to be received at the end of studied period can be obtained by
taking averages of the figures in table 5 across currencies from a particular country’s perspective. Results are presented in table 6. Table 6 Strategy End-of-period Wealth across Currencies For each hedging strategy, the end-of-period wealth under different hedging strategies is obtained by taking averages across seven foreign currencies taking stand points of particular countries. From each country’s perspective, the highest value is highlighted by “*”. Where a strategy beats the never-hedging strategy, the values are highlighted with bold numbers. The last row presents excess wealth created by the PFH strategy over the never-hedging strategy, expressed in percentage terms. Base Country Hedging New Strategy AustraliaCanada . Japan . ZldNH 1130 1388 904 1151 827 1004 760 1261 AH 1132 1172 989 1210 765 1577 618 1050 PH 1289 1445 1195* 1441 1025* 1462 916* 1191 FH 1268 1408 1182 1250 937 1653* 830 1570* PFH 1380* 1515* 1191 1464* 993 1459 793 1335 Excess 22% 33% 32% 27% 20% 45% 4% 6% From table 6, the FH strategy and PFH strategy have generated significantly greater wealth for corporations from view points of any countries, as compared with the unhedged strategy. The PH strategy achieved similar results, except for the . based study. Except for the Japan and the . based studies, the wealth created by the PFH strategy exceed that of the never-hedging strategy between 20 percent and 45 percent over the entire period. The best performed strategies from different countries’ perspectives vary among the three selective hedging strategies. The PFH strategy performed the best for managing foreign receivables from the perspective of Australia, Canada and New Zealand. From the view points of Japan and Switzerland based exporters, the PH strategy generally performed the best. While the FH strategy performed the best for . and . based studies, the overall results suggest that the PFH strategy is the one that has performed consistently well across countries, both PPP deviations and forward premiums attribute to the hedging efficiencies.
In order to have a clearer idea on hedging effects accumulated over time; average quarterly cash flows under the strategies are plotted in figures 5-11. For succinctness, only graphs for exporters based in Australia are presented. Fig. 5 Average Quarterly Cash FlowsFig. 6 Average Quarterly Cash Flows - A$ Based C$ Hedges - A$ Based Deutsche mark Hedges NH AH PHNHAH PH FH PFH FHPFH A$A$ 1250 13501100 1150950950 Year Year979899000102 03 04 97 98 99 00 01 02 03 04 Fig. 7 Average Quarterly Cash FlowsFig. 8 Average Quarterly Cash Flows -A$ Based Japanese yen Hedges - A$ Based Swiss franc Hedges NHAH PH NH AH PHFHPFH FH PFH A$ A$16001600 14001400 12001200 10001000 YearYear 979899000102 03 04 97 98 99 00 01 02 03 04 Average Quarterly Cash Flows Average Quarterly Cash Flows-A$ Based UK pound Hedges - A$ Based NZ$ Hedges NHAH PH NH AH PHFHPFH FH PFH A$ A$1150 12501050 1100950 950850 YearYear979899000102 03 04 97 98 99 00 01 02 03 04
Fig. 11 Average Quarterly Cash Flows - A$ Based US$ Hedges NHAH PHFHPFH A$ 1500 1300 1100 900 Year97 98 99 0001 02 03 04 The graphs clearly show that across the currencies under study, the PFH strategy consistently achieved superior performances both in terms cash flow levels and cash flow stabilities. 6. Conclusions Three conditional hedging strategies are developed in this study intending to capture information contents of exchange rate deviations from PPP and to take advantages of forward rate premiums. Efficacies of the strategies are examined against the never-hedging strategy for hedging three-month exposures to foreign receivables taking perspectives of eight developed countries. For the period between 1986 and 2004, the passive hedging strategy has often reduced return volatilities at the costs of substantially reduced returns. The PPP & forward-at-premium-hedging strategy is found to have performed consistently better than the unhedged strategy across the currencies from different countries view points. Superior performances of the PFH strategy are demonstrated by increased single-period returns, reduced return volatilities, improved risk-adjusted returns and substantially higher end-of-period cash flows. Average annualised single period returns under the PFH strategy exceed that of the never hedging strategy to percent for exporters based in seven countries. Exception is observed for the . based study.
