Mean Variance Carry Trade Strategy
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On the Risk and Return of the Carry Trade
Fabian Ackermann; Walt Pohl; Karl Schmedders
- CHKantonsschule Zürcher Oberland
- ?Zurcher Kantonalbank
- NONorwegian School of Economics
- CHUniversity of Zurich
- ?NHH Norwegian School of Economics
- CHInternational Institute for Management Development
- ?IMD Lausanne
Strategy in a nutshell
The strategy invests in 10 foreign currencies versus USD, using interest rate differentials to estimate expected excess returns. Monthly mean-variance optimization sets long/short positions, rebalanced monthly to maximize risk-adjusted returns.
Economic rationale
Although uncovered interest parity suggests carry profits should vanish, short-term exchange rates are largely unpredictable. Empirical evidence shows carry trades earn positive expected returns despite exchange rate risk.
Backtest performance
Annualised return1.7%
Volatility1.87%
Beta0.197
Sharpe ratio0.91
Sortino ratio-0.298
Win rate49%
Full Python code
from AlgorithmImports import *
import pandas as pd
from collections import deque
import data_tools
class MeanVarianceCarryTradeStrategy(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2009, 1, 1)
self.SetCash(100000)
self.tickers:dict[str, str] = {
'CME_AD1' : Futures.Currencies.AUD, # Australian Dollar Futures, Continuous Contract #1
'CME_BP1' : Futures.Currencies.GBP, # British Pound Futures, Continuous Contract #1
'CME_CD1' : Futures.Currencies.CAD, # Canadian Dollar Futures, Continuous Contract #1
'CME_EC1' : Futures.Currencies.EUR, # Euro FX Futures, Continuous Contract #1
'CME_JY1' : Futures.Currencies.JPY, # Japanese Yen Futures, Continuous Contract #1
'CME_MP1' : Futures.Currencies.MXN, # Mexican Peso Futures, Continuous Contract #1
'CME_NE1' : Futures.Currencies.NZD, # New Zealand Dollar Futures, Continuous Contract #1
'CME_SF1' : Futures.Currencies.CHF, # Swiss Franc Futures, Continuous Contract #1
}
self.period:int = 250
self.max_missing_days:int = 5
self.min_expiration_days:int = 0
self.max_expiration_days:int = 360
self.futures_data:dict[str, FuturesData] = {}
for qp_ticker, qc_ticker in self.tickers.items():
# quantpedia #1 Contract
data = self.AddData(data_tools.QuantpediaFutures, qp_ticker, Resolution.Daily)
data.SetFeeModel(data_tools.CustomFeeModel())
data.SetLeverage(5)
quantpedia_future_symbol:Symbol = data.Symbol
# QC futures
future:Future = self.AddFuture(qc_ticker, Resolution.Daily, dataNormalizationMode=DataNormalizationMode.Raw)
future.SetFilter(timedelta(days=self.min_expiration_days), timedelta(days=self.max_expiration_days))
self.futures_data[future.Symbol.Value] = data_tools.FuturesData(quantpedia_future_symbol, self.period)
self.recent_month:int = -1
def FindAndUpdateContracts(self, futures_chain, ticker) -> None:
near_contract:FuturesContract = None
dist_contract:FuturesContract = None
if ticker in futures_chain:
contracts:list[:FuturesContract] = [contract for contract in futures_chain[ticker] if contract.Expiry.date() > self.Time.date()]
if len(contracts) >= 2:
contracts:list[:FuturesContract] = sorted(contracts, key=lambda x: x.Expiry, reverse=False)
near_contract = contracts[0]
dist_contract = contracts[1]
self.futures_data[ticker].update_contracts(near_contract, dist_contract)
def OnData(self, data):
# daily update QC futures data
if data.FutureChains.Count > 0:
for ticker, future_obj in self.futures_data.items():
# check if near contract is expired or is not initialized
if not future_obj.is_initialized() or \
(future_obj.is_initialized() and future_obj.near_contract.Expiry.date() == self.Time.date()):
self.FindAndUpdateContracts(data.FutureChains, ticker)
# update QC futures rolling return
if future_obj.is_initialized():
near_c:FuturesContract = future_obj.near_contract
dist_c:FuturesContract = future_obj.distant_contract
if near_c.Symbol in data and data[near_c.Symbol] and dist_c.Symbol in data and data[dist_c.Symbol]:
raw_price1:float = data[near_c.Symbol].Value * self.Securities[ticker].SymbolProperties.PriceMagnifier
raw_price2:float = data[dist_c.Symbol].Value * self.Securities[ticker].SymbolProperties.PriceMagnifier
if raw_price1 != 0 and raw_price2 != 0:
daily_return:float = raw_price1 / raw_price2 - 1
future_obj.update_roll_return(daily_return)
# check if quantpedia data still coming
for _, future_obj in self.futures_data.items():
quantpedia_future:Symbol = future_obj.quantpedia_future
# if quantpedia_future in data and data[quantpedia_future]:
# future_obj.update_quantpedia_last_update(self.Time.date())
# rebalance monthly
if self.recent_month != self.Time.month:
self.recent_month = self.Time.month
self.Rebalance()
def Rebalance(self):
custom_data_last_update_date: Dict[Symbol, datetime.date] = data_tools.QuantpediaFutures.get_last_update_date()
self.Liquidate()
ready_futures:dict[Symbol, list] = {}
# filter ready futures and reset futures, which do not recieve new data
for _, future_obj in self.futures_data.items():
data_ready_flag = future_obj.is_ready()
if self.securities[future_obj.quantpedia_future].get_last_data() and self.time.date() > custom_data_last_update_date[future_obj.quantpedia_future]:
self.liquidate()
return
if data_ready_flag:
ready_futures[future_obj.quantpedia_future] = future_obj.reverse_roll_return()
elif data_ready_flag:
future_obj.reset_data()
ready_futures_length:int = len(ready_futures)
if ready_futures_length == 0: return
df:pd.DataFrame = pd.DataFrame(ready_futures, columns=ready_futures.keys())
optimization:data_tools.PortfolioOptimization = data_tools.PortfolioOptimization(df, 0, ready_futures_length)
opt_weight:list[float] = optimization.opt_portfolio()
if sum(opt_weight) == 0: return
for index in range(ready_futures_length):
weight:float = opt_weight[index]
if weight >= 0.001:
self.SetHoldings(df.columns[index], weight)