Error in cost calculation for dynamic optimisation

[robcarver17]

Should divide by weight per contract?

[robcarver17]

Probably easier to work backwards here

systems/provided/dynamic_small_system_optimise/optimisation.py

    def calculate_costs(self, weights: np.array) -> float:
        if self.no_prior_positions_provided:
            return 0.0
        trade_gap = weights - self.weights_prior_as_np_replace_nans_with_zeros
        costs_per_trade = self.costs_as_np
        trade_shadow_cost = self.trade_shadow_cost
        trade_costs = sum(abs(costs_per_trade * trade_gap * trade_shadow_cost))

So these costs are in weight units: cost to trade 100% of capital in notional position for a given instrument. For example, if you want to trade 50% of your capital as a notional positoin, and the cost per trade is 0.01, then it will cost you 0.5% of your capital as a cost.

[robcarver17]

systems/provided/dynamic_small_system_optimise/optimised_positions_stage.py

    @diagnostic()
    def get_cost_per_contract_as_proportion_of_capital(self, instrument_code) -> float:
        cost_per_contract = self.get_cost_per_contract_in_base_ccy(instrument_code)
        trading_capital = self.get_trading_capital()
        cost_multiplier = self.cost_multiplier()

        return cost_multiplier * cost_per_contract / trading_capital

    def get_cost_per_contract_in_base_ccy(self, instrument_code: str) -> float:
        raw_cost_data = self.get_raw_cost_data(instrument_code)
        multiplier = self.get_contract_multiplier(instrument_code)
        last_price = self.get_final_price(instrument_code)
        fx_rate = self.get_last_fx_rate(instrument_code)

        ### This is the cost in instrument currency of trading one contract
        cost_in_instr_ccy = raw_cost_data.calculate_cost_instrument_currency(
            1.0, multiplier, last_price
        )
        
        #### now in base
        cost_in_base_ccy = fx_rate * cost_in_instr_ccy

        return cost_in_base_ccy

[robcarver17]

Let's take eurodollar has an example.

s= futures_system() 
s.data.get_raw_cost_data('EDOLLAR')
instrumentCosts slippage 0.002500 block_commission 2.110000 percentage cost 0.000000 per trade commission 0.000000
s.data.get_raw_cost_data('EDOLLAR').calculate_cost_instrument_currency(1, s.data.get_value_of_block_price_move('EDOLLAR'), 97.5)
8.36

Commission is $2.11 + $0.0025*$2500 = $8.36

If we then divide by capital, that's a proportion of capital.

But assumes we're trading 100% of our capital in one go. But we're not. The notional value of a eurodollar position (the weight) is 97.5*2500 ~ $250k

Assuming $500k of capital, we actually pay $8.36 to trade about 50% of capital, but the calculation assumes we pay $8.36 to trade 100% of capital. To trade 100% of capital will actually cost us like $16.72

In this case our costs are overstated by a factor of two.

The correct calculation is:

$ cost per contract / (notional position size / capital) = $ cost per contract * capital / notional position size

For Eurodollar this comes out at $8.36 * 500k / 250k = $16.72

We then divide that by the capital, so it's actually just $ cost per contract / notional position size.

[robcarver17]

I'm not going to check this fix in as it will affect backtest results - need to see by how much first.

[robcarver17]

What about production? Really shouldn't be duplicate code

sysexecution/strategies/dynamic_optimised_positions.py

    data.log.msg("Getting costs")
    costs = calculate_costs_per_portfolio_weight(
        data, strategy_name=strategy_name, list_of_instruments=list_of_instruments
    )

def calculate_costs_per_portfolio_weight(
    data: dataBlob, strategy_name: str, list_of_instruments: list
) -> meanEstimates:

    capital = capital_for_strategy(data, strategy_name=strategy_name)
    costs = meanEstimates(
        [
            (
                instrument_code,
                get_cash_cost_in_base_for_instrument(data, instrument_code) / capital,
            )
            for instrument_code in list_of_instruments
        ]
    )

    return costs

def get_cash_cost_in_base_for_instrument(data: dataBlob, instrument_code: str):
    diag_instruments = diagInstruments(data)
    costs_object = diag_instruments.get_cost_object(instrument_code)
    blocks_traded = 1
    block_price_multiplier = get_block_size(data, instrument_code)
    price = recent_average_price(data, instrument_code)
    cost_instrument_ccy = costs_object.calculate_cost_instrument_currency(
        blocks_traded=blocks_traded,
        block_price_multiplier=block_price_multiplier,
        price=price,
    )
    fx = last_currency_fx(data, instrument_code)
    cost_base_ccy = cost_instrument_ccy * fx

    return cost_base_ccy

[robcarver17]

Production has the same error, so will create a single function that does this which both will call.

