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summary

Generate summary table of backtest results

Description

example

summaryTable = summary(backtester) generates a table of metrics to summarize the backtest. Each row of the table is a calculated metric and each column represents a strategy. You must run the summary function only after running the runBacktest function.

Examples

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The MATLAB® backtesting engine runs backtests of portfolio investment strategies over time series of asset price data. You can use summary to compare multiple strategies over the same market scenario. This example shows how to examine the results of a backtest with two strategies.

Load Data

Load one year of stock price data. For readability, this example uses a subset of the DJIA stocks.

% Read table of daily adjusted close prices for 2006 DJIA stocks
T = readtable('dowPortfolio.xlsx');

% Prune the table to include only the dates and selected stocks
timeColumn = "Dates";
assetSymbols = ["BA", "CAT", "DIS", "GE", "IBM", "MCD", "MSFT"];
T = T(:,[timeColumn assetSymbols]);

% Convert to timetable
pricesTT = table2timetable(T,'RowTimes','Dates');

% View the final asset price timetable
head(pricesTT)
ans=8×7 timetable
       Dates        BA       CAT      DIS      GE       IBM      MCD     MSFT 
    ___________    _____    _____    _____    _____    _____    _____    _____

    03-Jan-2006    68.63    55.86    24.18     33.6    80.13    32.72    26.19
    04-Jan-2006    69.34    57.29    23.77    33.56    80.03    33.01    26.32
    05-Jan-2006    68.53    57.29    24.19    33.47    80.56    33.05    26.34
    06-Jan-2006    67.57    58.43    24.52     33.7    82.96    33.25    26.26
    09-Jan-2006    67.01    59.49    24.78    33.61    81.76    33.88    26.21
    10-Jan-2006    67.33    59.25    25.09    33.43     82.1    33.91    26.35
    11-Jan-2006     68.3    59.28    25.33    33.66    82.19     34.5    26.63
    12-Jan-2006     67.9    60.13    25.41    33.25    81.61    33.96    26.48

The inverse variance strategy requires some price history to initialize, so you can allocate a portion of the data to use for setting initial weights. By doing this, you can "warm start" the backtest.

warmupRange = 1:20;
testRange = 21:height(pricesTT);

Create Strategies

Define an investment strategy by using the backtestStrategy function. This example builds two strategies:

  • Equal weighted

  • Inverse variance

This example does not provide details on how to build the strategies. For more information on creating strategies, see backtestStrategy. The strategy rebalance functions are implemented in the Rebalance Functions section.

% Create the strategies
ewInitialWeights = equalWeightFcn([],pricesTT(warmupRange,:));
ewStrategy = backtestStrategy("EqualWeighted",@equalWeightFcn,...
    'RebalanceFrequency',20,...
    'TransactionCosts',[0.0025 0.005],...
    'LookbackWindow',0,...
    'InitialWeights',ewInitialWeights);

ivInitialWeights = inverseVarianceFcn([],pricesTT(warmupRange,:));
ivStrategy = backtestStrategy("InverseVariance",@inverseVarianceFcn,...
    'RebalanceFrequency',20,...
    'TransactionCosts',[0.0025 0.005],...
    'InitialWeights',ivInitialWeights);

% Aggregate the strategies into an array
strategies = [ewStrategy ivStrategy];

Run Backtest

Create a backtesting engine and run a backtest over a year of stock data. For more information on creating backtesting engines, see backtestEngine. The software initializes several properties of the backtestEngine object to empty. These read-only properties are populated by the engine after you run the backtest.

% Create the backtesting engine using the default settings
backtester = backtestEngine(strategies)
backtester = 
  backtestEngine with properties:

               Strategies: [1x2 backtestStrategy]
             RiskFreeRate: 0
           CashBorrowRate: 0
          RatesConvention: "Annualized"
                    Basis: 0
    InitialPortfolioValue: 10000
                NumAssets: []
                  Returns: []
                Positions: []
                 Turnover: []
                  BuyCost: []
                 SellCost: []

Run the backtest using runBacktest.

% Run the backtest
backtester = runBacktest(backtester,pricesTT(testRange,:));

Examine Summary Results

The summary function uses the results of the backtest and returns a table of high-level results from the backtest.

s1 = summary(backtester)
s1=9×2 table
                       EqualWeighted    InverseVariance
                       _____________    _______________

    TotalReturn            0.17567           0.17155   
    SharpeRatio           0.097946           0.10213   
    Volatility           0.0074876         0.0069961   
    AverageTurnover      0.0007014         0.0024246   
    MaxTurnover           0.021107          0.097472   
    AverageReturn       0.00073178        0.00071296   
    MaxDrawdown           0.097647          0.096299   
    AverageBuyCost        0.018532          0.061913   
    AverageSellCost       0.037064           0.12383   

Each row of the table output is a measurement of the performance of a strategy. Each strategy occupies a column. The summary function reports on the following metrics:

  • TotalReturn — The nonannulaized total return of the strategy, inclusive of fees, over the full backtest period.

