Expected Currency Returns and Volatility Risk Premium

Home , Volatility risk

Expected Currency Returns and Volatility Risk Premium José Renato Haas Ornelas Banco Central do Brasil – Research Department The views expressed in this work are those of the author and do not necessarily reflect those of the Banco Central do Brasil or its members. Main Idea

Can currency volatility risk premium predict exchange rates returns?

Currency volatility risk premium: difference between an implied volatility and a realized volatility

Exchange rates returns: Returns of the other currencies against USD Motivation • Exchange rates are difficult to predict – Interest rate differentials (UIP) – Momentum – PPP • On equity markets, Volatility Risk Premium (VRP) can predict future equity returns Volatility Risk Premium: Equity • High Volatility Risk Premium (VRP) leads to positive future returns on equity markets • Intuition: when risk aversion sentiment increases, the market quickly discount the risky asset (e.g. stock), and latter this discount is accrued, leading to positive returns • Model by Bollerslev, Tauchen and Zhou (2009) gives an idea of how his intuition works • Papers giving empirical support using Equity Indexes: – Bollerslev, Tauchen and Zhou (2009): S&P500 – Bollerslev, Marronez, Xux and Zhou (2013): developed equity markets Intuition and Results • My results: High Volatility Risk Premium (VRP) leads to positive future returns for most currencies • Intuition: when risk aversion sentiment increases, the market quickly discount the risky asset (foreign currency), and latter this discount is accrued, leading to positive returns • For an emerging market currency or even a small developed country currency, this intuition seems fine – USD/BRL: it is clear the Brazilian Real is the risky asset – EUR/DKK: it is clear the Danish Krone is the risky asset • However, this intuition is not straightforward when we have a pair of currencies where it is not clear which currency is the “risky” asset… – E.g.: US Dollar/Euro or US Dollar/Yen Literature

• Articles using Currencies Volatility Risk Premium: – Londono & Zhou (2014): time-series – Della Corte et all (2015): cross-section • High Volatility Risk Premium (VRP) leads to negative future returns, i.e., the opposite results from equities and from my paper • Intuition: Cost of hedge for Della Corte et all (2015) • Explanation for different results? – They use options with longer maturities (6m-1Y) – I use one-month options and intraday realized volatilities VRP Calculation Methodology • The traditional way: current (date t) implied volatility and past realized volatility (t-T to t) ℚ ℙ 푉푅푃푏푎푐푘 = 퐸 휎푡,푡+∆푡 − 퐸 휎푡−∆푡,푡 Implied realized

• Another approach: implied volatility and realized volatility for the same period of the forecast.

ℚ ℙ 푉푅푃푓푤푑 = 퐸 휎푡−∆푡,푡 − 퐸 휎푡−∆푡,푡

Implied realized VRP Calculation Methodology

• The traditional way: current (date t) implied volatility and past realized volatility (t- ∆푡 to t) Realized Implied

t - ∆푡 t t + ∆푡 • My approach: implied volatility and realized volatility for the same period of the forecast. Realized and Implied

t - ∆푡 t t + ∆푡 Sample

• Core Sample: 20 currencies – 10 Developed and 10 EM • Six years of daily data – 2007 to 2014 • Realized volatility calculated with intraday data • Implied (“model-free”) volatility calculated used Bloomberg data and VIX style methodology

