Common Risk Factors in Currency Markets

Transcription

1 Common Risk Factors in Currency Markets Hanno Lustig, Nick Roussanov and Adrien Verdelhan UCLA, Wharton and BU CEPR / SNB - Zurich, September 28

2 Summary Example Subprime Mortgage Crisis: Currency Portfolios.1 Mortgage Crisis (July 27 February 28, One Month Returns) HML MSCI corr(hml,msci) = Jul Aug Sep Oct Nov Dec Jan Feb Mar Carry Trade and US Stock Market Returns during the Mortgage Crisis - July 27 to March 28.

3 Summary Example Literature Risk-based explanations: Hansen and Hodrick (198), Fama (1984),..., Bansal and Dahlquist (2), Backus, Foresi and Telmer (21), Harvey and Solnik and Zhou (22), Alvarez and Atkeson and Kehoe (25), Verdelhan (25), Graveline (26), Campbell, de Medeiros and Viceira (26), Bansal and Shaliastovich (26), Lustig and Verdelhan (27), Hau and Rey (27), Gabaix and Farhi (27), Colacito (28). Other explanations: Froot and Thaler (199), Lyons (21), Gourinchas and Tornell (24), Bachetta and van Wincoop (26), Frankel and Poonawala (26), Sarno, Leon and Valente (27), Plantin and Shin (27), Burnside, Eichenbaum and Rebelo (26, 27a, 27b, 28).

4 Summary Main Findings Our Findings Large excess returns after bid/ask spreads. These excess returns are risk premia: A single risk factor, HML FX, explains the cross-sectional variation in excess returns. These excess returns are predictable, and the expected excess returns are counter-cyclical (similar to bond and stock markets).

5 Summary Main Findings Understanding our Findings Using a standard affine no-arbitrage model of N currencies (a la CIR), we show that: By building portfolios of currency forward contracts, we extract the innovations to the SDF that are priced; HML FX measures the exposure to common innovations or world risk. A reasonably calibrated version of the model reproduces our findings: High interest rate currencies are more exposed to world risk; Sorting on interest rates sorting on exposure to world risk.

6 Summary Main Findings Outline 1 Summary Example Main Findings 2 Portfolios of Currency Excess Returns Notations Trading Costs and Currency Excess Returns 3 Cross-sectional Asset Pricing Risk Factors HML Bets Non-US Investors 4 Model Assumptions Extracting Risk Factors Calibrated Model 5 Predictability Portfolio-Specific and Average Forward Discounts Counter-cyclical Expected Excess Returns 6 Conclusion

7 Portfolios of Currency Excess Returns Notations Currency Excess Returns s t : Log of spot exchange rate in units of foreign currency per dollar (when s increases, the dollar appreciates). f t : Log of one-month forward exchange rate in units of foreign currency per dollar Log excess return on buying foreign currency forward and selling it in spot market: rx t+1 = f t s t+1 rx t+1 = s t+1 + f t s t s t+1 + i t i t. f t s t i t i t : forward discount s t+1 : % appreciation of the foreign currency

8 Portfolios of Currency Excess Returns Trading Costs and Currency Excess Returns Data Data from Barclays and Reuters. Start from daily spot and forward exchange rates in US dollars. Build end-of-month series from November 1983 to March 28. Sample of 37 developed and emerging countries: Australia, Austria, Belgium, Canada, Hong Kong, Czech Republic, Denmark, Euro area, Finland, France, Germany, Greece, Hungary, India, Indonesia, Ireland, Italy, Japan, Kuwait, Malaysia, Mexico, Netherlands, New Zealand, Norway, Philippines, Poland, Portugal, Saudi Arabia, Singapore, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Thailand, United Kingdom. Sample of 15 developed countries: Australia, Belgium, Canada, Denmark, Euro area, France, Germany, Italy, Japan, Netherlands, New Zealand, Norway, Sweden, Switzerland and United Kingdom.

9 Portfolios of Currency Excess Returns Trading Costs and Currency Excess Returns Currency Portfolios At the end of each month t, sort all currencies in 6 portfolios on forward discounts f t s t. Portfolios are ranked from low to high forward discounts f t s t. Compute the log currency excess return rx j t+1 j = 1,2...,6 by averaging: for each portfolio rx j t+1 = 1 N j i P j rx i t+1.

