Original paper
Abstract
We investigate two yield curve strategies: Curve carry selects bond maturities based on carry and betting-against-beta always selects the shortest maturities. We investigate these strategies for international bond markets. We find that the global curve carry factor has strong performance that cannot be explained by other factors. For betting-against-beta, however, this depends on the assumed funding rate. We also show that the betting-against-beta strategy has no added value for an investor that already invests in curve carry.
Keywords:Â Carry, Predictability, Betting-Against-Beta, Government Bonds
Trading rules
- Investment perimeter: bonds along with forward and futures contracts to construct long/short portfolios along yield curves in multiple developed countries (including Australia, Canada, Denmark, Germany, Japan, Norway, Sweden, Switzerland, UK, and the USA).
- Ensure an equal weight in all countries.
- Shape a carry portfolio by going long on high carry maturity buckets and short on low carry maturity buckets using 1y, 3y, 5y, 7y, 10y, and 15y forwards.
- Modify position allocations to reflect risk disparities among forwards with varying durations.
- Maintain long/short portfolios that are neutral in terms of duration.
- Calculate weight for each forward i at time t: Wi = z(rank(Ci/Di) - (N+1)/2)
- Ci: forward’s carry (sum of bond yield spread to risk-free rate + rolldown)
- Di: bond duration
- N: number of available forwards
- z: scalar ensuring the sum of long and short positions equals 1
- Portfolio return is the weighted sum of individual (duration-adjusted) forward returns
Python code
Backtrader
import backtrader as bt
import numpy as np
class InternationalCarryStrategy(bt.Strategy):
params = (
("countries", ["Australia", "Canada", "Denmark", "Germany", "Japan", "Norway", "Sweden", "Switzerland", "UK", "USA"]),
("maturities", [1, 3, 5, 7, 10, 15]),
)
def __init__(self):
self.forwards = {country: {maturity: self.datas[i] for i, maturity in enumerate(self.params.maturities)} for country in self.params.countries}
def next(self):
positions = []
for country, country_forwards in self.forwards.items():
for maturity, data in country_forwards.items():
ci = data.close[0] - data.close[-1] + (data.close[-1] - data.close[-2]) # Forward's carry
di = maturity # Bond duration (assuming 1:1 mapping for simplicity)
positions.append((ci / di, data))
n = len(positions)
z = 1 / (n / 2)
positions.sort(key=lambda x: x[0])
for i, (_, data) in enumerate(positions):
wi = z * (i - (n + 1) / 2)
if wi > 0:
self.buy(data, size=wi)
else:
self.sell(data, size=-wi)
class InternationalCarry(bt.Cerebro):
def __init__(self):
super().__init__()
self.addstrategy(InternationalCarryStrategy)
def run(self, **kwargs):
return super().run(**kwargs)
if __name__ == "__main__":
cerebro = InternationalCarry()
# Add data feeds for each country and maturity (not provided in this code snippet)
# ...
results = cerebro.run()
cerebro.plot()Please note that this code is a starting point and requires the appropriate data feeds for each country and maturity, which are not provided in this snippet. You will need to source this data and add it to your Backtrader instance. Additionally, the calculation for the forward’s carry (Ci) may need adjustments based on the specific data format you will be using.