# Optimum F Help, from Zubin Al Genubi

November 28, 2018 |

Ralph or anyone else. I need help with Ralph Vince's optimal f.

Take any one of Kora's excellent sample trade systems in SP with for example N0 Classical expectation is 60% winners, T=2.2, max historical drawdown 50pts, avg gain 4 pts avg loss 4 pts, with a million dollar stake; max acceptable drawdown 2%, a one year horizon rather than normal asymptotal assumption. R=risk free rate. Time horizon is close to close one day.

Traditionally one would use 8 contracts to limit loss to 2% on the max loss, or a fraction of .4 of stake.

What is the Optimum f use to achieve max TWR? Also what is appropriate n to compute optimal f: the 3 expected trades in the year, or the 30 over the history of the trade? Assume the current historical volatility in SP of 18. How does f change if vol is 9? Also how does the Vince bounded expectation differs from the classical unbounded expectation over a one year with 3 one day event horizon?

The solution in Vince, Risk Opportunity Analysis, p 171 is a 3 dimensional copula. (Escaping Flatland!). Is there a simple R routine or spreadsheet to compute this? The late Seattle Phil uses max drawdown as the main factor In his allocation formula. I think risk management is the most important aspect of investing.

## Ralph Vince replies:

Zubin,

So your criteria, from what you describe, is to maximize your gain over this period of time, all else be damned, withing a given (but unidentified) risk constraint. So you are talking about being at the peak of the curve (there are other points, or paths through the space, for different criteria), and you;re talking about a portfolio of one item.

But you do not know what this one-year future time window has in store for you, and I've found the best approximation for where the peak is to divide the percent of profitable compounding periods (in this case, since you have only one component, a compounding period we can say is the same as a trade) by 2. I won;t go into the math for why this is hte best guess aside from saying it will minimize the price you pay, worst-case, between this best-guess point and where, after the year, the actual point turns out to be. So in this example, it starts out at 60% winners, so

.6 / 2 = .3 ad therefore, the best guess point to use as the peak is .3, asymptotically. But you;re talking about only 3 trades over the course of the year, and since the expectation, if you make one play, is to be positive, then if you were to quit at 1 trade, your f would be 1.0, at two trades, the best guess is (f one play less-the asymptotic f) / 2 + the asymptotic or (1-.3)/2 + .3= .7/2+.3=.35+.3 = .65 and for three trades (.65 - .3 ) /2 + .3 = .175 + .3 = .475

So that;s an approximation, that .475, and that;s how I would arrive at it, absent knowledge of the future. It is a good, robust approximation and mathematically sound. I prefer robust approximations as opposed to the exact mathematical answers based solely on past data

Software for this can be found at Josh Ulrich's R implementation for it. I do not have the link offhand. The paper you cit gives the exact formula for determining the landscape and optimal fractions therein, but that is on past data. In the foxhole looking at tomorrow, or next year, I prefer robust approximations that will mimic what the actual formula might provide.

Next, you need to determine a worst-case loss situation. Perhaps you are going long, and you could use the value of 0 for your worst case. or maybe you have a stop in there, and you can use that plus some ridiculous amount of slippage for worst case or perhaps you are using options, etc. But you really need a worst case situation. Dividing the worst-case dollar amount by .475 will tell you how many units (the same quantity you determined the worst case dollar amount on, say, 1 contract 100 shares, whatever) to have on.

Understand, however, that when this worst-case is hit, you will be hit for 47.5% of your stake! So my point is, I think you need to rethink your criteria as it is unlikely what I paraphrase it to be in my first paragraph here. Perhaps you want to allocate a smaller percentage of your capital to this endeavor such that 47.5% is akin to 2% or your total capital. Maybe your criteria actually has you traversing a path in the landscape this curve in 2D space.

## Orson Terrill writes:

Is Ulrich, or anyone, still maintaining quantmod? I still have some code that runs on parts of it, that I'll refactor to save time, but hadn't seen much activity around it.

## Ralph Vince writes:

I'm certain there is a robust community around it.