backtestStrategy
Create backtestStrategy
object to define portfolio allocation
strategy
Description
Create a backtestStrategy
object which defines a portfolio
allocation strategy.
Use this workflow to develop and run a backtest:
Define the strategy logic using a
backtestStrategy
object to specify how the strategy rebalances a portfolio of assets.Use
backtestEngine
to create abacktestEngine
object that specifies the parameters of the backtest.Use
runBacktest
to run the backtest against historical asset price data and, optionally, trading signal data.Use
equityCurve
to plot the equity curves of each strategy.Use
summary
to summarize the backtest results in a table format.
For more detailed information on this workflow, see Backtest Investment Strategies.
Creation
Description
creates a strategy
= backtestStrategy(name
,rebalanceFcn
)backtestStrategy
object.
sets properties using
name-value pair arguments and any of the arguments in the previous syntax.
You can specify multiple name-value pair arguments. For example,
strategy
= backtestStrategy(___,Name,Value
)strat =
backtestStrategy('MyStrategy',@myRebalFcn,'TransactionCost',0.005,'LookbackWindow',20)
.
Input Arguments
name
— Strategy name
string
Strategy name, specified as a string.
Data Types: string
rebalanceFcn
— Rebalance function
function handle
Rebalance function, specified as a function handle. A function handle
computes new portfolio weights during the backtest. The
rebalanceFcn
argument implements the core logic
of the trading strategy and must have one of the following signatures:
new_weights = rebalanceFcn(weights,assetPrices)
new_weights = rebalanceFcn(weights,assetPrices,signalData)
The rebalance function is called by the backtestEngine
object each time the strategy must be
rebalanced. The backtestEngine
object calls the rebalance function with
the following arguments:
weights
— The current portfolio weights before rebalancing, specified as decimal percentages.assetPrices
— Atimetable
containing a rolling window of adjusted asset prices.NaN
s are allowed in theassetPrices
timetable.Note
If the backtest engine encounters a
NaN
return for an asset with a non-zero position, an error is generated. To correct this, either remove missing asset prices from theassetPrices
timetable or have the rebalance functions avoid investing in assets that encounter invalid returns.signalData
— Atimetable
containing a rolling window of signal data.NaN
s or<missing>
are allowed in thesignalData
timetable.If you provide signal data to the
backtestEngine
object, then the engine object passes it to the strategy rebalance function using the three input argument syntax. If do not provide signal data thebacktestEngine
object, then the engine object calls the rebalance function with the two input argument syntax.The rebalance function must return a single output argument for
new_weights
which is a vector of asset weights specified as decimal percentages.If the
new_weights
sum to1
, then the portfolio is fully invested.If the
new_weights
sum to less than1
, then the portfolio will has the remainder in cash, earning theRiskFreeRate
specified in thebacktestEngine
object.If the
new_weights
sum to more than1
, then there is a negative cash position (margin) and the cash borrowed accrues interest at the cash borrowing rate specified in theCashBorrowRate
property of thebacktestEngine
object.
For more information on developing a
rebalanceFcn
function handle, see Backtest Investment Strategies.
Data Types: function_handle
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: strat =
backtestStrategy('MyStrategy',@myRebalFcn,'TransactionCost',0.005,'LookbackWindow',20)
RebalanceFrequency
— Rebalance frequency during backtest
1
(default) | integer | duration
object | calendarDuration
object | vector of datetime
objects
Rebalance frequency during the backtest, specified as the
comma-separated pair consisting of
'RebalanceFrequency'
and a scalar integer,
duration
object,
calendarDuration
object, or a vector of
datetime
objects.
If using an integer, the integer represents the number of time
steps between rebalancing. For example, if you provide the backtestEngine
object with daily price data, then the
RebalanceFrequency
specifies the number of
days between rebalancing. The default is 1
,
meaning the strategy rebalances with each time step.
If using a duration
object or
calendarDuration
, the
backtest engine creates a rebalance schedule of times, starting at
the backtest start time, with rebalance times occurring after each
step of the specified duration.
If using a vector of datetime
objects, the
RebalanceFrequency
defines an explicit
schedule of rebalance times. The backtest engine will rebalance at
each datetime in the provided schedule.
Note
For both the duration and datetime syntaxes, if a rebalance time is not found in the backtest dataset, the engine will rebalance at the nearest time prior to the scheduled time. For example, if the rebalance schedule contains a weekend, the rebalance will occur on the Friday before.
