Endogenous vs exogenous models

Endogenous: Historical share price and trading volume Exogenous: fundamental data on performance and competitiveness

TODO: refine

1. Trading vs Investing: Buyside vs sell side traders vs portfolio mgrs alpha vs outperformance

Buyside = companies that buy/invest in stocks etc. Eg hedge funds. Sellside = market makers, provide advisory eg. investment banks

a. hedge funds: generate +ve returns independ of overall moves in the market = alpha

b. portfolio managers also measure outperformance as compared to a benchmark.

a is different from b

b comes from long asset holdings exposed to market or company risks. a attempts to hedge or minimise these risks.

frequent transactions vs portfolio rebalancing

portfolio rebalancing: give more weight to undervaluued assets used by portfolio managers. Use fundamental analysis

short term vs long term: traders are much short term. They ignore fundamental analysis

buy side quant methods vs sell side quant methods

Complex trading strategies: Quantitative Trading (Accounts for 90% of trading volume!) Algorithmic Trading (70% of US trading volume) High Frequency Trading (Subset of algo trading. ms or us timescale.)

data + complex straging strategies = alpha

• a set of rules to generate orders and manage position risk
• use statistical analysis to identify patterns in the market of an asset or index.
• can be low or high frequency.
• forecasting, predict future value of instrument.
• mean reversion
• correlation and cointegration.

cointegration: difference between means of two series is stationary correlation does not imply cointegration

• momentum. buy past winners. sell past losers. opposite of mean reversion.

momentum stock tends to be riskier. beta?

high frequency trading exploits millisecond and sub millisecond market microstructure inefficiences.

• focus on infrastructure flaws
• models behaviour of major competitors
• uncover large order otherwise hidden by stealth strategies

when a fund wants to purchase a large quantity of a stock, it tries to hide the order by breaking it up so that it doesnt reveal its plan to the competitors

• takes the emotion out
• unambiguous path/strategy
• mathematically optimal

• risky!
• Knight capital lost 500mm in one hour
• market is about 80% quant already!
• depends on assumptions
• no guarantee of profit with risk
• changing markets

Exchange arbitrage: riskless, pure

bid price usually < ask price bid price: price an investor can sell the security at. ask price: price an investor can buy the security at. bid and ask can be thought to be from the bank's pov. Bank bids for shares and bank asks for a price for the share. thus buying at ask price and selling at bid price will normally incur a loss equal to the bid ask spread.

If the situation is reversed and ask price < bid price. A riskless profit can be made. Can happen with an instrument listed on 2 indices Eg. ask price on nyse is 100 and bid price on nasdaq is 100.10.

Carry arbtirage: TODO

Statistical arbitrage: mean reversion. ie Things regress to their mean generally eg. mean 100 +- 5% Buy when 95 sell when 105

Pairs Trading: choose 2 stock trading on the same exchange. Go long on one and short the other.aka trading a spread

Challenges in statistical arbitrage: paying for liquidity (?) short sale charges trading, clearing and exchange fees risk based charges (?)

Index arbitrage: high frequency trading sell etf and buy component stocks or vice versa

Backtesting Validation backtest: simulation to measure the performance and risk applied to historical data. allows for comparison of strats informs about capital required, risk, frequency etc.

• split window backtest. Take a dataset A U B ( B more recent ). Train on A, test on B.

paper trade strategy => simulation of real world data.

• sliding window backtest. consider a sliding window of training and testing sets over the historical data. Generally more robust than split window. Data used efficiently for training.

Backtesting objectives: consider a set of strategies for testing and filter out strats that dont perform. can optimise strat by tweaking parameters.

Sharpe ratio = return/risk Calmar ratio = return/max drawdown (?)

Backtesting gotchas:

• dependence on correlations which might be temporary
• shitty data
• handling of:
  • slippage: difference between last market bid/offer and price that is actually paid/received. (model needs to factor that actual price received could be worse.)
  • market impact costs

Backtesting Biases:

• Optimisation Bias: Overfitting to dataset.
• Look-ahead Bias: introducing future information into training data.
• survivorship bias: only considering instruments that still exist
• drawdown tolerance bias: TODO: what is a drawdown.

development backtesters vs implementation backtesters

Forecasting = Predicting the future (based on past and present data)

1. Qualitative
2. Quantitative: based on patterns in past data.
   • Causal Methods => We use some variables as features to model data. Eg. Regression
   • Timeseries => We only use past data Eg. Moving Average

note: BigQueryML by Google simplifies ML modelling

Series of data points indexed in time order

Stationary Time Series => Statistics of series is independent of time. ie mean and sd dont depend on time.

Non stationary data has "trends"

(?) Augmented Dicky Fuller Test tests for stationarity

Time series components:

• Trend
• Seasonal
• Cyclical
• Irregular

(?) Why stationarity?

Stock prices are typically not stationary

TODO: Details about time series

Autocorrelation: A correlation of a variable with itself at different periods

Use data from previous timepoitns to predict at later timepoints

Take previous error terms as input instead. in the past.

AR Integrated Moving Average ARIMA(p,d,q)

Time series of past observations instead of independent features for predictions

ARIMA VS regression

• both stationary
• both linear

...

? Plotting residuals ? Ljung-box test