Here is an article that looks at the concept of contract allocation and active portfolio management from the point of view of a high frequency trading desk (prop desk). It’s a subject that is taking on greater significance among hedge funds and alternative asset managers.

There are two main parts to creating a quant approach to money and risk management:

1. Analysis of Individual Traders

2. The Portfolio Allocation Model

## 1. Analysis of Individual Traders

The simplest of examples of a trading system and an approach to capital allocation (trading limits) is with a game of coin toss.

Consider offering this coin toss game to your traders. Tossing heads means they win two units and a tails means they lose one unit. Suppose they were each given $10,000 as a starting bank roll and can bet as much of as little as they like and play the game many times over.

Now it is clear the odds are stacked in the player’s favour. $2 for a win versus $1 for a loss. That’s a ‘good trade’. But how much of the $10,000 should they bet? Once knowing the potential win is double the potential loss, most people would bet a large amount, perhaps half of the $10,000.

The key to making the most money from this coin toss game is to calculate the optimal percentage allocation. This is not an arbitrary or gut feel amount. It is science and the difference between one choice and another can be significant.

Suppose we pick three individuals to trade this system: Andy, Brett and Chris. The only choice we give them is how much to bet on each trade based on a percentage of the $10,000 starting capital.

Andy thinks of himself as conservative and chooses to bet 10%. Brett thinks of himself as a ‘middle of the road’ risk taker and bets 40%.

Given Brett is trading four times the amount of Andy, you’d think the results would be significantly different and you’d estimate in the long run Brett would come out well ahead.

However, the reality is different. Here is the equity curve after 100 trades:

Both traders make money, but they end up making about the same money. The only difference is volatility. Andy’s more conservative approach had far lower volatility. Brett’s allocation of four times Andy’s amount served only to increase risk, but not return.

That shows what a huge different an approach to contract allocation can make.

The mathematically optimal amount to bet in this example is not 10% or 40%. It is 25%. Suppose our third trader, Chris bets 25%. Here are the equity curves after 100 trades:

After 100 trades, the first two guys were up to about $470,000. The optimal allocation of 25% however takes the same trading system and makes $3.6million.

That is a massive difference from trading 10%, 40% or 25%. You’d never expect the difference to be that great, but it is a statistical fact.

## Mega Point #1. With the trading data generated from each individual trader, you can calculate allocations, trading limits and stop losses in order to optimise returns.

What you can also do with trading statistics is calculate the risk of ruin (i.e. maximum allowed loss being reached). Using the same data, you can calculate the probability of certain trading losses being reached based on past trading results.

In the above example, remember the 10% and 40% allocation model yielded the same profit. The risk of losing the whole $10,000 for the 10% trader is less than 0.10% whereas it’s almost 1 in 5 for the 40% trader. It is in fact 181 times more likely for the 40% trader to go bankrupt than the 10% trader.

Having that information alone would make a significant impact on long term results. You could for example have a good trader – one that is making the right trading decisions, but has a poor approach risk management. Simply taking time to apply the right contract allocation to his trading style could easily mean the difference between a profitable trader and a guy looking for another job.

## Mega Point #2. Even using the same trading system, the risk of ruin (bankruptcy etc) can vary significantly given small changes in contract allocation and trading limits.

## Real World Stuff

A room full of traders is not a coin toss game. The coin toss has fixed probabilities and fixed results. In trading, there is variability and uncertainty. To apply the proper quant models to allocations, you need ‘long run’ data.

For a trading system that generates only a few trades per month, the ‘long run’ would be a few years. That would be the time required to collect enough data to analyse and make appropriate changes. It’s not very practical.

For a prop trading business however, the long run comes very quickly. You could apply these concepts to trading data on a weekly basis and hence constantly optimise risk management and trading allocations.

## Mega Point #3. An environment in which there is high frequency trading by many individuals across different markets is the ideal scenario for applying a quantitative trading model. The model can easily be optimised on a rolling basis (e.g. weekly reviews).

The situation is analogous to that of a blackjack player. As cards are dealt the composition of the deck changes along with associated probabilities. The correct betting strategy is one that adjusts to the shifting probabilities.

## 2. The Portfolio Allocation Model

All of the above looks at one trader at a time. If we start thinking of each trader in the room as a single investment or stock then we can take the analysis one step further and build a complete approach to managing risk and optimising trading profits.

When you look at each trader as an individual stock, you can calculate not just returns, but risk and correlation. This allows you to build an approach to individual or group/sector allocations that is designed to improve profits and identify and minimise risks.

You could even drill down further and look at things such as:

- Seasonality of results – Are some traders better in the morning session versus the afternoon? Do some traders perform better earlier in the week? Etc

- Conditional probabilities -All traders have runs of losses and runs of profits. Are the runs of losses or profits from any one trader within reasonable expectations or is something amiss?

Without turning this into an academic paper, the idea here is to combine expected returns, expected risk and correlations between traders/groups of traders to create a portfolio that maximises returns for a given level of risk.

The method relies on estimates based on past data but can be designed with intuitive/qualitative input. That is, it can adjust for any views that the management hold about traders or groups of traders. The resulting portfolio is intuitive and diversified.

## Overall

These ideas are not meant to replace an existing qualitative framework of managing traders. It will add to it. Just that simple coin toss example shows the benefit of a quant approach over an intuitive approach. Intuition leaves a lot to chance. A quant allocation and risk model is designed to make the most money and risk the least given a certain scenario.