푛 2푒푟푇 ∆퐾 퐸ℚ 휎2 = 푖 휃 퐾 푡,푡+푇 푇 퐾2 푡,푡+푇 푖 푖=1 푖 ATM Model-free Realized Volatility Risk Premium Interest Volatility Volatility Volatility Forward Backward Rate AUD 13.25 18.87 14.03 4.96 4.85 4.30 CAD 10.32 14.61 10.56 4.14 4.05 1.38 CHF 11.03 15.66 11.17 4.52 4.48 0.45 DKK 9.86 13.93 10.15 3.71 3.78 1.51 EUR 10.90 15.47 10.16 5.34 5.31 1.18 GBP 9.96 14.16 9.89 4.31 4.27 1.43 JPY 11.44 16.40 10.95 5.55 5.45 0.26 NOK 13.23 18.55 13.74 4.71 4.81 2.70 NZD 13.96 19.90 14.92 5.13 4.98 3.88 SEK 13.47 18.95 13.83 5.01 5.11 1.77 Summary BRL 15.10 21.89 14.77 7.25 7.12 9.80 CLP 12.76 18.15 11.11 6.99 7.04 0.37 CZK 13.45 19.11 14.31 4.70 4.80 1.40 Statistics ILS 9.22 13.15 9.80 3.40 3.35 2.03 INR 10.30 13.97 8.25 5.64 5.73 7.28 MXN 12.98 18.80 12.00 6.83 6.81 4.76 MYR 7.77 9.56 7.03 2.43 2.53 2.85 PLN 16.57 23.71 16.47 7.26 7.24 3.94 TRY 12.99 18.44 12.31 6.22 6.13 9.32 ZAR 17.36 24.86 18.34 6.63 6.53 6.70 Overall Mean 12.30 17.41 12.19 5.24 5.22 3.36 Developed Mean 11.74 16.65 11.94 4.74 4.71 1.88 Emerging Mean 12.85 18.16 12.44 5.74 5.73 4.84 Aggregated Variance Risk Premium Regressions

푅푡,푡+21 = 훼 + 훽1푉푅푃푡−1 + 휀푡

Average Currency returns Average Volatility Risk Premium

Panel B – Aggregated Volatility Risk Premium Volatility Risk Premium Backward Forward coefficient t-statistics adjusted R2 coefficient t-statistics adjusted R2 Overall 0.067 0.60 0.25 0.184 2.04 6.61 Developed 0.040 0.35 0.06 0.168 1.97 5.52 Emerging 0.094 0.82 0.48 0.199 2.05 6.88

Newey-West HAC adjusted Panel A – Currency by Currency Volatility Risk Premium Volatility Risk Premium Backward Forward coefficient t-statistics adjusted R2 coefficient t-statistics adjusted R2 Individual Currency AUD 0.312 1.81 2.65 0.317 2.50 7.99 Returns CAD 0.130 1.53 1.02 0.209 2.44 7.95 CHF -0.111 -0.70 0.44 0.119 1.07 1.56 x DKK -0.027 -0.19 -0.02 0.117 1.17 1.82 EUR -0.030 -0.21 -0.01 0.117 1.17 1.80 Global Volatility Risk GBP -0.088 -0.75 0.40 0.170 1.47 4.82 Premium JPY 0.018 0.16 -0.04 -0.095 -1.31 1.38 NOK 0.072 0.64 0.15 0.254 2.59 7.51 NZD 0.158 0.72 0.66 0.264 1.84 5.75 SEK -0.030 -0.19 -0.03 0.209 1.79 4.31 BRL 0.232 1.64 1.35 0.320 3.13 7.68 푅푡,푡+21 = 훼 + 훽1푉푅푃푡−1 + 휀푡 CLP 0.397 3.61 5.82 0.330 3.71 11.64 CZK -0.158 -0.81 0.59 0.128 0.87 1.15 ILS -0.147 -1.39 1.51 0.086 0.97 1.47 Individual Global INR 0.151 1.83 1.38 0.129 2.11 2.98 Currency Volatility MXN 0.069 0.49 0.14 0.174 1.41 3.45 returns Risk MYR 0.016 0.22 -0.02 0.095 1.82 3.34 Premium PLN -0.173 -0.72 0.56 0.171 0.91 1.69 TRY 0.123 0.88 0.46 0.237 1.75 5.45 ZAR 0.431 2.84 4.32 0.324 2.31 7.10 Volatility Risk Premium Volatility Risk Premium Backward Forward 2 2 훽1 t-statistics adjusted R 훽1 t-statistics adjusted R Individual Currency AUD 0.240 2.02 2.04 0.262 2.66 9.87 CAD 0.148 1.52 1.08 0.252 2.51 7.28 Returns CHF -0.192 -1.26 1.45 0.244 1.65 4.19 DKK -0.043 -1.18 0.48 -0.018 -0.43 0.05 x EUR -0.111 -0.97 0.55 0.164 1.46 2.13 GBP -0.218 -1.61 1.60 0.256 1.76 5.28 Individual Volatility JPY -0.111 -1.07 0.81 0.013 0.18 -0.03 NOK -0.059 -0.87 0.13 0.142 1.83 2.66 Risk Premium NZD 0.104 0.83 0.39 0.291 3.08 9.25 SEK -0.028 -0.31 -0.02 0.188 1.83 3.65 BRL 0.109 2.35 1.48 0.079 2.02 2.29 푅푡,푡+21 = 훼 + 훽1푉푅푃푡−1 + 휀푡 CLP 0.079 1.48 0.97 0.087 2.24 2.51 CZK 0.039 0.39 0.16 0.112 1.55 2.72 ILS 0.043 0.66 0.21 0.075 1.36 1.31 INR 0.066 1.28 0.59 0.031 0.68 0.21 Individual Individual MXN 0.025 0.44 0.11 0.036 0.88 0.86 Currency Volatility MYR -0.010 -0.34 -0.01 -0.011 -0.37 0.01 returns Risk PLN -0.054 -0.47 0.26 0.071 0.69 0.92 Premium TRY 0.024 0.34 0.02 0.109 1.71 3.07 ZAR 0.195 3.12 3.97 0.106 2.12 3.08 Mean 0.81 3.07 Dev Mean 0.85 4.43 EM Mean 0.78 1.70 Global x Individual VRP Backward x Forward VRP

