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

Stock and Bond Returns Predict Currency Returns

Academic paper

Foreign Currency Forecasting: What Can Stock and Bond Markets Tell Us?

AuthorsKate Phylaktis; Ehab Abdel-Tawab Yamani

Institute

City, University of London
?City University London - The Business School
Chicago State University

Paper linkhttps://papers.ssrn.com/sol3/papers.cfm?abstract_id=3775939

Strategy in a nutshell

Universe: 28 currencies vs USD. Each month, use the past 120 months of equity- and bond-based predictors to forecast next-month currency returns. Long currencies with positive predicted returns, short those with negative predicted returns. Equally weighted, monthly rebalanced.

Economic rationale

Currency returns are linked to equity and bond market signals:

Return-chasing: strong local equity returns → currency appreciation.

Portfolio-rebalancing: strong equity returns → FX exposure reduced → depreciation.

Incorporating bonds (via UIP) enhances predictive power, exploiting cross-market information

Backtest performance

Annualised return8.47%

Volatility3.88%

Beta-0.009

Sharpe ratio2.11

Sortino ratio-0.3

Win rate49%

Full Python code

1import statsmodels.api as sm
2from AlgorithmImports import *
3import data_tools
4
5class TheSerialDependenceoftheCommodityFuturesReturns(QCAlgorithm):
6
7def Initialize(self):
8self.SetStartDate(2000, 1, 1)
9self.SetCash(100000)
10
11# equity etf and 10Y bond yield symbols by currency symbol
12self.symbols = {
13    "AUDUSD" : ("EWA", "AU10YT"),
14    "CADUSD" : ("EWC", "CA10YT"),
15    "EURUSD" : ("EWG", "DE10YT"),
16    "JPYUSD" : ("EWJ", "JP10YT"),
17    "NZDUSD" : ("ENZL", "NZ10YT"),
18    "USDNOK" : ("ENOR", "NO10YT"),
19    "CHFUSD" : ("EWL", "CH10YT"),
20    "GBPUSD" : ("EWU", "GB10YT"),
21    "USDINR" : ("INDA", "IN10YT"),
22    "USDMXN" : ("EWW", "MX10YT"),
23    "USDPLN" : ("EPOL", "PL10YT"),
24    "USDSGD" : ("EWS", "SG10YT"),
25    "USDTRY" : ("TUR", "TR10YT"),
26    }
27
28self.us_bonds = self.AddData(data_tools.QuantpediaBondYield, "US10YT", Resolution.Daily).Symbol
29self.us_equities = self.AddEquity("VTI", Resolution.Daily).Symbol
30
31self.daily_period = 21
32self.period = 120 + 1
33self.SetWarmUp(self.period * self.daily_period, Resolution.Daily)
34
35self.perf_data = {}
36self.last_month_price = {}
37self.bond_yield_values = {}
38
39for currency_symbol, (equity_symbol, bond_symbol) in self.symbols.items():
40    # currency
41    data = self.AddForex(currency_symbol, Resolution.Daily, Market.Oanda)
42    data.SetFeeModel(data_tools.CustomFeeModel())
43    data.SetLeverage(5)
44    
45    # equity
46    self.AddEquity(equity_symbol, Resolution.Daily)
47    
48    # bond
49    self.AddData(data_tools.QuantpediaBondYield, bond_symbol, Resolution.Daily)
50    self.bond_yield_values[bond_symbol] = []
51    
52    # price and performance data needed
53    symbols_needed = [currency_symbol, equity_symbol, bond_symbol]
54    for symbol in symbols_needed:
55        self.last_month_price[symbol] = None    
56        self.perf_data[symbol] = RollingWindow[float](self.period)
57
58self.last_month_price[self.us_equities] = None    
59self.perf_data[self.us_equities] = RollingWindow[float](self.period)
60
61self.perf_data[self.us_bonds] = RollingWindow[float](self.period)
62self.bond_yield_values[self.us_bonds] = []
63
64self.recent_month = -1
65
66def OnData(self, data):
67# store daily bond yields
68bond_yield_symbols = [x[1][1] for x in self.symbols.items()]
69for bond_symbol in bond_yield_symbols + [self.us_bonds]:
70    if bond_symbol in data and data[bond_symbol]:
71        self.bond_yield_values[bond_symbol].append(data[bond_symbol].Value)
72
73# rebalance once a month
74if self.recent_month == self.Time.month:
75    return
76self.recent_month = self.Time.month
77
78if len(self.bond_yield_values[self.us_bonds]) == 0:
79    return
80
81us_data_available = False
82
83# store monthly performance for us bonds and equities
84if self.Securities[self.us_equities].GetLastData() and (self.Time.date() - self.Securities[self.us_equities].GetLastData().Time.date()).days < 5 and    \
85    self.Securities[self.us_bonds].GetLastData() and (self.Time.date() - self.Securities[self.us_bonds].GetLastData().Time.date()).days < 5:
86    
87    us_eq_price = self.Securities[self.us_equities].Price
88
89    # symbol has last month's price stored
90    if self.last_month_price[self.us_equities] is not None:
91        self.perf_data[self.us_equities].Add(us_eq_price - self.last_month_price[self.us_equities])
92    
93    # store monthly price
94    self.last_month_price[self.us_equities] = us_eq_price
95    
96    # calculate monthly bond yield equity performance
