1. Paper written by: Piet Sercu, Martina Vandebroek, Xueping Wu Presentation made by: Pavla Bláhová, Tereza Sklenářová, Zdeněk Sýkora, Tereza Májková

2. Outline Theoretical background Previous results The data Regression tests of UIP A trading-rule test Explaining the forward bias Conclusion Related literature/papers Contact information 2

3. Theoretical background COVERED INTEREST RATE PARITY (CIP) For no-arbitrage condition to hold: Works with forward rate 3

4. Theoretical background UNCOVERED INTEREST RATE PARITY (UIP) Uncovered = works with future spot price E( ) For no-arbitrage condition to hold: 4

5. Theoretical background UNCOVERED INTEREST RATE PARITY (UIP) Possible approximation (Feenstra & Taylor, 2008): “home interest rate must be equal to the foreign i. r. plus the expected rate of depreciation of the home currency“ 5

6. Theoretical background By combining previous equations we get:  This means that the forward rate should be an unbiased estimator of the future spot rate 6

7. Previous Results CIP is empirically proven, but this relationship: usually does not hold   there is a space for forward premium Why? Missing variable (risk premium) with large variation over time X small expected profits? Connecting variables to USD? 7

8. The data 1985 – 1998 weekly changes in exch. rates against DEM BEF DKK core ERM members FRF NLG CHF ITL informally associated to ERM GBP USD CAD other currencies JPY 8

9. Predictability in intra-European exchange rates (1/2) A slight autocorrelation of exchange rate changes (against the USD) leads to profitable momentum- based trading results Large cross-correlations among ERM-member rates as a result of narrow fluctuation band A substantial predictability in both daily and weekly exchange rate changes 9

10. Predictability in intra-European exchange rates (2/2) 10

11. Regression tests of UIP Standard tests (1/2) Based on the UIP, hypothesis, we expect that K0=0 and K1=1 In case of this database (10 currencies, 13 years), K1=0.57 When using a larger database, K1 is usually closer to unity -> static buy-and-hold strategies should have similar payoffs accross currencies in the long run 11

12. Regression tests of UIP Standard tests (2/2) Poor results in case of the slope coefficient K1 (bizzare size of the estimates between 1992-1994, negative sign in the other two subsamples) Puzzling significance of the slope coefficient K2 -> the first-order autocorrelation among ERM members is still present (in spite of adding the forward premium as a regressor) 12

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15. Regression tests of UIP Tests on “extreme” observations Based on the expectation that the expected changes of observations taken from subsamples with large forward premium should be unusually large as well The results are weekly in line with the hypothesis 15

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17. Introducing the trading rule Mid-summary 1) Intra-ERM rates are predictable (to a non-trivial extend) 2) One-week interest rates do not pick this up  Average returns from trading must be positive (at least before transaction costs) The question is: Are they? 17

18. Solution = The trading rule Show that simple (linear) trading rule provides information with clear economic significance (More sophisticated rules can perform much better) 18

19. The trading rule How is it made Daily trading assumed We know: European exchange rates against DEM have negative first- and second-order autocorrelation What needs to be found: linear trading rule that tries to measure potential gains from what we know DEM is taken as home currency How is the rule made: Estimate first- and second-order partial correlation coefficients (using 2 years of past data). These estimates are updated using the most recent 2-year sample. 19

20. The trading rule Predicting net return against DEM (s t – F ͡ P t-1 ) = ρ -1 (s t-1 – FP t-2 ) + ρ -2 (s t-2 – FP t-3 ) s t = percentage change from t-1 to t in the exchange rate against DEM F ͡ P t-1 = forward premium at t-1 for delivery in t φ = pre selected cut off of net return (filter) i. (s t – F ͡ P t-1 ) > φ => buy FX ii. (s t – F ͡ P t-1 ) sell FX 20

21. The trading rule What to do with the predicted return? Pooled (buying and selling possible) i. (s t – F ͡ P t-1 ) > φ => Buy FX => go long in FX and short in DEM ii. (s t – F ͡ P t-1 ) Sell FX => go long in DEM and short in FX iii. - φ No signal => do nothing Buy: only long FX is allowed i. (s t – F ͡ P t-1 ) > φ => Buy FX => go long in FX and short in DEM ii. (s t – F ͡ P t-1 ) do nothing Sell: only short FX allowed (s t – F ͡ P t-1 ) Sell FX => go long in DEM and short in FX (s t – F ͡ P t-1 ) > - φ => do nothing 21