Mean Adjusted R2 Individual Global Individual Global Backward Backward Forward Forward Mean 0.81 1.07 3.07 4.54 Dev Mean 0.85 0.52 4.43 4.49 EM Mean 0.78 1.61 1.70 4.60

For EM, it is better to use global VRP Individual VRP, ATM Global VRP, ATM adjusted Robustness coefficient t-statistics adjusted R2 coefficient t-statistics R2 AUD 0.183 1.87 4.25 0.313 1.93 4.62 CAD 0.283 2.33 5.30 0.258 2.27 7.19 CHF 0.321 1.90 5.42 0.136 1.17 1.20 Uses ATM implied DKK -0.019 -0.30 0.00 0.116 0.98 1.05 EUR -0.193 -1.22 1.10 -0.155 -1.32 1.57 volatility, GBP 0.367 2.04 6.58 0.303 2.33 9.12 instead of Model- JPY -0.080 -0.86 0.59 -0.230 -3.59 4.96 NOK 0.126 1.09 1.23 0.335 2.49 7.78 Free (VIX-style) NZD 0.276 3.02 6.58 0.368 2.94 6.63 SEK 0.243 1.86 3.39 0.303 2.39 5.38 implied volatility BRL 0.095 2.17 2.20 0.418 3.04 7.76 CLP 0.094 1.49 1.33 0.344 2.29 7.49 CZK 0.134 1.73 2.57 0.212 1.63 1.93 ILS 0.131 1.30 2.27 0.208 2.55 5.33 INR 0.061 0.63 0.42 0.171 2.16 3.11 푅푡,푡+∆푡 = 훼 + 훽1푉푅푃푡−1 + 휀푡 MXN 0.076 1.71 2.21 0.314 2.19 6.69 MYR 0.077 1.05 0.77 0.132 2.69 3.85 PLN 0.150 1.51 2.40 0.370 2.18 4.79 TRY 0.115 1.56 1.87 0.310 1.67 5.55 ZAR 0.056 1.09 0.60 0.273 1.30 2.95 Individual Volatility Risk Premium Individual Volatility Risk Premium Robustness Forward, One Week Forward, Three Months coefficient t-statistics adjusted R2 coefficient t-statistics adjusted R2 AUD 0.183 2.29 3.65 0.08 1.06 1.74 CAD 0.169 2.29 3.33 0.16 2.29 5.12 Individual Variance CHF -0.031 -0.49 0.04 0.02 0.19 -0.03 DKK -0.015 -0.40 0.02 0.02 0.47 0.07 Risk Premium EUR 0.074 0.84 0.42 0.03 0.30 0.08 GBP 0.008 0.11 -0.05 0.24 2.83 8.62 Regressions JPY 0.117 2.44 2.71 -0.13 -1.79 2.93 NOK 0.039 0.88 0.18 0.03 0.69 0.15 NZD 0.083 1.06 0.72 0.15 1.67 3.86 One-Week and SEK 0.062 1.03 0.34 0.06 1.09 0.54 BRL 0.034 0.63 0.28 0.06 1.34 1.82 Three-month CLP 0.074 1.64 1.78 0.09 1.37 1.91 Options CZK 0.077 2.27 1.48 0.06 0.82 0.72 ILS 0.072 1.67 1.37 0.00 -0.03 -0.06 INR 0.023 0.66 0.08 0.07 1.22 1.31 MXN 푅푡,푡+∆푡 = 훼 + 훽1푉푅푃푡−1 + 휀푡 0.001 0.04 -0.05 0.10 2.78 7.55 MYR -0.003 -0.10 -0.05 0.02 0.66 0.16 PLN 0.047 0.68 0.34 0.17 2.35 5.76 TRY 0.099 1.86 2.07 0.03 0.41 0.10 ZAR 0.111 2.43 3.60 -0.02 -0.44 0.06 Adding Control Variables