[robcarver17]

While the sim is running, notice that the effect of this will be to understate most costs, except for the rare case when the notional value per contract>capital. The smaller the notional value per capital, the bigger the understatement. We're likely to trade more slowly with this change - the only issue is whether we are trading too slowly.

[robcarver17]

original benchmark

s = futures_system()
x=s.accounts.optimised_portfolio().percent
x.sharpe()
1.297599817425156
x.costs.ann_mean()
-0.9265973865963101
x.gross.ann_mean()
30.71431689614817
s.accounts.total_optimised_portfolio_level_turnover()
40.44772954255738
x=s.accounts.optimised_portfolio().percent.costs
y=x.to_frame()
y.mean()
cost_by_instrument = y.mean()*256
cost_by_instrument.sort_values().head(20)
VIX         -1.164753
BRE         -0.670079
GAS-LAST    -0.628998
FEEDCOW     -0.572250
SP400       -0.534354
GBPEUR      -0.525749
USIRS10     -0.456133
V2X         -0.454633
EU-DIV30    -0.435479
AEX         -0.409705
YENEUR      -0.396126
US10        -0.394711
LIVECOW     -0.394305
PALLAD      -0.390222
MXP         -0.390105
IRON        -0.389512
EURCHF      -0.389227
EU-TRAVEL   -0.385487
GBP         -0.376358
US20        -0.361808

[robcarver17]

With changes

x.sharpe()
1.1728641168584288
x.costs.ann_mean()
-0.5035027084018666
x.gross.ann_mean()
25.44198831412299
s.accounts.total_optimised_portfolio_level_turnover()
19.87288303635569
cost_by_instrument.sort_values().head(20)
FEEDCOW       -0.585442
GAS-LAST      -0.531244
SP400         -0.492409
VIX           -0.472806
IRON          -0.461838
LIVECOW       -0.434577
GAS_US_mini   -0.393565
AEX           -0.377109
PALLAD        -0.373499
LEANHOG       -0.350137
YENEUR        -0.308646
US20          -0.300477
SOYBEAN       -0.273900
PLAT          -0.256224
BOBL          -0.256054
CHF           -0.252500
BUND          -0.250095
OAT           -0.231265
GASOILINE     -0.226915
SOYOIL        -0.210265

As expected, but it looks like we are probably now trading too slowly.

[robcarver17]

As expected, we are probably trading too little (costs have dropped by a half, turnover ditto).
We have two levers to pull, shadow cost (or cost multiplier - amounts to the same thing) and buffering.

The buffer already feels reasonably tight, so let's play with the shadow cost

system.config.small_system['shadow_cost'] = 50

x.sharpe()
1.31964248836861
x.costs.ann_mean()
-0.8112750405188187
x.gross.ann_mean()
30.832656709134852
system.accounts.total_optimised_portfolio_level_turnover()
34.55946643927831
cost_by_instrument.sort_values().head(20)
VIX           -1.079285
BRE           -0.663061
GAS-LAST      -0.625846
SP400         -0.599349
FEEDCOW       -0.587329
V2X           -0.543151
BONO          -0.528349
GBPEUR        -0.524362
IRON          -0.488972
PALLAD        -0.409050
AEX           -0.408949
YENEUR        -0.398791
LIVECOW       -0.397260
US10          -0.386689
US20          -0.384039
GAS_US_mini   -0.370554
EURCHF        -0.369261
BUXL          -0.356043
GBP           -0.347841
SOYBEAN       -0.328201

That seems fine let's not get too excited about over optimisation.
Costs by instrument are now much more evenly distributed.

I've checked this in but need to test the production code (which is a bit messy anyway)

[robcarver17]

Production test has worked, so treating this as fixed now. Code does need tidying up though!

[meldinman]

Hi Rob,
I'm curious if you are still using the reduced shadow cost of 50 in your updated configs.
I seem to be doing a bit more trades than you are since dropping the shadow cost (though with a slightly smaller USD denominated account) and I was just curious if you've decided a shadow cost of 50 is too low.

[robcarver17]

Yes still using it.