Here's one of Vince's papers on the subject. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2577782 I don't think Vince's argument is that Optimal f is superior, more that Kelly is inappropriate for many trades. For instance, short sales, instruments/trades with non-linear payoffs, multi-leg strategies, and so on. Also, don't forget that Kelly and Optimal f are utility functions. You can create your own and use whatever risk aversion parameters you think are appropriate.
You might like what Aaron Brown has to say about 'risk ignition' in his book "Red-Blooded Risk'. He talks about maximizing position size when you think you have a trade with an unusual edge, constrained by a VaR limit. It's related to Vince's ideas.
May I ask why Kelly is inappropriate for instruments/trades with non-linear payoffs? I tried to read the paper but the math was way too hard for me to understand and the words/terms (leverage space manifold...) were Greeks to me. I traded options (with non-linear payoffs) and used Kelly as a guide.
Maybe start with Kelly's original paper and/or just think through what Kelly proposed: maximize expected logarithmic utility given known and independent events, probabilities of the events, payoffs, a loss limited to the bet,..., I'm probably leaving something out. Does this sound like your trade? If so, then you're fine. Otherwise, you may not be maximizing utility in the way Kelly proposed.
As a corollary, something rvince99 wrote earlier in this thread caught my attention. I haven't actually worked this out, but given logarithmic utility, it seems inconsistent to add to a losing position/widen a stop loss (this is when the loss of utility is greatest) or to add ('scale-in') to a winning position (diminishing marginal utility). That seems more appropriate for risk-affine or convex utility.
I am not sure I understand what you said. Here is what I do: I have an option setup that I traded since around 2013. After I collected enough trades I computed the win rate and average win:loss for Kelly. I rechecked the win rate and win:loss now and then to make sure they were still within range. I am not a math person so I just used a simple Kelly formula that I found on the internet and set trade size to be a fraction of that. After a while, it is intuitive that each trade should not be > x% of total trading capital and x is quite consistent with what everyone on ET said about trade size and risk management. Any comments or coaching is greatly appreciated.
The math and assumptions are critical when working with utility functions like the Kelly Criterion, but I think I can answer your questions by walking through some plots. Take a look at this Wikipedia link on risk aversion. Go the section labeled 'Example' (or, just see the images I've pasted below). You'll see 3 utility function plots there: risk-averse, risk-neutral, and risk-affine (i.e., risk seeking). Let's walk through these curves. To be clear, I don't know what utility functions are used in these plots. This is for illustrative purposes. Let's assume the first plot is logarithmic utility (i.e. 'Kelly'). With a logarithm we get decreasing marginal utility. Note in the plot that the slope is steep for small values of W and less steep for larger values. In wealth terms, we can say that our preference for the next dollar of wealth diminishes as our wealth increases - that's built into Kelly. Loosely speaking, because this curve turns inward and down, we call it 'concave'. In contrast, the risk-affine plot turns outward and up - we call that 'convex'. Let's take a quick look at the other two plots. The risk neutral plot has a constant slope. A bettor with risk neutral utility is indifferent to an uncertain bet and receiving cash. This bettor seeks to earn the expected value of the bet and doesn't require a risk premium (RP). Fractional kelly betting, relative to full Kelly, is increasing risk aversion. For a visual, consider the risk-averse and risk-neutral curves on the same plot. Increasing the risk aversion parameter (smaller Kelly fraction) would reduce the curvature of the risk-averse utility curve. As an exercise, look at the risk-averse plot and see if it makes sense that as risk aversion increases (smaller Kelly fraction), a greater risk premium is required as U(E(W)) increases. The risk affine plot has an increasing slope. This represents increasing marginal utility. In wealth terms, we can say that our preference for the next dollar of wealth increases as our wealth increases. Now, let's go back to what I mentioned about widening stop-loss targets and 'scaling in'. Here's what I was thinking... Consider the risk-averse and risk-affine curves on the same plot. Pick a fixed point on the y-axis; call that your trade entry point. As you move below that point the utility loss is smaller for the risk-affine curve. As you move above that point the utility gain is greater for the risk-affine curve. Building on that observation, we could say that the risk-affine bettor gains more utility (relative to the risk-averse bettor) from scaling-in (adding to a winning position) and loses less utility from adding to a losing position. It was in that sense that I commented that adding to a losing position/widening a stop-loss, or adding to a winning position is more consistent with risk-affine utility than risk-aversion. [For a famous example of a bettor with risk-affine characteristics read the story of Jesse Livermore in "Reminiscences of a Stock Operator".] Regarding your individual trade, if Kelly seems to be working for you in the way that you'd expect that's great. The assumptions of Optimal f aren't as restrictive though. N.B. Disclaimer: I'm not an expert on Kelly betting, but I've done a decent amount of reading on the topic. So, I'm not representing my understanding as the absolute truth on this. For anyone who is an expert or disagrees, we'd love to hear from you. risk-averse: risk-neutral: risk-affine: https://en.wikipedia.org/wiki/Risk_aversion