Monday, October 31, 2011

Sell in May and Go Away? (Historical performance)

Here's the historical performance at The Big Picture



We can see that the Nov- April periods have been relatively volatile, too. A more important question remains, will this pattern stay in the future?

Dangers
It is dangerous to assume that this pattern would persist into the future, without a robust fundamental theory. Statistically speaking a sample size of 50~ means nothing. From my experience, there's no such thing as "statistically significant" with financial time series. A tradeable edge requires solid fundamental theory.

What this pattern CAN be used for
Sales at brokerage firms in November.

Monday, September 19, 2011

More on HFT(High Frequency Trading) core strategies

Prof. Brogaard, a relatively known scholar within mathematical finance community, has published as part of the UK Foresight project titled “High Frequency Trading, Information and Profits.” Here the writer explains some core logic applied by existing firms at a level above orderbook HFT logic.

HFT basic strategies


1) Market Making : This is about getting paid from market orders (bid/offer spread) for liquidity provision.

2) Liquidity Rebates: Getting paid from the exchange with respect to liquidity provision.This is why understanding individual exchange fee-structure is critical to making money.

3) Statistical pattern detection: This is probably the most volatile of all strategies. From personal experience, "statistical significance" is always questionable around market data samples.

4) Pure Arbitrage: Inter-exchange, inter-continental, inter-instrument... it all takes very high speed to pull off today, as price discrepancies between "obvious" arbitrage opportunities have become very tight.

Wednesday, September 7, 2011

Option Trading by Euan Sinclair (Book Review)

Yeah I've been reading a lot of stuff on option trading for work, since our option transaction fees have grown significantly low due to high turnover volumes as a market maker for a number of instruments. Here're some things from the book that's really caught my attention:


"
' Although it is always perilous to assume that the future will be like the past, it is at least instructive to find out what the past was like. Experience suggests that for predicting future values, historica data appear to be quite useful with respect to standard deviations, reasonably useful for correlations, and virtually useless for expected returns.' - William Sharpe

My view is that the theory is correct in the same way that the theory that the earth is spherical is correct. The earth is not perfectly spheroid, but from a sufficient distance it looks spherical. The planet's bumps and irregularities are small and the idea of a spherical earth is a far better descriptive theory than the one it replaced, the idea that the earth was flat. Using the spherical earth theory has allowed us to do many useful things such as flying around the world. However, a pilot who blindly believed in the theory would put us in grave danger: his theory has no place for 'anomalies' such as mountains.

The efficient market theory is similar.


... a good trader makes money by exploiting the small deviations from the theory without bothering to argue that markets are totally inefficient.
"

Yep, that is pretty much how it is, reality vs. academic theories.

Prerequisite mathematical understanding

To fully understand everything in the book, understanding of basic calculus and probability theory is required. The math involves mostly partial derivatives and basic integrations.

Basic calculus tutorial: Karl's Calculus Tutor
Basic statistics tutorial: StatTrek

The math is needed for theoretical valuations, volatility estimates, and strategy P/L expectations. Important stuff.

Defining an edge

Sinclair does a good job of explaining the concept of trading with a positive expected value.

EV = P(win) * Payoff(win) + P(loss) * Payoff(loss)
where
P(win) =  probability of winning
Payoff(win) = expected payoff per winning trade
P(loss) =  probability of losing
Payoff(loss) = expected payoff per losing trade

From my experience, really understanding this concept is what makes someone make money over time. Also a really good point Sinclair's made is that while backtesting shows if something's worked in the past, "we need to know why they will do so in the future." The point being, there're an infinite number of combinations of trade ideas, parameters, and products that have produced successful trades in the past; and without knowing WHY something's worked in the first place, it is very tough to know if it's stopped working. This is a very realistic risk not recognized by many in the algorithmic trading field.

Taleb has mentioned that a good trading strategy must hold a robust theory, empirical evidence (backtesting) is a secondary requirement. 

Market Making Techniques

Some good concepts are mentioned around inventory (risk) management and quoting widths. Keep in mind that a number of high frequency trading algorithms hold market making as core.

Volatility Trading

While the idea of implied volatility converging with historical vol or "volatility arbitrage" is probably discussed to death, the academic guys have made a lot of inpractical assumptions around transaction costs. It is NOT a riskfree arbitrage.

So while our expected return off this trade is

P/L = Vega (Implied Vol - Historical Vol)
it is true only on average. This book explores reality of vega trading while estimating transaction costs from hedging and path taken by the position. Basically, it takes a lot more than that to exploit these deviations, and it could easily turn into a loss with less-than-optimal hedging frequency and/or undesirable path of the underlying while the position is open.

Over all it is one of the better books I've read around financial trading.

Wednesday, February 2, 2011

Kth Nearest Neighbor Algorithmic Predictions


So I noticed that Adaptive Trading Systems claimed to have achieved a fairly nice looking equity curve forecasting S&P500 Futures via KNN (Kth Nearest Neighbor) with the below inputs,

"
S&P500 Futures
S&P500 Index
Russel 2000 Index
OEX Put/Call Ratio
"
Fundamentally, these variables look at sentiment, futures basis, and relative performance, and are probably the main causes for this strategy's success.

Applying KNN

Here's a simple guide to implementing KNN in Excel. There're also a number of Matlab packages available.

Wednesday, November 3, 2010

About Ito's Process


Besides Black & Scholes, Kiyoshi Ito is one of the really popular guys in mathematical finance. Everybody in the scene knows his diffusion process, and I have some problems with it!

Ito's Diffusion Process (Simplest form):

Given that X(t) is a random variable, representing price of a financial security at time t, the change in X can be represented by,

dX(t)= aX(t)dt + sdW(t)

where

a, s: constants with respect to the model applied
W(t): Brownian motion


Stylized Facts
Empirical findings have however shown that the markets are NOT truly random as suggested by the Brownian motion. D. Whitcomb has pointed out a negative serial correlation off Index returns since 1979! Here's an article about his findings. This means the drift parameter a above does not always make sense. Yeah, there's always the drift due to inflation on indexes, but not all securities can even keep up with it, especially those with high credit risk.

The conditional variance contradicts with a lot of existing academic assumptions around Heston's stochastic volatility paper. Well it isn't so stochastic if you've actually observed volatility time series critically. I can't get into the volatility thing until a later time.

That's it for now!