Transcript Bayesian Adaptive Trading with Daily Cycle

Bayesian Adaptive
Trading with Daily Cycle
Mr Chee Tji Hun
Ms Loh Chuan Xiang
Mr Tie JianWang Algernon
Abstract
 The Bayesian Adaptive Trading with Daily Cycle (BATDC) paper
presents the idea of an optimal trading schedule to minimise the total
expected cost of trading.
 The key idea in BATDC paper is that there exists a value α which
represents the true drift generated by Institutional Traders.
 Institutional traders, start with a daily target size and by observing price
evolution throughout the day, one can adjust the α estimate and
uncover the order’s nature (Buy/Sell) and tailor an optimal trading
schedule using the adjusted α estimate to finally reduce trading cost.
 As part of the BATDC paper, they have uncovered a proprietary trading
strategy but have ignored it for the purpose of their paper.
 The purpose of this paper is to test the proprietary trading strategy and
implement certain variants to the strategy.
Assumptions
 Prior belief that α is normally distributed
α ~ N(ᾱ, v2 )
 Underlying asset price’s distribution, conditional on α,
is also normally distributed
St = S0 + αt + σBt for t ≥ 0
St ~ N(ᾱt, (σ2 + v2t)t)
 Using Bayesian update the optimal value for α
α*|St ~ N( (ᾱσ2 + v2(St – S0))/(σ2 + v2t), σ2v2/(σ2 + v2t) )
Methodology and Trading Strategy 1

We seek to optimise 2 parameters
1.
2.

The size of the rolling window
The size of a trading cycle
Prop Strategy
1.
2.
Start each m-period with 0 position
Use a n-period rolling window (past data) & m-period trading cycle
St – S0 = αt + σBt
3.
4.
5.
6.
7.
8.
where t ε [1, 2, …, m]
Estimate α by a regression without intercept;
Estimate of σ is the standard error of the regression model; and
Estimate of v, the prior’s standard deviation, is the standard deviation
of the estimate of α
With the information calculate α* at time t
If α* > 0 long the asset else short the asset
If position at period m-1 not equal to 0 then sell at period m end day
price so that position is back to 0 at the end of period m.
Methodology and Trading Strategy 2

After taking a sparse sample from the range of 1100 days for close out and rolling window. We
notice that the strategies performed better within the
4-44 day ranges. Optimization was then applied at
a finer grain within this range.
 We propose 2 different strategies:
1. A pure proprietary strategy as suggested in the
paper
2. A modified strategy with a liquidation component
that slowly negates the position to 0 over the mperiods
Pure Proprietary Strategy 1
 The pure proprietary strategy is explained in
slide 4 and exactly replicates the strategy
explained in the BATDC paper.
 Performance data for the strategy is collated
and the graphical representation is attached
in the following slides.
Pure Proprietary Strategy 2
 P&L for Pure Prop Strategy
Pure Proprietary Strategy 3
 Sharpe Ratio of Pure Prop Strategy
Pure Proprietary Strategy 4
 Omega of Pure Prop Strategy
Pure Proprietary Strategy 5
 Observing the data, we notice that using P&L
the plateau is achieved between 30, 31 & 32
close out period and 42, 43 & 44 rolling
window period.
 Using Sharpe Ratio and Omega, there does
not seem to be a stand out optimal close out
and rolling window period.
Modified Proprietary Strategy 1

We now consider an additional liquidating strategy to complement the
proprietary strategy.

The idea is also in line with the ideas in the BATDC paper.

For each n-period rolling window & m-period trading cycle, we apply
the proprietary strategy as explained in slide 4 and also consider the
following:
1.
2.
If time t ε [1, 2, …, m] and position is not 0
We choose to sell (position > 0) or buy (position < 0)
Position / (m-t) units
of the underlying asset in addition to the proprietary strategy

We consider this additional liquidation strategy because one cannot
reasonably expect to get the price at the end of the m-period if the
accumulated position is huge.
Modified Proprietary Strategy 2
 P&L for Modified Prop Strategy
Modified Proprietary Strategy 3
 Sharpe Ratio for Modified Prop Strategy
Modified Proprietary Strategy 4
 Omega for Modified Prop Strategy
Modified Proprietary Strategy 5
 Using P&L, we observe from the data that stability is
achieved in the 27-35 period trading cycle and 16-22
period rolling window.
 Sharpe Ratio is much improved under this strategy
and is stable in the 35-38 period trading cycle and 422 period rolling window
 On average, Omega under this strategy is larger than
under the pure prop strategy. However, similar to the
pure prop strategy, it is stable over the entire range of
trading cycle and rolling window periods
combinations considered
Conclusions and Comparisons
 Although the pure Prop Strategy out performs the modified Prop
Strategy in P&L, the volatility of the P&L for the modified Prop
Strategy is less than that of the pure Prop Strategy.
 The modified Prop Strategy out performs the pure Prop Strategy
in Sharpe Ratio and Omega. However, this difference is not
significant.
 The data seems to suggests a that a 35 period trading cycle and
a 18 period rolling window are the optimal parameters for the
modified Prop strategy based on Sharpe Ratio and P&L.
However, one can only use P&L to decide the optimal
parameters for the pure Prop Strategy.