Optimize Trade Time Trading Strategy

This example shows how to optimize the strategy for a single stock by minimizing trading costs using transaction cost analysis from the Kissell Research Group. The optimization minimizes trading costs associated with the trade time trading strategy and a specified risk aversion parameter Lambda. The trading cost minimization is expressed as

$$\min \left[\left(MI+PA\right)+Lambda\cdot TR\right],$$

where trading costs are market impact MI, price appreciation PA, and timing risk TR. For details, see marketImpact, priceAppreciation, and timingRisk. This example finds a local minimum for this expression. For details about searching for the global minimum, see Optimization Troubleshooting and Tips.

Here, you can optimize the trade time trade strategy. To optimize percentage of volume and trade schedule strategies, see Optimize Percentage of Volume Trading Strategy and Optimize Trade Schedule Trading Strategy.

To access the example code, enter edit KRGSingleStockOptimizationExample.m at the command line.

• Retrieve Market-Impact Parameters and Create Example Data

• Create Single Stock Data

• Define Optimization Parameters

• Minimize Trading Costs for Trade Strategy

• Estimate Trading Costs for Optimized Strategy

Retrieve Market-Impact Parameters and Create Example Data

Retrieve the market-impact data from the Kissell Research Group FTP site. Connect to the FTP site using the ftp function with a user name and password. Navigate to the MI_Parameters folder and retrieve the market-impact data in the MI_Encrypted_Parameters.csv file. miData contains the encrypted market-impact date, code, and parameters.

f = ftp('ftp.kissellresearch.com','username','pwd');
mget(f,'MI_Encrypted_Parameters.csv');
close(f)

miData = readtable('MI_Encrypted_Parameters.csv','delimiter', ...
    ',','ReadRowNames',false,'ReadVariableNames',true);

Create a Kissell Research Group transaction cost analysis object k.

k = krg(miData);

Create Single Stock Data

The structure tradeData contains data for a single stock. Use a structure or table to define this data. The fields are:

• Number of shares

• Average daily volume

• Volatility

• Stock price

• Initial trade time trade strategy

• Alpha estimate

tradeData.Shares = 100000;
tradeData.ADV = 1000000;
tradeData.Volatility = 0.25;
tradeData.Price = 35;
tradeData.TradeTime = 0.5;
tradeData.Alpha_bp = 50;

Define Optimization Parameters

Define risk aversion level Lambda. Set Lambda from 0 to Inf.

Lambda = 1;

Define lower LB and upper UB bounds of strategy input for optimization.

LB = 0;
UB = 1;

Define the function handle fun for the objective function. To access the code for this function, enter edit krgSingleStockOptimizer.m.

fun = @(tradetime)krgSingleStockOptimizer(tradetime,k,tradeData,Lambda);

Minimize Trading Costs for Trade Strategy

Minimize the trading costs for the trade time trade strategy. fminbnd finds the optimal value for the trade time trade strategy based on the lower and upper bound values. fminbnd finds a local minimum for the trading cost minimization expression.

[tradeData.TradeTime,totalcost] = fminbnd(fun,LB,UB);

Display the optimized trade strategy tradeData.TradeTime.

tradeData.TradeTime

ans =

    0.19

Estimate Trading Costs for Optimized Strategy

Estimate the trading costs tradeTimeCosts using the optimized trade strategy.

mi = marketImpact(k,tradeData);
tr = timingRisk(k,tradeData);
pa = priceAppreciation(k,tradeData);
tradeTimeCosts = [totalcost mi pa tr];

Display trading costs.

tradeTimeCosts

tradeTimeCosts =

        100.04         56.15          4.63         39.27

The trading costs are:

• Total cost

• Market impact

• Price appreciation

• Timing risk

For details about the preceding calculations, contact the Kissell Research Group.

References

[1] Kissell, Robert. “Algorithmic Trading Strategies.” Ph.D. Thesis. Fordham University, May 2006.

[2] Kissell, Robert. The Science of Algorithmic Trading and Portfolio Management. Cambridge, MA: Elsevier/Academic Press, 2013.

[3] Glantz, Morton, and Robert Kissell. Multi-Asset Risk Modeling. Cambridge, MA: Elsevier/Academic Press, 2013.

[4] Kissell, Robert, and Morton Glantz. Optimal Trading Strategies. New York, NY: AMACOM, Inc., 2003.