  • SharpeRatio — The nonannualized Sharpe ratio of each strategy over the backtest. For more information, see sharpe.

  • Volatility — The nonannualized standard deviation of per-time-step strategy returns.

  • AverageTurnover — The average per-time-step portfolio turnover, expressed as a decimal percentage.

  • MaxTurnover — The maximum portfolio turnover in a single rebalance, expressed as a decimal percentage.

  • AverageReturn —The arithmetic mean of the per-time step portfolio returns.

  • MaxDrawdown — The maximum drawdown of the portfolio, expressed as a decimal percentage. For more information, see maxdrawdown.

  • AverageBuyCost — The average per-time-step transaction costs the portfolio incurred for asset purchases.

  • AverageSellCost — The average per-time-step transaction costs the portfolio incurred for asset sales.

Sometimes it is useful to transpose the summary table when plotting the metrics of different strategies.

s2 = rows2vars(s1);
s2.Properties.VariableNames{1} = 'StrategyName'
s2=2×10 table
       StrategyName        TotalReturn    SharpeRatio    Volatility    AverageTurnover    MaxTurnover    AverageReturn    MaxDrawdown    AverageBuyCost    AverageSellCost
    ___________________    ___________    ___________    __________    _______________    ___________    _____________    ___________    ______________    _______________

    {'EqualWeighted'  }      0.17567       0.097946      0.0074876        0.0007014        0.021107       0.00073178       0.097647         0.018532          0.037064    
    {'InverseVariance'}      0.17155        0.10213      0.0069961        0.0024246        0.097472       0.00071296       0.096299         0.061913           0.12383    

bar(s2.AverageTurnover)
title('Average Turnover')
ylabel('Average Turnover (%)')
set(gca,'xticklabel',s2.StrategyName)

Figure contains an axes object. The axes object with title Average Turnover contains an object of type bar.

Examine Detailed Results

After you run the backtest, the backtestEngine object updates the read-only fields with the detailed results of the backtest. The Returns, Positions, Turnover, BuyCost, and SellCost properties each contain a timetable of results. Since this example uses daily price data in the backtest, these timetables hold daily results.

backtester
backtester = 
  backtestEngine with properties:

               Strategies: [1x2 backtestStrategy]
             RiskFreeRate: 0
           CashBorrowRate: 0
          RatesConvention: "Annualized"
                    Basis: 0
    InitialPortfolioValue: 10000
                NumAssets: 7
                  Returns: [230x2 timetable]
                Positions: [1x1 struct]
                 Turnover: [230x2 timetable]
                  BuyCost: [230x2 timetable]
                 SellCost: [230x2 timetable]

Returns

The Returns property holds a timetable of strategy (simple) returns for each time step. These returns are inclusive of all transaction fees.

head(backtester.Returns)
ans=8×2 timetable
       Time        EqualWeighted    InverseVariance
    ___________    _____________    _______________

    02-Feb-2006      -0.007553        -0.0070957   
    03-Feb-2006     -0.0037771         -0.003327   
    06-Feb-2006     -0.0010094        -0.0014312   
    07-Feb-2006      0.0053284         0.0020578   
    08-Feb-2006      0.0099755         0.0095781   
    09-Feb-2006     -0.0026871        -0.0014999   
    10-Feb-2006      0.0048374         0.0059589   
    13-Feb-2006     -0.0056868        -0.0051232   

binedges = -0.025:0.0025:0.025;
h1 = histogram(backtester.Returns.EqualWeighted,'BinEdges',binedges);
hold on
histogram(backtester.Returns.InverseVariance,'BinEdges',binedges);
hold off
title('Distribution of Daily Returns')
legend([strategies.Name]);

Figure contains an axes object. The axes object with title Distribution of Daily Returns contains 2 objects of type histogram. These objects represent EqualWeighted, InverseVariance.

Positions

The Positions property holds a structure of timetables, one per strategy.

backtester.Positions
ans = struct with fields:
      EqualWeighted: [231x8 timetable]
    InverseVariance: [231x8 timetable]

The Positions timetable of each strategy holds the per-time-step positions for each asset as well as the Cash asset (which earns the risk-free rate). The Positions timetables contain one more row than the other results timetables because the Positions timetables include initial positions of the strategy as their first row. You can consider the initial positions as the Time = 0 portfolio positions. In this example, the Positions timetables start with February 1, while the others start on February 2.

head(backtester.Positions.InverseVariance)
ans=8×8 timetable
       Time           Cash          BA       CAT       DIS        GE       IBM       MCD       MSFT 
    ___________    ___________    ______    ______    ______    ______    ______    ______    ______