22. The trading rule Net return of the pooled strategy Returns for long (R A,t …assets) and short (R L,t …liabilities) positions computed separately R A,t = D b,t-1 (s t + r * t-1 ) + (1 - D b,t-1 )r t-1 R L,t = (1 + D s,t-1 )r t-1 – D s,t-1 (s t + r * t-1 + s t r * t-1 ) D b,t-1 = 1 when „buy FX“, =0 otherwise D s,t-1 = -1 when „sell FX“, =0 otherwise r t-1 = one day return on DEM (home currency) r * t-1 = one day return on FX s t = percentage change from t-1 to t in the FX => N R,t = R A,t – R L,t = (D b,t-1 + D s,t-1 )*[(s t + r * t-1 + s t r * t-1 ) – r t-1 ] 22

23. The trading rule Illustrative example (DEM as a foreign currency) 23

24. The trading rule Use of the “Buy” and “Sell” strategies The “Buy” and “Sell” strategies are for liquidity traders (only long or a short position desired) 1. Test for symmetry in the gains 2. Test for peso-type realignment risk (a risk of having expectations affected by one event with a very high potential and a very small probability of occurrence) If a positive and significant difference between average returns of “Buy” and “Sell” strategies is found, then peso- type realignment risk among ERM countries exists 24

25. The trading rule Significance measures The trading rule suffers from difference in riskiness of various currencies, because of differences across countries in: i. The average risk premium ii. Length of periods in long and short positions  Static control strategy formulated (to compare its results to the trading rule) Static control strategy = the trader holds static position in a currency, determined by the length of periods being long and short in the currency (according to our rule) 25

26. The trading rule Significance measures The position is given by D ̅ b + D ̅ s (corresponding to average D b + D s ) Net return on the trading rule is NR t Net return on the control strategy is NR t Net excess net return is XNR = NR t - NR t (per day) In practice: Receiving the signal for a period („buy FX“ for three days means holding the position for 3 days (not reopening it each day) Net excess return p.a. (daily excess net returns are summed up over a one year horizon) 26

27. The trading rule -Empirical results 27

28. The trading rule Empirical results Excess net returns are positive and significant for all ERM currencies and CHF (informally affiliated to ERM) Non-ERM currencies exhibit no significant excess net return Lower the phi increases the coefficients The division to sub periods (Panel B) has little impact on the results No asymmetry on the Buy and Sell strategies The trading rule brings gains to liquidity traders (transaction costs not considered) 28

29. Explaining the forward bias Regular risk premium Peso risk Learning Transaction costs 29

30. Explaining the forward bias Regular risk premium Covariance with a stochastic discount factor which is usually specified as the return on a portfolio CAMP or InCAMP 30

31. Explaining the forward bias Regular risk premium - CAMP E(r i – r f ) = β i * E(r M – r f ) E(r M – r f ) = market risk premium β i = ρ i,m [σ(s)/σ(r m )] << 1 Never get near 14-% average for an exchange rate 31

32. Explaining the forward bias Regular risk premium - CAMP Being only long (7.5%) and being short (6.5%) => this requires a time-varying beta Time proportion: Long – 37% Short – 29% Out – 34% CAPM-equilibrium expected returns swing from +20 to -20% p.a. in a matter of days => impossible 32

33. Explaining the forward bias Regular risk premium - InCAMP Two-country version => own-variance risk premium E(r i – r f ) = A w cov(s i,r w ) + (1 - A i )(W i /W w )var(s i ) Quick swing from strong risk-preference to risk- aversion in a matter of days 33

34. Explaining the forward bias Peso risk Realignments and devaluations Occured frequently Average devaluation jump size = 4% Idea that 14% is the product of a small probability of devaluation times a huge jump size = totally implausible 34

35. Explaining the forward bias Transaction costs Claims that gains are small, risky, and wiped out by transaction costs Unclear whether the small filters would have been profitable to round-trip speculators Larger filters have been profitable even after transaction costs => we cannot claim that transaction costs would have wiped out the gains that were observed 35

36. Conclusion They observed non-zero expectations from the data Forward bias = big problem even in Europe Refusing risk premium – not explaining the results Possible market inefficiency? 36

37. Related literature/papers Froot & Thaler (1990): Anomalies: Foregin Exchange Menzie Chinn (2007): Forward Premium Puzzle Daniel L. Thornton (1989): Tests of CIRP Bansal & Dahlqist (1998): The forward premium puzzle: different tales from developed and emerging economies 37

38. If you have any questions, do not hesitate to ask us directly or write us an email. Introduction & data– Tereza M. (35520670@fsv.cuni.cz) Regression tests of UIP – Tereza S.(35890232@fsv.cuni.cz) A trading-rule test – Pavla (pblahova@email.cz) Explaining the forward bias – Zdeněk (71229303@fsv.cuni.cz) 38