The conditional hedging strategy based on forward premium anomaly alone has generally outperformed the unhedged strategy as well, however, mainly in terms of risk reductions. Improvements over single-period returns under the FH strategy, however, are limited. Another conditional hedging strategy based solely on observations of exchange rate deviations from PPP has also outperformed the unhedged strategy for corporations based in six out of the eight countries under study. For exporters based in countries other than Japan and the ., the PH strategy has offered benefits of both risk reduction and return improvement. It is noteworthy that for exporters based in Switzerland and Japan, two countries which currencies have experienced continuing appreciation against the other countries, the PPP-hedging strategy often appears to be the best strategy. This evidence indicates that the PPP-deviation rule is more capable of picking up long-lasting trends of exchange rate movements than the forward premium rule. The second order stochastic dominance analysis results confirm the above findings that the selective hedging strategy combining both PPP deviation and forward premium information dominates the never-hedging strategy in 79 percent of comparisons (44 out of 56 comparisons). The PPP-hedging and forward-at-premium hedging strategies sometimes dominate the strategy of combined conditions, however, both strategies failed to dominate the unhedged strategy as consistently as the PFH strategy does. Consequently, the PPP & forward-at-premium-hedging strategy is recommended for managing foreign transaction exposures. The overall evidence indicates that both information contents of exchange rate deviations from PPP and forward premiums contribute to the success of proposed selective forward hedging strategy. The strategy, developed from robust observations of exchange market regularities, is theoretically intuitive and easy to carry out in
practice. It is appealing to international corporations wishing to manage expected foreign receivables more efficiently under the current floating exchange rate system. The results can be generalised to situations of importers exposed to foreign payables. For dealing with occasional large foreign currency transactions, or dealing with a foreign currency showing long-term trends of appreciation, however, the strategy should be taken with caution. One possible extension to this study is the hedging effects of managing different terms’ exchange exposures. The study can also be extended to use other derivative products as hedging vehicles. Further, adding more hedging criteria for hedging decision, such as filter rules, interest rate differentials, may also improve hedging performance. It would also be interesting to see possible applications of the proposed hedging strategy in managing currency risk of internationally diversified portfolios.
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Appendix 1 Foreign Exchange Rates (Index) Jan 1986-Aug 2004 Figure A US dollar Exchange Rates (Indices)A$DMYenUK₤Index2402202001801601401201008060Year86889092949698000204 Figure B US dollar Exchange Rates (Indices)C$NZ$SFIndex1901701501301109070Year86889092949698000204
Appendix 2 Mean-Variance Single-Period-Return Analysis Statistics Table Mean-Variance Return Analysis Statistics- Australia Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. A$ NH AH PH FH PFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test C$ DM NZD SF UK£ Yen USD Percentage that means are no less than that of the NH strategy % (%) % (%) 100% (%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 100% 100% 100% Percentage that returns-per-unit-of-risk are no less than that of %%100%the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 36
Table Mean-Variance Return Analysis Statistics - Canada Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. C$ NHAHPHFHPFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test A$ ** DM NZD SF UK£ Yen USD Percentage that means are no less than that of the NH strategy % (%) % (%) 100% (%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 100% 100% 100% Percentage that returns-per-unit-of-risk are no less than that of %100%100%the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 37
Table Mean-Variance Return Analysis Statistics - German Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. DM NHAHPHFHPFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test A$ C$ NZD SF UK£ Yen USD Percentage that means are no less than that of the NH strategy % (%) % (%) 100% (%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 7 - 100% 7 - 100% 7 - 100% Percentage that returns-per-unit-of-risk are no less than that of 5 – % 6 – % 7 - 100% the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 38
