Choosing Strategy Capital Based on Ruin Risk and Trading Capacity
Summary
The discussion frames starting capital as a tradeoff between potential return on invested capital and the chance that losses force a strategy to stop. It gives a normally distributed daily profit example to illustrate why a small account may face a substantial one-day ruin risk, while a much larger account can absorb more losses but produces a lower return on the initial amount. One response emphasizes that there is no universally best risk-return balance because it depends on an investor’s risk aversion.
Other responses suggest practical bounds: estimate the minimum capital needed to trade the required positions and a maximum consistent with market liquidity and avoiding excessive market impact. The text also mentions measuring loss risk using tools such as value at risk, stopping times, or the distribution of minimum wealth, and points to prospect theory and the Kelly criterion. These are suggestions rather than a worked sizing framework; the proposed midpoint between capital bounds is not justified as generally optimal, and assumptions about profits and liquidity may not hold in practice.
Key ideas
- Small starting capital can increase the probability that losses exhaust the account.
- The preferred tradeoff between return and ruin risk depends on risk tolerance.
- Minimum capital can be estimated from the positions a strategy must hold.
- Liquidity and market impact can limit the capital deployed in a strategy.
- Risk analysis, prospect theory, and Kelly sizing are mentioned as possible approaches.
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Full text
# How to determine the optimal start capital for a strategy? # How to determine the optimal start capital for a strategy? Suppose my strategy generates a stream of daily profits distributed like 𝒩[μ=1€, σ=10€]. Intuitively, if I trade with 10€ start capital: - I could very well be ruined on the first day, if the first day profit is below -10€, which could happen with 13.6% probability (given μ=1€, σ=10€) - However if, by lucky chance, I don’t face any nasty drawdown, I can build a fortune starting with only 10€ capital, i.e. stellar ROI On the other hand, if I trade with 10'000€ start capital: - I will be able to withstand the ugliest drawdowns, I will never stop trading! - but my ROI will be terribly worse, because the initial investment is 1000 times higher than the previous case So: - 10€ start capital: stellar ROI, but too risky - 10'000€ start capital: no risk of ruin, but terrible ROI How do determine the start capital, with the best risk-reward trade off? ## Answer by Ezy (score 0, accepted) https://quant.stackexchange.com/a/43289 From an academic standpoint there is not an objective best risk-reward tradeoff. Here the ROI is a direct function of your aversion to the risk of ruin. It is an entirely subjective parameter. ## Answer by Ishan Shah (score 0) https://quant.stackexchange.com/a/43321 The optimal starting point should be between minimum and maximum capital available. The minimum capital required for a strategy is you will be buy the required quantity of securities as per your strategy. For example, if your strategy trades in 5 different securities and you are required to buy 1 quantity of all 5 of them and the sum of the prices of 5 instruments in `$1000` then the minimum capital required is `$1000`. The maximum capital on the other hand is with that capital you will not overwhelm the order book or move the market against you by placing order. For example, if you only trade in a ill liquid security where only 5 quantities are traded in a minute and price of the security is `$1000` then the maximum capital you should have is `$5000`. In real life, the maximum can be determined through the average daily traded volume of a security. Your strategy requirement for a security shouldn't exceed the average daily volume traded for a security. Optimal capital should be between your minimum and maximum possible. Generally, you can take average of of the two to determine the capital allocation to a strategy. ## Answer by Jónás Balázs (score 0) https://quant.stackexchange.com/a/43323 The answer depends on personal risk-aversion. Two ideas came to my mind. The first is based on statistics (eg. value at risk, stopping time, distribution of the minimum) which is easy to measure. The second is prospect theory. Kelly criterion answers a more general question specifically what is the optimal size of a series of bets in order to maximise wealth.
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