10 Portfolios of Currency Excess Returns Trading Costs and Currency Excess Returns Portfolio Allocation 1 One Month Forward Discount Japan 6 Portfolio Allocation Japan Annual Percentage 5 5 Portfolio Number One Month Forward Discount UK 6 Portfolio Allocation UK Annual Percentage 1 5 Portfolio Number

11 Portfolios of Currency Excess Returns Trading Costs and Currency Excess Returns Cross-section Higher forward discounts mean higher returns: Portfolio Excess Return: rx j (without b-a) Mean SR Excess Return: rxnet j (with b-a) Mean SR High-minus-Low: rxnet j rx1 net (with b-a) Mean SR Annualized monthly returns. Monthly data. Sample is 11/1983-3/28.

12 Portfolios of Currency Excess Returns Trading Costs and Currency Excess Returns Developed Countries Portfolio Excess Return: rx j (without bid-ask) Mean SR Excess Return: rxnet j (with bid-ask) Mean SR Long-Short: rx j net rx 1 net Mean SR Notes: Annualized monthly returns. Monthly Data. Sample is 11/1983-3/28.

13 Portfolios of Currency Excess Returns Trading Costs and Currency Excess Returns Portfolios of Currency Excess Returns.4 Mean Excess Returns (Annualized, x 12) Stdev of Excess Returns (Annualized, x sqrt(12)) Sharpe Ratio (Annualized) Large sample, 11/1983-3/28, after bid-ask spreads.

14 Cross-sectional Asset Pricing Risk Factors Principal Components Portfolio Principal component % Var The sample period is 11/1983-3/28.

15 Cross-sectional Asset Pricing Risk Factors Covariances (PC, Excess Returns) Portfolio Number Portfolio Number Portfolio Number Portfolio Number Portfolio Number Portfolio Number

16 Cross-sectional Asset Pricing Risk Factors Cross-Sectional Asset Pricing Rx j t+1 has a zero price: E[M t+1 Rx j t+1 ] =. M is linear in the pricing factors f : M t+1 = 1 b(f t+1 µ), where b is the vector of factor loadings.

17 Cross-sectional Asset Pricing Risk Factors Risk Factors Two principal components explain 85 % of excess returns variations. Two candidate risk factors: level or dollar factor: slope or carry-trade factor: RX FX,t = Rxt. i i=1 HML FX,t = Rx 6 t Rx 1 t. Investing in currencies is like placing HML bets.

18 Cross-sectional Asset Pricing HML Bets No Arbitrage Restrictions The Euler equation E[MRx j ] = E[Rx j b(f µ)rx j ] = implies that: E[Rx j ] = Σ ff b E[(f µ)rxj ] Σ ff. β-pricing model: E[Rx j ] = λ β j, No arbitrage implies: and λ HML = E[HML FX ], λ RX = E[RX FX ].

19 Cross-sectional Asset Pricing HML Bets Risk Prices λ HML λ RX b HML b RX R 2 RMSE χ 2 FMB [1.82] [1.34] [.19] [.25] 13.2 (1.83) (1.34) (.2) (.25) Mean Notes: Monthly Data. Sample is 11/1983-3/28.

20 Cross-sectional Asset Pricing HML Bets α in the Carry Trade? Significant βs? Portfolio α j β j HML β j RX R 2 χ 2 (α) p value 1.56 [.52].39 [.2] 1.6 [.3] [.76].13 [.3].97 [.5] [.82].12 [.3].95 [.4] [.86].2 [.4].93 [.6] [.8].5 [.4] 1.3 [.5] [.52].61 [.2] 1.6 [.3] 93.3 All

21 Cross-sectional Asset Pricing HML Bets Model Fit 5 OLS betas*mean(factor) 4 6 Actual Mean Excess Return (in %) Predicted Mean Excess Return (in %) The predicted excess return is the OLS estimate of β times the sample mean of the factors. All returns are annualized.

22 Cross-sectional Asset Pricing HML Bets Model Fit - Developed Countries OLS betas*mean(factor) 5 3 Actual Mean Excess Return (in %) Predicted Mean Excess Return (in %) The predicted excess return is the OLS estimate of β times the sample mean of the factors. All returns are annualized.

23 Cross-sectional Asset Pricing Non-US Investors Robustness Checks Foreign Investors; Sub-samples (Time-windows and countries); Beta-sorted portfolios; Daniel and Titman (25) s critique;

24 Cross-sectional Asset Pricing Non-US Investors Model Fit - Foreign Investors 6 US 6 UK Actual Mean Excess Return (in %) Actual Mean Excess Return (in %) Predicted Mean Excess Return (in %) Predicted Mean Excess Return (in %) 6 Japan 6 Switzerland Actual Mean Excess Return (in %) Actual Mean Excess Return (in %) Predicted Mean Excess Return (in %) Predicted Mean Excess Return (in %) The predicted excess return is the OLS estimate of β times the sample mean of the factors. All returns are annualized.