Table Mean-Variance Return Analysis Statistics – New Zealand Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. NZ$ NHAHPHFHPFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test A$ C$ DM SF UK£ Yen USD Percentage that means are no less than that of the NH strategy % (%) % (0%) % (%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 100% 100% 100% Percentage that returns-per-unit-of-risk are no less than that of 100%%100%the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 39
Table Mean-Variance Return Analysis Statistics - Switzerland Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. SF NHAHPHFHPFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test A$ C$ DM NZD UK£ Yen USD Percentage that means are no less than that of the NH strategy % (%) % (%) % (%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 100% 100% 100% Percentage that returns-per-unit-of-risk are no less than that of % % % the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 40
Table Mean-Variance Return Analysis Statistics – UK Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. UK£ NHAHPHFHPFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test A$ C$ DM NZD SF Yen USD Percentage that means are no less than that of the NH strategy 100% (100%) 100% (%) 100% (%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 100% 100% 100% Percentage that returns-per-unit-of-risk are no less than that of 100%100%100%the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 41
Table Mean-Variance Return Analysis Statistics - Japan Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. Yen NHAHPHFHPFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test A$ C$ DM NZD SF UK£ USD Percentage that means are no less than that of the NH strategy % (%) % (%) % (%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 100% 100% 100% Percentage that returns-per-unit-of-risk are no less than that of %%%the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 42
Table Mean-Variance Return Analysis Statistics - US Based “NH” stands for the never-hedging strategy, “AH” represent the always-hedging strategy, “PH” denotes the PPP-hedging strategy, “FH” refers to the forward-at-premium-hedging strategy and “PFH” stands for the PPP & forward-at-premium-hedging strategy. “Mean” stands for average returns, annualized and expressed in percentage terms. “Std.” is a risk representative measured by standard deviation of returns. “RTR” is the short term for reward-to-risk ratio, a combined measure of risk-return trade-off. P-values are reported for t-tests with null hypothesis that a strategy has an equal mean as the NH strategy. Where a strategy has a mean return greater than that of the NH strategy, the mean is highlighted and relevant t-test statistics is also highlighted if the difference in mean is statistically significant at 10% level. US$ NHAHPHFHPFH Based Mean Std. RPR Mean Std. RPR Mean Std. RPR t-test Mean Std. RPR t-test Mean Std. RPR t-test A$ C$ DM NZD SF UK£ Yen Percentage that means are no less than that of the NH strategy % (0%) % (%) % (0%) (percentage that are statistically significant at 5% level) percentage that risks are no greater than that of the NH strategy 100% 100% 100% Percentage that returns-per-unit-of-risk are no less than that of %100%%the NH strategy Note: The numbers denoted with a “*” sign which are return-per-unit-of-risks, these relative values of these two numbers seem not make sense where the smaller value was generated from a bigger numerator while the denominators are the same. This is a rounding problem. 43
Appendix 3 Statistics on Skewness of Return Distributions under the Hedging Strategies Base Cur./ Strategy Hedged Currencies A$ Based C$ DM NZ$ SF UK£ Yen US$ NH PH FH PFH C$ Based A$ DM NZ$ SF UK£ Yen US$ NH PH FH PFH DM Based A$ C$ NZ$ SF UK£ Yen US$ NH PH NZ$ Based A$ C$ DM SF UK£ Yen US$ NH PH FH PFH SF Based A$ C$ DM NZD UK£ Yen US$ NH PH FH PFH UK £ Based A$ C$ DM NZD SF Yen US$ NH PH FH PFH Yen Based A$ C$ DM NZD SF UK£ US$ NH PH FH PFH US$ Based A$ C$ NZ$ DM SF UK£ Yen NH PH FH PFH Note: The Jarque-Bera normality tests on the return series have been done but detailed results were omitted here. The results indicate that almost all of the series are not normally distributed at 1 percent significance level. The only exception is the return distributions under the PPP-Hedging strategy for UK based Australian dollar hedges. 44