97    monthly_us_bond_perf = self.bond_yield_equity_performance(np.array(self.bond_yield_values[self.us_bonds]))     # take any count there is for a given month of daily bond yield values
98    self.perf_data[self.us_bonds].Add(monthly_us_bond_perf)
99
100    us_data_available = True
101
102long = []
103short = []
104for currency_symbol, (equity_symbol, bond_symbol) in self.symbols.items():
105    # bond and equity data is still comming in
106    if self.Securities[currency_symbol].GetLastData() and (self.Time.date() - self.Securities[currency_symbol].GetLastData().Time.date()).days < 5 and \
107        self.Securities[bond_symbol].GetLastData() and (self.Time.date() - self.Securities[bond_symbol].GetLastData().Time.date()).days < 5 and \
108        self.Securities[equity_symbol].GetLastData() and (self.Time.date() - self.Securities[equity_symbol].GetLastData().Time.date()).days < 5:
109        
110        symbols_needed = [currency_symbol, equity_symbol]
111        
112        # store monthly prices and performance
113        for symbol in symbols_needed:
114            price = self.Securities[symbol].Price
115            
116            # symbol has last month's price stored
117            if self.last_month_price[symbol] is not None:
118                self.perf_data[symbol].Add(price - self.last_month_price[symbol])
119            
120            # store monthly price
121            self.last_month_price[symbol] = price
122        
123        # bond yield value collection is not empty and it's size is equall to size of us bond yield values
124        if len(self.bond_yield_values[bond_symbol]) != 0:
125            # compute monthly bond yield equity performance
126            monthly_bond_perf = self.bond_yield_equity_performance(np.array(self.bond_yield_values[bond_symbol]))   # take any count there is for a given month of daily bond yield values
127            self.perf_data[bond_symbol].Add(monthly_bond_perf)
128        
129        symbols_needed += [bond_symbol]
130        
131        # regression data is ready
132        if all(self.perf_data[symbol].IsReady for symbol in symbols_needed + [self.us_bonds, self.us_equities]) and us_data_available:
133            # linear regression
134            y = np.array([x for x in self.perf_data[currency_symbol]][:-1])
135            x = np.array([
136                [x for x in self.perf_data[bond_symbol]][1:],
137                [x for x in self.perf_data[self.us_bonds]][1:],
138                [x for x in self.perf_data[equity_symbol]][1:],
139                [x for x in self.perf_data[self.us_equities]][1:]
140                ])
141        
142            # prediction
143            model_result = self.multiple_linear_regression(x, y)
144            x_pred = np.array([
145                1,
146                self.perf_data[bond_symbol][0],
147                self.perf_data[self.us_bonds][0],
148                self.perf_data[equity_symbol][0],
149                self.perf_data[self.us_equities][0]
150                ])
151            
152            y_pred = model_result.predict(x_pred)[0]
153            if y_pred > 0:
154                # reverse position if needed
155                if currency_symbol[-3:] == 'USD':
156                    long.append(currency_symbol)
157                else:
158                    short.append(currency_symbol)
159            else:
160                # reverse position if needed
161                if currency_symbol[-3:] == 'USD':
162                    short.append(currency_symbol)
163                else:
164                    long.append(currency_symbol)
165    
166    self.bond_yield_values[bond_symbol] = []
167
168self.bond_yield_values[self.us_bonds] = []
169
170if self.IsWarmingUp:
171    return
172
173# trade execution
174invested = [x.Key.Value for x in self.Portfolio if x.Value.Invested]
175for symbol in invested:
176    if symbol not in long + short:
177        self.Liquidate(symbol)
178        
179for symbol in long:
180    self.SetHoldings(symbol, 1 / len(long))
181for symbol in short:
182    self.SetHoldings(symbol, -1 / len(short))
183
184def multiple_linear_regression(self, x:np.array, y:np.array):
185x = x.T
186x = sm.add_constant(x)
187result = sm.OLS(endog=y, exog=x).fit()
188return result
189
190def bond_yield_equity_performance(self, bond_yield_values:np.array) -> float:
191x:np.array = 1+bond_yield_values[:-1]/100/250
192y:np.array = 7.7 * (bond_yield_values[:-1] - bond_yield_values[1:]) / 100
193z:np.array = x+y
194
195previous_equity:float = 1.0
196eq:list = [previous_equity]
197
198# calculate next equity value from the previous one
199for value in z:
200    new_eq = value*previous_equity
201    eq += [new_eq]
202    previous_equity = new_eq
203    
204performance:float = (eq[-1] / eq[0] - 1)
205return performance