Original paper
Abstract
We discover a new currency strategy with highly desirable return and diversification properties, which uses the predictive capability of currency volatility risk premia for currency returns. The volatility risk premium -- the difference between expected realized volatility and model-free implied volatility -- reflects the costs of insuring against currency volatility fluctuations, and the strategy sells high-insurance-cost currencies and buys low-insurance-cost currencies. The returns to the strategy are mainly generated by movements in spot exchange rates rather than interest rate differentials, and the strategy carries a large weight in a minimum-variance portfolio of commonly employed currency strategies. We explore alternative explanations for the profitability of the strategy, which cannot be understood using traditional risk factors.
Keywords:Â Exchange Rates, Volatility Risk Premium, Predictability, Minimum-Variance Currency Portfolio
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