Adding 12 more emerging markets currencies Adding Control Variables

• Lag Return: lagged currency one-month return; • Δi: one-month Libor-like deposit interest rates differential against the USD Libor; • Equity VRP: US Equity VRP calculated using equation (2) with VIX index as implied volatility and one-month daily realized volatility and; • PPP: Undervaluation in percentage points of the current exchange rate against US Dollar Purchase Power Parity (PPP) published by the World Bank Individual Control Variables x Returns

푹풕,풕+ퟐퟏ = 휶 + 휷ퟏ푿풕−ퟏ + 휺풕

Group Average Currency returns One Control Variable at a time

Coefficients Adjusted R2 Cur. Lag Equity Cur. Lag Equity PPP Δi PPP Δi VRP Return VRP VRP Return VRP Overall 0.170** 0.096 0.022 0.048* -0.14 6.72 0.89 0.94 4.26 0.17

Dev. 0.168** 0.010 0.029 0.079* -0.89** 5.52 -0.05 1.38 3.88 2.89

EM 0.171* 0.125 0.019 0.040* -0.03 6.92 1.53 0.69 4.26 -0.03

LatAm 0.199** 0.196 0.030 0.036* -0.18 7.72 3.89 1.49 3.82 0.27

Europe 0.157 0.040 0.014 0.122*** -0.09 3.81 0.10 0.22 9.96 0.13

Asia-Pacific 0.163** 0.054 0.025 0.017 -0.10 8.58 0.25 1.77 2.40 0.08 All Variables together