Data Types: double
| object
TransactionCosts
— Transaction costs for trades
0
(not computed) (default) | numeric | vector | function handle
Transaction costs for trades, specified as the comma-separated
pair consisting of 'TransactionCosts'
and a
scalar numeric, vector, or function handle. You can specify
transaction costs in three ways:
rate
— A scalar decimal percentage charge to both purchases and sales of assets. For example ,if you setTransactionCosts
to0.001
, then each transaction (buys and sells) would pay 0.1% in transaction fees.[buyRate, sellRate]
— A1
-by-2
vector of decimal percentage rates that specifies separate rates for buying and selling of assets.computeTransactionCostsFcn
— A function handle to compute customized transaction fees. If you specify a function handle, thebacktestEngine
object calls theTransactionCosts
function to compute the fees for each rebalance. The user-defined function handle must have the following signature:[buyCosts,sellCosts] = computeCostsFcn(deltaPositions)
The user-defined function handle takes a single input argument
deltaPositions
, which is a vector of changes in asset positions for all assets (in currency units) as a result of a rebalance. Positive elements in thedeltaPositions
vector indicate purchases while negative entries represent sales. The user-defined function handle must return two output argumentsbuyCosts
andsellCosts
, which contain the total costs (in currency) for the entire rebalance for each type of transaction.
Data Types: double
| function_handle
LookbackWindow
— Lookback window
[0 Inf]
(default) | 1
-by-2
vector using
integers | duration
object | calendarDuration
object
Lookback window, specified as the comma-separated pair consisting
of 'LookbackWindow'
and a
1
-by-2
vector of integers,
a duration
object, or
calendarDuration
object.
When using a 1
-by-2
vector
with integers that defines the minimum and maximum size of the
rolling window of data (asset prices and signal data) that you
provide to the rebalanceFcn
argument. You
specify these limits in terms of the number of time steps. When
specified as integers, the lookback window is defined in terms of
rows of data from the asset (pricesTT
) and signal
(signalTT
) timetables used in the backtest.
The lookback minimum sets the minimum number of rows of asset price
data that must be available to the rebalance function before a
strategy rebalance can occur. The lookback maximum sets the maximum
size for the rolling window of price data that is passed to the
rebalance function.
For example, if the backtestEngine
object is provided with daily price
data, then LookbackWindow
specifies the size
bounds of the rolling window in days. The default is [0
Inf]
, meaning that all available past data is given to
the rebalance function. If you specify a non-zero minimum, then the
software does not call rebalanceFcn
until
enough time steps process to meet the minimum size.
If you specify LookbackWindow
as a single
scalar value, then the value is both the minimum and maximum of the
LookbackWindow
(that is, a fixed-sized
window).
If using a duration
object or
calendarDuration
, the
lookback window minimum and maximum are defined in terms of
timespans relative to the time at a rebalance. For example if the
lookback minimum was set to five days (that is,
days(5)
), the rebalance will only occur if
the backtest start time is at least five days prior to the rebalance
time. Similarly, if the lookback maximum was set to six months (that
is, calmonths(6)
), the lookback window would
contain only data that occurred at six months prior to the rebalance
time or later.
Note
Alternatively, the LookbackWindow
can be
set to a single scalar value indicating that the rolling window
should be exactly that size (either in terms of rows or a time
duration). The minimum and maximum size will both be set to the
provided value.
Data Types: double
| object
InitialWeights
— Initial portfolio weights
[ ]
(default) | vector
Initial portfolio weights, specified as the comma-separated pair
consisting of 'InitialWeights'
and a vector. The
InitialWeights
vector sets the portfolio
weights before the backtestEngine
object begins the backtest. The size of
the initial weights vector must match the number of assets used in
the backtest.
Alternatively, you can set the InitialWeights
name-value pair argument to empty ([ ]
) to
indicate the strategy will begin with no investments and in a 100%
cash position. The default for InitialWeights
is empty ([ ]
).
Data Types: double
Properties
Name
— Strategy name
string
Strategy name, specified as a string.
Data Types: string
RebalanceFcn
— Rebalance function
function handle
Rebalance function, specified as a function handle.
Data Types: function_handle
RebalanceFrequency
— Rebalance frequency during backtest
1
(default) | numeric
Rebalance frequency during the backtest, specified as a scalar numeric.
Data Types: double
TransactionCosts
— Transaction costs
0
(default) | numeric | vector | function handle
Transaction costs, specified as a scalar numeric, vector, or function handle.