25 Cross-sectional Asset Pricing Non-US Investors Beta-Sorted Currency Portfolios Portfolio Forward Discount: f j s j Mean Std Excess Return: rx j (without b-a) Mean SR High-minus-Low: rx j rx 1 (without b-a) Mean SR Notes: Data are monthly, from Barclays and Reuters (Datastream). The sample period is 11/1983-3/28.

26 Model Assumptions How to interpret our results? To answer this question, we build a toy model: N countries; In each country, the SDF a la Cox, Ingersoll and Ross (1981) is driven by two risk factors: a country-specific factor, a world factor; One source of heterogeneity: countries differ in their loadings on the world factor. In this setting: HML FX measures the exposure to the world factor; RX measures the exposure to the country-specific factor; We reproduce our asset pricing and predictability results.

27 Model Assumptions Factor Model N countries. In each country i, the log SDF m i follows the law of motion: mt+1 i = λ i zt i + γ i ztu i t+1 i + τ i zt w + δ i zt w ut+1 w. Country-specific volatility: World volatility: z i t+1 = (1 φ i )θ i + φ i z i t + σ i z i tv i t+1. z w t+1 = (1 φ w )θ w + φ w z w t + σ w z w t v w t+1. All shocks uncorrelated across countries, iid gaussian, with zero mean and unit variance.

28 Model Assumptions Real Interest Rates and Real Exchange Rates Real Interest Rates: r i t = E t (mt+1) i 1 2 Var t(mt+1), i = (λ i 12 ) γi zt i + (τ i 12 ) δi zt w. Financial markets are complete, but some friction in the goods markets prevent perfect risk-sharing across countries.

29 Model Extracting Risk Factors Currency Risk Premia Real exchange rate: q i t+1 = m t m i t The log currency excess return rx i for a home investor who buys risk-free bonds in country i is: rx i,t+1 = q i t+1 + r i t r t. The expected excess return is thus: E t [rxt+1] i Var t[rxt+1] i = ( ) δ i δ δ i zt w + γz t. Variation in δ i is necessary for cross-sectional variation in currency risk premia.

30 Model Extracting Risk Factors Carry and Dollar Risk Factors Risk factors: hml t+1 = 1 N H rxt+1 i 1 N i H L rxt+1 i. i L rx t+1 = 1 N i rx i t+1. Real interest rates are: r i t = (λ 12 γ ) z i t + (τ 12 δi ) z w t. Real interest rates decline when z w increases if: < τ < 1 2 δi,

31 Model Extracting Risk Factors Risk Factors in the Model: hml FX and rx Use LLN in in each portfolio. hml t+1 E t [hml t+1 ] = rx t+1 E t [rx t+1 ] = γ z t u t+1 ( ) z δt L δt H w t ut+1 w Carry trade risk factor HML measures exposure to the common shock u w t+1. Dollar risk factor RX measures exposure to the US-specific risk factor u t+1.

32 Model Extracting Risk Factors Cross-sectional Asset Pricing Conditional betas of portfolio j: β j hml,t = δ δ j t δ L t δ H t, β j rx,t = 1. On average high δ i currencies end up in low portfolios ranking on interest rates => ranking on δ, ranking on δ => ranking on β hml.

33 Model Calibrated Model Distributions of Summary Statistics - Simulated Data Nominal Interest Rates Averages Real Exchange Rates Standard deviations Nominal Interest Rates Standard deviations Nominal Exchange Rates Standard deviations UIP Coefficients

34 Model Calibrated Model Portfolios - Summary statistics - Simulated Data Portfolio Spot change: s j Mean Std Forward Discount: f j s j Mean Std Excess Return: rx j Mean SR High-minus-Low: rx j rx 1 Mean SR

35 Model Calibrated Model Portfolios - Asset Pricing - Simulated Data λ RX λ HMLFX b RX b HMLFX R 2 RMSE χ 2 FMB [.26] [.31] [.39] [.33].7 (.26) (.31) (.39) (.34) 1.19 Mean

36 Model Calibrated Model Portfolios of Currency Excess Returns - Simulated Data Actual Mean Excess Return (in %) Predicted Mean Excess Return (in %)

37 Predictability Predictability I skip most of our predictability results today - they are in the paper and in a separate appendix though. I focus on two points: Average forward discounts imply high R2s; no residual predictability in portfolio-specific discounts. Expected excess returns are counter-cyclical.

