Currency · Global · CFDs, forwards, futures, swaps · Monthly · Global Free

US Equity Tail Risk and Currency Risk Premia

Academic paper

AuthorsZhenzhen Fan; Juan M. Londoño; Xiao Xiao

Institute

CAUniversity of Manitoba
?University of Manitoba - Department of Accounting and Finance
City, University of London
?City University London - Bayes Business School

Paper linkhttps://ssrn.com/abstract=3399980

Strategy in a nutshell

The strategy trades developed market currencies, including Australia, Canada, Denmark, the Euro area, Hong Kong, Israel, Japan, New Zealand, Norway, Singapore, South Korea, Sweden, Switzerland, and the UK. It quantifies U.S. equity tail risk by constructing a zero-cost portfolio that goes long the CBOE PPut Index and short the S&P 500 Index, using the log return of this spread as the measure of U.S. tail risk. For each currency, tail betas are estimated through 60-month rolling regressions of monthly excess returns against both the S&P 500 and the U.S. tail risk factor. Currencies are then sorted into five portfolios by tail betas, with the strategy taking long positions in the lowest-beta portfolio (hedge currencies) and short positions in the highest-beta portfolio (pro-cyclical currencies). The portfolios are equally weighted and rebalanced monthly.

Economic rationale

U.S. equity markets exert a dominant influence on global asset pricing—U.S. returns lead global markets, while the reverse influence is limited. During periods of heightened U.S. tail risk, currencies that appreciate against the U.S. dollar act as effective hedges, providing lower expected returns due to their safe-haven properties. Conversely, currencies that depreciate during market stress carry higher risk premiums. The option-implied tail risk factor, derived from tradable instruments, offers a forward-looking and high-frequency measure of downside risk, capturing both the likelihood and potential magnitude of extreme market events. This makes it a powerful and transparent tool for pricing risk in international currency markets, outperforming traditional volatility-based metrics.

Backtest performance

Annualised return4.57%

Volatility8.16%

Beta-0.029

Sharpe ratio0.56

Win rate45%

Full Python code

1from AlgorithmImports import *
2from collections import deque
3import numpy as np
4class USEquityTailRiskandCurrencyRiskPremia(QCAlgorithm):
5def Initialize(self):
6self.SetStartDate(2000, 1, 1)
7self.SetCash(100000)
8
9self.symbols = {
10                "CME_AD1",   # Australian Dollar Futures, Continuous Contract #1
11                "CME_CD1",   # Canadian Dollar Futures, Continuous Contract #1
12                "CME_EC1",   # Euro FX Futures, Continuous Contract #1
13                "CME_JY1",   # Japanese Yen Futures, Continuous Contract #1
14                "CME_NE1",   # New Zealand Dollar Futures, Continuous Contract #1
15                "CME_SF1",    # Swiss Franc Futures, Continuous Contract #1
16                "CME_BP1"   # British Pound Futures, Continuous Contract #1
17}
18
19# Daily ROC data.
20self.data = {}
21self.period = 21
22self.SetWarmUp(self.period)
23# Regression data rolling window.
24self.regression_period = 60
25self.regression_data = {}
26self.pput_index = self.AddData(PPUT, 'PPUT', Resolution.Daily).Symbol
27self.data[self.pput_index] = self.ROC(self.pput_index, self.period, Resolution.Daily)
28
29self.market = self.AddEquity('SPY', Resolution.Daily).Symbol
30self.data[self.market] = self.ROC(self.market, self.period, Resolution.Daily)
31
32for symbol in self.symbols:
33    data = self.AddData(data_tools.QuantpediaFutures, symbol, Resolution.Daily)
34    data.SetFeeModel(data_tools.CustomFeeModel())
35    data.SetLeverage(5)
36    
37    self.data[symbol] = self.ROC(symbol, self.period, Resolution.Daily)
38    
39    self.regression_data[symbol] = deque(maxlen = self.regression_period)
40
41self.Schedule.On(self.DateRules.MonthStart(self.market), self.TimeRules.AfterMarketOpen(self.market), self.Rebalance)
42def Rebalance(self):
43# Regression data.
44# Source: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3399980
45dol_factor_return = None
46mkt_factor_return = None
47tail_factor_return = None
48
49if self.data[self.market].IsReady and self.data[self.pput_index].IsReady:
50    # To measure the US tail risk, construct a zero-investment strategy that longs the CBOE PPut index and shorts the S&P 500 index.
51    tail_factor_return = (self.data[self.pput_index].Current.Value - self.data[self.market].Current.Value) / 2
52    mkt_factor_return = self.data[self.market].Current.Value
53
54currency_returns = {x : self.data[x].Current.Value for x in self.symbols if self.data[x].IsReady}
55if len(currency_returns) != 0:
56    dol_factor_return = np.average([x[1] for x in currency_returns.items()])
57
58# Factors for regression are ready.
59if dol_factor_return and mkt_factor_return and tail_factor_return:
60    
61    tail_beta = {}
62    
63    for symbol, symbol_return in currency_returns.items():
64        reg_data = (symbol_return, dol_factor_return, mkt_factor_return, tail_factor_return)
65        self.regression_data[symbol].append(reg_data)
66        
67        if len(self.regression_data[symbol]) == self.regression_data[symbol].maxlen:
68            symbol_returns = [x[0] for x in self.regression_data[symbol]]
69            dols = [x[1] for x in self.regression_data[symbol]]
70            mkts = [x[2] for x in self.regression_data[symbol]]
71            tails = [x[3] for x in self.regression_data[symbol]]
72            
73            # Regression.
74            x = [dols[:-1], mkts[:-1], tails[:-1]]
75            regression_model = data_tools.MultipleLinearRegression(x, symbol_returns[1:])
76            tail_beta[symbol] = regression_model.params[3]
77            
78    sorted_by_beta = sorted(tail_beta.items(), key = lambda x:x[1], reverse = True)
79    quintile = int(len(sorted_by_beta) / 5)
80    long = [x[0] for x in sorted_by_beta[-quintile:]]
81    short = [x[0] for x in sorted_by_beta[:quintile]]
82
83    # Trade execution.
84    long_count = len(long)
85    short_count = len(short)
86    
87    invested = [x.Key.Value for x in self.Portfolio if x.Value.Invested]
88    for symbol in invested:
89        if symbol not in long + short:
90            self.Liquidate(symbol)
91    
92    for symbol in long:
93        self.SetHoldings(symbol, 1 / long_count)
94    for symbol in short:
95        self.SetHoldings(symbol, -1 / short_count)
96        
97# PPUT index.
98# NOTE: IMPORTANT: Data order must be ascending (datewise)
99# Data source: http://www.cboe.com/products/strategy-benchmark-indexes/put-protection-index
100class PPUT(PythonData):
101def GetSource(self, config, date, isLiveMode):
102return SubscriptionDataSource("data.quantpedia.com/backtesting_data/index/pput.csv", SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
103def Reader(self, config, line, date, isLiveMode):
104data = PPUT()
105data.Symbol = config.Symbol
106
107if not line[0].isdigit(): return None
108split = line.split(';')
109
110data.Time = datetime.strptime(split[0], "%m/%d/%Y") + timedelta(days=1)
111data['close'] = float(split[1])
112data.Value = float(split[1])
113return data