Original paper
Abstract
We investigate the relation between global foreign exchange (FX) volatility risk and the cross-section of excess returns arising from popular strategies that borrow in low-interest rate currencies and invest in high-interest rate currencies, so-called 'carry trades'. We find that high interest rate currencies are negatively related to innovations in global FX volatility and thus deliver low returns in times of unexpected high volatility, when low interest rate currencies provide a hedge by yielding positive returns. Our proxy for global FX volatility risk captures more than 90% of the cross-sectional excess returns in five carry trade portfolios. In turn, these results provide evidence that there is an economically meaningful risk-return relation in the FX market. Further analysis shows that liquidity risk also matters for expected FX returns, but to a lesser degree than volatility risk. Finally, exposure to our volatility risk proxy also performs well for pricing returns of other cross sections in foreign exchange, U.S. equity, and corporate bond markets.
Trading rules
- Focus on currencies from the following developed countries: Australia, Canada, Denmark, Eurozone, Japan, New Zealand, Norway, Sweden, Switzerland, and UK.
- Calculate FX volatility indicator: Take the absolute daily logarithmic returns for each currency and compute their monthly average.
- Calculate the FX innovations indicator: Use AR(1) for volatility level, residuals as proxy for innovations, or use monthly change in FX volatility.
- Sort the currencies into five portfolios based on their historical beta in relation to global FX volatility.
- Use 36-month rolling window for beta estimates.
- Take a long position in currencies with a low volatility beta (indicative of high volatility risk) and a short position in those with high volatility beta (signifying low volatility risk).
- Equally weighted portfolio, rebalanced every 6 months.
Python code
Backtrader
import backtrader as bt
import numpy as np
import pandas as pd
import statsmodels.api as sm
class FXVolatilityStrategy(bt.Strategy):
params = (
('rebalance_months', 6),
('lookback_period', 36),
)
def __init__(self):
self.months_passed = 0
def next(self):
if len(self.data) < self.params.lookback_period:
return
if self.months_passed % self.params.rebalance_months == 0:
self.rebalance_portfolio()
self.months_passed += 1
def rebalance_portfolio(self):
currencies_data = self.get_currencies_data()
betas = self.calculate_betas(currencies_data)
longs, shorts = self.get_long_short_positions(betas)
for i, d in enumerate(self.datas):
if d._name in longs:
self.order_target_percent(d, target=1 / len(longs))
elif d._name in shorts:
self.order_target_percent(d, target=-1 / len(shorts))
else:
self.order_target_percent(d, target=0)
def get_currencies_data(self):
currencies_data = {}
for d in self.datas:
currency_data = pd.Series(d.close.get(size=self.params.lookback_period))
currencies_data[d._name] = currency_data.pct_change().apply(np.log).abs().resample('M').mean()
return currencies_data
def calculate_betas(self, currencies_data):
betas = {}
for currency, data in currencies_data.items():
x = sm.add_constant(data.shift(1).dropna())
y = data.diff().dropna()
model = sm.OLS(y, x).fit()
betas[currency] = model.params[1]
return betas
def get_long_short_positions(self, betas):
sorted_betas = sorted(betas.items(), key=lambda x: x[1])
n = len(sorted_betas) // 5
longs = [x[0] for x in sorted_betas[:n]]
shorts = [x[0] for x in sorted_betas[-n:]]
return longs, shorts