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
- 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?