1993issue C031-5
Portfolio heat, optimal f, and drawdown limits
Editorial: treat stake selection as a three-step filter, not an entry problem. Add every open risk slice into one position-heat budget, read optimal f as the peak of a heat-test curve, then impose a drawdown limit that forces the book to run cooler than that peak before any trade is placed.
- Position heat is additive: a book risking 2 percent on each of five instruments has the same 10 percent heat as one risking 5 percent on each of two.
- Optimal f is the heat level at which a heat-test curve of growth versus stake peaks. Choosing that heat is presented as more important than retuning trade-timing parameters.
- Below the peak, cycle results rise roughly in line with heat. Above it they fall as losses dominate, and drawdowns are described as scaling with the square of heat.
- A multi-instrument heat test peaked near 140 percent heat, where average drawdown was about 40 percent per year and maximum drawdown exceeded 90 percent, so a drawdown limit well below mathematical optimal f is the practical filter.
Position heat stacks across the book
Position heat is the book’s stacked predetermined risk: the sum of per-instrument stop-based fractions held at the same time. Portfolio heat is position heat viewed across several instruments at once. Different mixes can share the same total.
Position heat is additive. A book risking 2 percent on each of five instruments has the same 10 percent heat as one risking 5 percent on each of two.
A heat test names optimal f
A heat test is a sweep of fixed-fraction bet sizes that records how growth and drawdown change as heat rises. It maps growth and volatility across bet sizes so a betting policy can be agreed before live risk begins, rather than after results disappoint on heat.
Systems are treated as having a built-in optimal-f heat, and choosing that heat is presented as more important than retuning trade-timing parameters. Optimal f is the heat level at which a heat-test curve of growth versus stake peaks, after which larger fractions let losses dominate.
The coin model peaks, then falls
In a heads-win-two, tails-lose-one coin model, one balanced cycle peaks at a 25 percent fraction and leaves a 12.5 percent cycle result after a 50 percent rise and a 25 percent drawdown.
Below that peak, cycle results rise roughly in line with heat. Above it they fall as losses dominate, with drawdowns described as scaling with the square of heat. Even in the coin model, a cooler 15 to 20 percent fraction is offered as a way to give up some cycle growth in order to cut drawdown stress.
A drawdown limit runs cooler than the peak
A simultaneous multi-instrument historical heat test reproduced the same rise-then-fall shape, with simulated optimal heat near 140 percent, or about 28 percent on each of five instruments.
At that simulated peak, average drawdown was about 40 percent per year and maximum drawdown exceeded 90 percent. A drawdown limit is a ceiling on acceptable equity decline that typically requires a cooler fraction than the mathematical heat peak, so a drawdown limit well below mathematical optimal f is the practical filter.
All readings on this track · 12 readings
- 1990Constructing optimal f when trade sizes differ
- 1993Portfolio heat, optimal f, and drawdown limits
- 1994Construct historical-optimum-leverage from one equity-path
- 1995Optimal f as a leverage bound for commodity account growth
- 1998Secure f keeps Optimal f sizing inside a Drawdown limit
- 1998Optimal f contract counts versus equity fractions
- 1999Match futures starting capital to system risk
- 1999Search system inputs together with Optimal f sizing
- 2001Bounded crash risk with capital units and optimal f
- 2002Optimal f sizing and risk of ruin as exposure filters
- 2003Cap ruin and drawdown before optimal-f
- 2006Ruin odds, the Kelly fraction and optimal f as size filters