Working with Transaction Costs

The difference between net and gross portfolio returns is transaction costs. The net portfolio return proxy has distinct proportional costs to purchase and to sell assets which are maintained in the PortfolioCVaR object properties BuyCost and SellCost. Transaction costs are in units of total return and, as such, are proportional to the price of an asset so that they enter the model for net portfolio returns in return form. For example, suppose that you have a stock currently priced $40 and your usual transaction costs are 5 cents per share. Then the transaction cost for the stock is 0.05/40 = 0.00125 (as defined in Net Portfolio Returns). Costs are entered as positive values and credits are entered as negative values.

Setting Transaction Costs Using the `PortfolioCVaR` Function

To set up transaction costs, you must specify an initial or current portfolio in the InitPort property. If the initial portfolio is not set when you set up the transaction cost properties, InitPort is 0. The properties for transaction costs can be set using the PortfolioCVaR object. For example, assume that purchase and sale transaction costs are in the variables bc and sc and an initial portfolio is in the variable x0, then transaction costs are set:

bc = [ 0.00125; 0.00125; 0.00125; 0.00125; 0.00125 ];
sc = [ 0.00125; 0.007; 0.00125; 0.00125; 0.0024 ];
x0 = [ 0.4; 0.2; 0.2; 0.1; 0.1 ];
p = PortfolioCVaR('BuyCost', bc, 'SellCost', sc, 'InitPort', x0);
disp(p.NumAssets)
disp(p.BuyCost)
disp(p.SellCost)
disp(p.InitPort)

Setting Transaction Costs Using the `setCosts` Function

You can also set the properties for transaction costs using setCosts. Assume that you have the same costs and initial portfolio as in the previous example. Given a PortfolioCVaR object p with an initial portfolio already set, use setCosts to set up transaction costs:

bc = [ 0.00125; 0.00125; 0.00125; 0.00125; 0.00125 ];
sc = [ 0.00125; 0.007; 0.00125; 0.00125; 0.0024 ];
x0 = [ 0.4; 0.2; 0.2; 0.1; 0.1 ];

p = PortfolioCVaR('InitPort', x0);
p = setCosts(p, bc, sc);
        
disp(p.NumAssets)
disp(p.BuyCost)
disp(p.SellCost)
disp(p.InitPort)

You can also set up the initial portfolio's InitPort value as an optional argument to setCosts so that the following is an equivalent way to set up transaction costs:

bc = [ 0.00125; 0.00125; 0.00125; 0.00125; 0.00125 ];
sc = [ 0.00125; 0.007; 0.00125; 0.00125; 0.0024 ];
x0 = [ 0.4; 0.2; 0.2; 0.1; 0.1 ];

p = PortfolioCVaR;
p = setCosts(p, bc, sc, x0);
        
disp(p.NumAssets)
disp(p.BuyCost)
disp(p.SellCost)
disp(p.InitPort)

Setting Transaction Costs with Scalar Expansion

Both the PortfolioCVaR object and setCosts function implement scalar expansion on the arguments for transaction costs and the initial portfolio. If the NumAssets property is already set in the PortfolioCVaR object, scalar arguments for these properties are expanded to have the same value across all dimensions. In addition, setCosts lets you specify NumAssets as an optional final argument. For example, assume that you have an initial portfolio x0 and you want to set common transaction costs on all assets in your universe. You can set these costs in any of these equivalent ways:

x0 = [ 0.4; 0.2; 0.2; 0.1; 0.1 ];
p = PortfolioCVaR('InitPort', x0, 'BuyCost', 0.002, 'SellCost', 0.002);

x0 = [ 0.4; 0.2; 0.2; 0.1; 0.1 ];
p = PortfolioCVaR('InitPort', x0);
p = setCosts(p, 0.002, 0.002);

x0 = [ 0.4; 0.2; 0.2; 0.1; 0.1 ];
p = PortfolioCVaR;
p = setCosts(p, 0.002, 0.002, x0);

To clear costs from your PortfolioCVaR object, use either the PortfolioCVaR object or setCosts with empty inputs for the properties to be cleared. For example, you can clear sales costs from the PortfolioCVaR object p in the previous example:

p = PortfolioCVaR(p, 'SellCost', []);