Data Types: double
| function_handle
LookbackWindow
— Lookback window
[0 Inf]
(default) | numeric | vector
Lookback window, specified as a scalar numeric or vector.
Data Types: double
InitialWeights
— Initial weights
[ ]
(default) | vector
Initial weights, specified as a vector.
Data Types: double
Examples
Create Backtesting Strategies
Define a backtest strategy by using a backtestStrategy
object. backtestStrategy
objects contain properties specific to a trading strategy, such as the rebalance frequency, transaction costs, and a rebalance function. The rebalance function implements the core logic of the strategy and is used by the backtesting engine during the backtest to allow the strategy to change its asset allocation and to make trades. In this example, to illustrate how to create and use backtest strategies in MATLAB®, you prepare two simple strategies for backtesting:
An equal weighted strategy
A strategy that attempts to "chase returns"
The strategy logic for these two strategies is defined in the rebalance functions.
Set Strategy Properties
A backtestStrategy
object has several properties that you set using parameters for the backtestStrategy
function.
Initial Weights
The InitialWeights
property contains the asset allocation weights at the start of the backtest. The default value for InitialWeights
is empty ([]
), which indicates that the strategy begins the backtest uninvested, meaning that 100% of the capital is in cash earning the risk-free rate.
Set the InitialWeights
to a specific asset allocation. The size of the initial weights vector must match the number of assets in the backtest.
% Initialize the strategies with 30 weights, since the backtest % data comes from a year of the 30 DJIA stocks. numAssets = 30; % Give the initial weights for both strategies equal weighting. Weights % must sum to 1 to be fully invested. initialWeights = ones(1,numAssets); initialWeights = initialWeights / sum(initialWeights);
Transaction Costs
The TransactionCosts
property allows you to set the fees that the strategy pays for trading assets. Transaction costs are paid as a percentage of the total change in position for each asset. Specify costs in decimal percentages. For example, if TransactionCosts
is set to 1% (0.01
) and the strategy buys $100 worth of a stock, then the transaction costs incurred are $1.
Transaction costs are set using a 1
-by-2
vector that sets separate fee rates for purchases and sales of assets. In this example, both strategies pay the same transaction costs — 25 basis points for asset purchases and 50 basis points for sales.
% Define the Transaction costs as [buyCosts sellCost] and specify the costs % as decimal percentages. tradingCosts = [0.0025 0.005];
You can also set the TransactionCosts property to a function handle if you need to implement arbitrarily complex transaction cost structures. For more information on creating transaction cost functions, see backtestStrategy
.
Rebalance Frequency
The RebalanceFrequency
property determines how often the backtesting engine rebalances and reallocates the portfolio of a strategy using the rebalance function. Set the RebalanceFrequency
in terms of time steps in the backtest. For example, if the backtesting engine is testing a strategy with a set of daily price data, then set the rebalance function in days. Essentially, RebalanceFrequency
represents the number of rows of price data to process between each call to the strategy rebalance function.
% Both strategies rebalance every 4 weeks (20 days).
rebalFreq = 20;
Lookback Window
Each time the backtesting engine calls a strategy rebalance function, a window of asset price data (and possibly signal data) is passed to the rebalance function. The rebalance function can then make trading and allocation decisions based on a rolling window of market data. The LookbackWindow
property sets the size of these rolling windows. Set the window in terms of time steps. The window determines the number of rows of data from the asset price timetable that are passed to the rebalance function.
The LookbackWindow
property can be set in two ways. For a fixed-sized rolling window of data (for example, "50 days of price history"), the LookbackWindow
property is set to a single scalar value (N
= 50
). The software then calls the rebalance function with a price timetable containing exactly N
rows of rolling price data.
Alternatively, you can define the LookbackWindow property by using a 1
-by-2
vector [min max]
that specifies the minimum and maximum size for an expanding window of data. In this way, you can set flexible window sizes. For example:
[10 Inf]
— At least 10 rows of data[0 50]
— No more than 50 rows of data[0 Inf]
— All available data (that is, no minimum, no maximum); this is the default value[20 20]
— Exactly 20 rows of data; this is equivalent to settingLookbackWindow
to the scalar value20
The software does not call the rebalance function if the data is insufficient to create a valid rolling window, regardless of the value of the RebalanceFrequency
property.
If the strategy does not require any price or signal data history, then you can indicate that the rebalance function requires no data by setting the LookbackWindow
property to 0
.