푅푡,푡+21 = 훼 + 훽1퐶푉푅푃푡−1 + 훽2푅푡−22,푡−1 + 훽3퐸푉푅푃푡−1 + 훽4푃푃푃푡−1 + 훽5∆푖푡−1 + 휀푡

Coefficients t statistics Adj R2

Cur. Lag Equity Cur. Lag Equity PPP Δi PPP Δi VRP Return VRP VRP Return VRP

Overall 0.196 -0.024 -0.018 0.072 -0.78 2.24 -0.29 -0.83 2.72 -2.64 14.3 Develop 0.174 -0.075 -0.005 0.093 -1.05 1.82 -0.95 -0.25 1.49 -2.21 13.0 EM 0.195 0.010 -0.027 0.063 -0.59 2.35 0.11 -1.21 3.06 -2.38 14.0 LatAm 0.185 0.120 -0.031 0.043 -0.43 2.29 1.24 -1.41 2.05 -1.61 13.3 Europe 0.122 0.012 -0.008 0.109 -0.24 1.25 0.16 -0.27 3.16 -0.93 12.5 Asia- 0.202 -0.073 -0.015 0.008 -0.28 2.99 -0.67 -0.75 0.49 -1.56 10.4 Pacific 2 Coefficients Adj R2 Coefficients Adj R Cur. Lag Equity Cur. Lag Equity PPP Δi PPP Δi VRP Return VRP Return VRP VRP BRL 0.318 0.060 -0.059 0.051 -0.07 11.8 AUD 0.303 -0.006 -0.010 0.041 -0.40 10.0 CLP 0.326 -0.037 -0.002 0.017 0.04 12.1 CAD 0.323 -0.247 -0.051 0.062 -0.62 16.7 CZK 0.112 0.013 -0.002 0.088 -0.17 6.7 ILS 0.125 -0.036 -0.063 0.104 -0.18 8.3 CHF 0.164 -0.130 -0.036 0.202 -0.59 11.2 INR 0.132 -0.009 -0.036 0.026 -0.06 8.0 DKK 0.094 -0.061 0.034 0.119 -0.19 7.2 MXN 0.103 0.097 -0.058 0.110 -0.26 14.8 EUR 0.087 -0.069 0.039 0.078 -0.60 8.1 MYR 0.130 -0.045 -0.032 0.018 -0.02 5.5 GBP 0.171 -0.025 -0.043 0.074 -0.56 14.2 PLN 0.188 0.047 -0.036 0.063 -0.72 9.5 TRY 0.220 -0.027 -0.001 0.038 0.04 8.7 JPY -0.168 -0.078 0.077 0.019 -0.47 11.2 ZAR 0.338 -0.085 0.013 0.027 -0.14 10.4 NOK 0.265 -0.071 -0.024 0.120 -0.73 14.5 BGN 0.113 0.001 -0.008 0.104 -0.08 14.7 NZD 0.273 -0.139 -0.067 0.092 -1.18 20.6 COP 0.141 0.111 -0.038 0.075 -0.79 13.6 SEK 0.218 -0.063 -0.045 0.101 -0.50 10.0 HUF 0.024 0.229 -0.068 0.151 0.05 14.5 IDR 0.412 -0.043 -0.042 0.008 -0.09 18.9 ISK 0.417 -0.105 -0.042 0.092 -0.21 18.8 KRW 0.511 -0.218 -0.086 0.031 -0.20 17.6 PEN 0.047 0.173 -0.022 0.020 0.08 6.7 PHP 0.055 0.037 -0.014 0.020 0.00 4.6 RON 0.091 -0.021 -0.005 0.005 -0.02 3.0 RUB 0.069 0.031 -0.030 0.063 0.01 9.4 SGD -0.048 0.187 -0.100 0.095 0.01 21.6 30 out of 32 coefficients are positive THB 0.103 -0.099 -0.028 0.046 0.18 8.5 15 stat sig. Summary of Main Results

Core Sample: 20 currencies • Individual currency VRP has a positive relationship with future currency returns in 18 out of 20 cases, with statistically positive coefficients in 11

Enlarged Sample: 32 currencies • Average currency VRP has a positive relationship with individual future currency returns in 30 cases, with statistically positive coefficients in 15 • Average currency VRP has a statistically sig. positive relationship with returns of a basket of the 32 currencies – Adjusted R2 of 14% Final Remarks

• Empirical evidence: support for a positive relationship of currency VRP and future currency returns • Using the average VRP of all currencies - a Global VRP – provides better results, especially for emerging markets • Stronger results for non-European currencies • Stronger results for the individual VRP of “commodities” currencies Further Steps

• Analyze if the use of the “commodities” currencies VRP can forecast commodities price movements • Test alternative techniques to deal with overlapping – E.g., Hjalmarsson (2011) t-stat adjustment instead of Newey-West (1987) Appendix Aggregated Variance Risk Premium Regressions For different Forecast Horizons

Mean Adjusted R Square x Forecast Horizon Individual Average Volatility Risk 6 Currency returns Premium, one month

5 푅 = 훼 + 훽 푉푅푃 + 휀 푡,푡+∆푡 1 푡−1 푡 4

Mean AdjustedMean Square R

0 0 10 20 30 40 50 60 Forecast Horizon