    01-Feb-2006              0    1401.2    682.17    795.14    2186.8    1900.1    1874.9    1159.8
    02-Feb-2006              0    1402.8    673.74    789.74    2170.8    1883.5    1863.6      1145
    03-Feb-2006     1.0987e-12    1386.5     671.2     787.2    2167.3    1854.3    1890.5      1139
    06-Feb-2006     1.0971e-12    1391.9    676.78    785.62    2161.1    1843.6    1899.1    1123.8
    07-Feb-2006              0      1400    661.66    840.23    2131.9    1851.6    1902.3    1114.5
    08-Feb-2006    -2.2198e-12    1409.8     677.9    846.58    2160.4    1878.2      1911    1113.2
    09-Feb-2006              0    1414.8    674.35    840.87    2172.2      1869    1908.3    1102.6
    10-Feb-2006              0    1425.1    677.29     839.6    2195.8    1890.6    1909.3    1103.9

% Plot the change of asset allocation over time
t = backtester.Positions.InverseVariance.Time;
positions = backtester.Positions.InverseVariance.Variables;
h = area(t,positions);
title('Inverse Variance Positions');
xlabel('Date');
ylabel('Asset Positions');
datetick('x','mm/dd','keepticks');
ylim([0 12000])
xlim([t(1) t(end)])
cm = parula(numel(h));
for i = 1:numel(h)
    set(h(i),'FaceColor',cm(i,:));
end

Figure contains an axes object. The axes object with title Inverse Variance Positions contains 8 objects of type area.

Turnover

The Turnover timetable holds the per-time-step portfolio turnover.

head(backtester.Turnover)
ans=8×2 timetable
       Time        EqualWeighted    InverseVariance
    ___________    _____________    _______________

    02-Feb-2006          0                 0       
    03-Feb-2006          0                 0       
    06-Feb-2006          0                 0       
    07-Feb-2006          0                 0       
    08-Feb-2006          0                 0       
    09-Feb-2006          0                 0       
    10-Feb-2006          0                 0       
    13-Feb-2006          0                 0       

Depending on your rebalance frequency, the Turnover table can contain mostly zeros. Removing these zeros when you visualize the portfolio turnover is useful.

nonZeroIdx = sum(backtester.Turnover.Variables,2) > 0;
to = backtester.Turnover(nonZeroIdx,:);
plot(to.Time,to.EqualWeighted,'-o',to.Time,to.InverseVariance,'-x',...
    'LineWidth',2,'MarkerSize',5);
legend([strategies.Name]);
title('Portfolio Turnover');
ylabel('Turnover (%)');

Figure contains an axes object. The axes object with title Portfolio Turnover contains 2 objects of type line. These objects represent EqualWeighted, InverseVariance.

BuyCost and SellCost

The BuyCost and SellCost timetables hold the per-time-step transaction fees for each type of transaction, purchases, and sales.

totalCost = sum(backtester.BuyCost{:,:}) + sum(backtester.SellCost{:,:});
bar(totalCost);
title('Total Transaction Costs');
ylabel('$')
set(gca,'xticklabel',[strategies.Name])

Figure contains an axes object. The axes object with title Total Transaction Costs contains an object of type bar.

Generate Equity Curve

Use equityCurve to plot the equity curve for the equal weighted and inverse variance strategies.

equityCurve(backtester)

Figure contains an axes object. The axes object with title Equity Curve contains 2 objects of type line. These objects represent EqualWeighted, InverseVariance.

Rebalance Functions

This section contains the implementation of the strategy rebalance functions. For more information on creating strategies and writing rebalance functions, see backtestStrategy.

function new_weights = equalWeightFcn(current_weights, pricesTT) %#ok<INUSL> 
% Equal weighted portfolio allocation

nAssets = size(pricesTT, 2);
new_weights = ones(1,nAssets);
new_weights = new_weights / sum(new_weights);

end
function new_weights = inverseVarianceFcn(current_weights, pricesTT) %#ok<INUSL> 
% Inverse-variance portfolio allocation

assetReturns = tick2ret(pricesTT);
assetCov = cov(assetReturns{:,:});
new_weights = 1 ./ diag(assetCov);
new_weights = new_weights / sum(new_weights);

end

Input Arguments

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Backtesting engine, specified as a backtestEngine object. Use backtestEngine to create the backtesting engine and then use runBacktest to run a backtest.

Data Types: object

Output Arguments

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Metrics summarizing the backtest, returned as a table where each row of the table is a calculated metric and each column represents a strategy. The reported metrics are as follows:

  • TotalReturn — The total return of the strategy over the entire backtest

  • SharpeRatio — The Sharpe ratio for each strategy

  • Volatility — The volatility of each strategy over the backtest

  • AverageTurnover — Average turnover per-time-step as a decimal percent

  • MaxTurnover — Maximum turnover in a single time step

  • AverageReturn — Average return per-time-step

  • MaxDrawdown — Maximum portfolio drawdown as a decimal percent

  • AverageBuyCost — Average per-time-step transaction costs for asset purchases

  • AverageSellCost — Average per-time-step transaction costs for asset sales

Introduced in R2020b