% The equal weight strategy does not require any price history data. ewLookback = 0; % The "chase returns" strategy bases its decisions on the trailing % 10-day asset returns. The lookback window is set to 11 since computing 10 days % of returns requires the close price from day 0. chaseLookback = 11;
Rebalance Function
The rebalance function (rebalanceFcn
) is the user-authored function that contains the logic of the strategy. The backtesting engine calls the strategy rebalance function with a fixed set of parameters and expects it to return a vector of asset weights representing the new, desired portfolio allocation after a rebalance. For more information, see the rebalance functions.
Create Strategies
Using the prepared strategy properties, you can create the two strategy objects.
% Create the equal weighted strategy. The rebalance function @equalWeights % is defined in the Rebalance Functions section at the end of this example. equalWeightStrategy = backtestStrategy("EqualWeight",@equalWeight,... 'RebalanceFrequency',rebalFreq,... 'TransactionCosts',tradingCosts,... 'LookbackWindow',ewLookback,... 'InitialWeights',initialWeights)
equalWeightStrategy = backtestStrategy with properties: Name: "EqualWeight" RebalanceFcn: @equalWeight RebalanceFrequency: 20 TransactionCosts: [0.0025 0.0050] LookbackWindow: 0 InitialWeights: [0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 ... ]
% Create the "chase returns" strategy. The rebalance function % @chaseReturns is defined in the Rebalance Functions section at the end of this example. chaseReturnsStrategy = backtestStrategy("ChaseReturns",@chaseReturns,... 'RebalanceFrequency',rebalFreq,... 'TransactionCosts',tradingCosts,... 'LookbackWindow',chaseLookback,... 'InitialWeights',initialWeights)
chaseReturnsStrategy = backtestStrategy with properties: Name: "ChaseReturns" RebalanceFcn: @chaseReturns RebalanceFrequency: 20 TransactionCosts: [0.0025 0.0050] LookbackWindow: 11 InitialWeights: [0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 ... ]
Set Up Backtesting Engine
To backtest the two strategies, use the backtestEngine
object. The backtesting engine sets parameters of the backtest that apply to all strategies, such as the risk-free rate and initial portfolio value. For more information, see backtestEngine
.
% Create an array of strategies for the backtestEngine. strategies = [equalWeightStrategy chaseReturnsStrategy]; % Create backtesting engine to test both strategies. backtester = backtestEngine(strategies);
Rebalance Functions
Strategy rebalance functions defined using the rebalanceFcn
argument for backtestStrategy
must adhere to a fixed API that the backtest engine expects when interacting with each strategy. Rebalance functions must implement one of the following two syntaxes:
function new_weights = exampleRebalanceFcn(current_weights,assetPriceTimeTable) function new_weights = exampleRebalanceFcn(current_weights,assetPriceTimeTable,signalDataTimeTable)
All rebalance functions take as their first input argument the current allocation weights of the portfolio. current_weights
represents the asset allocation just before the rebalance occurs. During a rebalance, you can use current_weights
in a variety of ways. For example, you can use current_weights
to determine how far the portfolio allocation has drifted from the target allocation or to size trades during the rebalance to limit turnover.
The second and third arguments of the rebalance function syntax are the rolling windows of asset prices and optional signal data. The two tables contain the trailing N
rows of the asset and signal timetables that are passed to the runBacktest
function, where N
is set using the LookbackWindow
property of each strategy.
If optional signal data is provided to the runBacktest
function, then the backtest engine passes the rolling window of signal data to each strategy that supports it.
The equalWeight
strategy simply invests equally across all assets.
function new_weights = equalWeight(current_weights,assetPrices) %#ok<INUSD> % Invest equally across all assets. num_assets = numel(current_weights); new_weights = ones(1,num_assets) / num_assets; end
The chaseReturns
strategy invests only in the top X stocks based on their rolling returns in the lookback window. This naive strategy is used simply as an illustrative example.
function new_weights = chaseReturns(current_weights,assetPrices) % Set number of stocks to invest in. numStocks = 15; % Compute rolling returns from lookback window. rollingReturns = assetPrices{end,:} ./ assetPrices{1,:}; % Select the X best performing stocks over the lookback window [~,idx] = sort(rollingReturns,'descend'); bestStocksIndex = idx(1:numStocks); % Initialize new weights to all zeros. new_weights = zeros(size(current_weights)); % Invest equally across the top performing stocks. new_weights(bestStocksIndex) = 1; new_weights = new_weights / sum(new_weights); end
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