38 Predictability Portfolio-Specific and Average Forward Discounts Return Predictability: R 2 Portfolio 1-month 2-month 3-month 6-month 12-month Forward Discount Average Forward Discount Residual Predictability Notes: Data are monthly. Sample is 11/1983-3/28.

39 Predictability Portfolio-Specific and Average Forward Discounts Predictability: Model Expected excess return in portfolio j: rp j t = 1 2 γ (z t z j t ) + 1 ) (δ δ 2 j zt w. LLN z j t constant No foreign country-specific predictability Average forward discount predicts currency excess returns

40 Predictability Business Cycle Properties: Corr [Êt rx j t+1 t], y Counter-cyclical Expected Excess Returns Ê t rx j t+1 = γj + γj 1 (f j t s j t). Portfolio IP Pay Help Spread slope vol Notes: Monthly Data. Sample is 11/1983-3/28.

41 Predictability Counter-cyclical Expected Excess Returns Forecasted Currency Excess Return and US Business Cycle One-month ahead forecasted excess returns on portfolio 2 (Ê trxt+1 2 ). All returns are annualized. The dashed line is the year-on-year log change in US Industrial Production Index.

42 Conclusion Conclusion Excess returns are large and predictable; Predictable variation is highly counter-cyclical; Cross-sectional variation is explained by a single risk factor; This suggests: A common risk factor; Heterogenous loadings on the common risk factor.

43 Conclusion CAPM Model Fit 5 OLS betas*mean(factor) 6 4 Actual Mean Excess Return (in %) Predicted Mean Excess Return (in %)

44 Conclusion US Market Correlation Spread 1.2 corr 6 corr 1 1 β HML This figure plots Corr τ [R m t,rx 6 t ] Corr τ [R m t,rx 1 t ], where Corr τ is the sample correlation over the previous 12 months [τ 11, τ]. Monthly returns. Monthly data.

45 Conclusion Portfolios of Countries in Burnside et al (26) Portfolio Spot change: s j Mean Std Forward Discount: f j s j Mean Std Excess Return: rx j (without b-a) Mean Std SR Notes: Countries in the sample: Belgium, Canada, Euro area, France, Germany, Italy, Japan, Netherlands, Switzerland, and United Kingdom. The sample period is 11/1983-1/27. Excess returns are computed without bid-ask spreads.

46 Conclusion Asset Pricing - Portfolios of Countries in Burnside et alii (26) Panel A: HML FX λ HML β 1 β 2 β [.4] [.3] [.4] Panel B: RX λ RX β 1 β 2 β [.4] [.3] [.4] Panel C: Pricing errors R 2 RMSE p val Notes: Market prices of risk are not estimated; sample means are used instead. The sample period is 11/1983-1/27. Excess returns are computed without bid-ask spreads.

47 Conclusion Burnside et alii (26) Actual Mean Excess Return (in %) Predicted Mean Excess Return (in %) Notes: The predicted excess return is the OLS estimate of β times the sample mean of the factors.

48 Conclusion Burnside et alii (26) Build one unique portfolio; Test our carry trade risk factor HML FX,t on their data set: rx t = c + βhml FX,t + ǫ t. β =.48 s.e =.6 R 2 =.27

49 Conclusion T-Bills Lustig and Verdelhan, 27: build baskets of T-Bills (8 countries) Two issues: financial openness, defaults.

50 Conclusion T-Bills λ HML λ RX b HML b RX R 2 RMSE χ GMM [1.25] [1.1] [2.76] [3.6] GMM [.81] [.91] [1.95] [3.5] FMB [1.17] (1.21) [.84] (.84) [2.34] (2.43) [2.54] (2.56) Mean Notes: Annual data.

51 Conclusion T-Bills Notes: Annual Data λ HML λ RX b HML b RX R 2 RMSE χ GMM [2.7] [1.93] [3.29] [4.17] GMM [1.9] [1.18] [1.96] [2.73] 8.26 FMB [1.66] (1.73) [1.3] (1.3) [2.37] (2.49) [2.55] (2.57) Mean

52 Conclusion Consumption Betas β HML c p(%) R 2 β HML d p(%) R 2 Panel A: Nondurables Panel B: Durables HML FX,t+1 = β + β 1 f t + ǫ t [.44] 2.23 [.4] [.52].28 [.6].63 Notes: Annual data.