Applying Kelly Criterion to Trading Position Sizes

# How to use Kelly Criterion to place an order in financial market


# How to use Kelly Criterion to place an order in financial market












I tried to write a real-time trading system, however do not know how to fit a Kelly model into the system. The system will automatically calculate everyday 12AM while I want to add another function which is auto placed order with certain stakes (by applied Kelly criterion model) once got the calculated forecast price.

Source Code：Real Time Trading System (Trial)

Below coding is that I tried to use `looping` to calculate the data history, calculate the staking, profit & lose, and also bankroll.

```
...
...
...
  ## merge dataset
  fitm <- cbind(fit1, forClose = fit2$Point.Forecast) %>% tbl_df

  ## convert to probability.
  fitm %<>% mutate(ProbB = pnorm(Point.Forecast, mean = forClose, sd = sd(forClose)), 
                   ProbS = 1 - ProbB) #ProbS = pnorm(Point.Forecast, mean = forClose, sd = sd(forClose), lower.tail = FALSE)

  ## The garch staking models (Kelly criterion) P&L column.
  ## staking model and bankroll management.
  ## need to refer to Niko Martinen's fund management formula to maximise the stakes and profit base on Kelly models.
  ## https://github.com/scibrokes/betting-strategy-and-model-validation/blob/master/references/Creating%20a%20Profitable%20Betting%20Strategy%20for%20Football%20by%20Using%20Statistical%20Modelling.pdf
  #.... dynamic staking model need to adjusted based on updated bankroll but not portion of fixed USD100 per bet.
  fitm %<>% mutate(BR = .initialFundSize) %>% 
    #'@ mutate(Return.Back = ifelse(Prob > 0.5, Diff * Back * stakes, 0), 
    #'@        Return.Lay = ifelse(Prob < 0.5, -Diff * Lay * stakes, 0))
    mutate(fB = 2 * ProbB - 1, fS = 2 * ProbS - 1, 
           EUB = ProbB * log(BR * (1 + fB)) + (1 - ProbB) * log(BR * (1 - fB)), 
           EUS = ProbS * log(BR * (1 + fS)) + (1 - ProbS) * log(BR * (1 - fS)), 
           #'@ Edge = ifelse(f > 0, EUB, EUS), #For f > 0 need to buy and f <= 0 need to sell.
           #need to study on the risk management on "predicted profit" and "real profit".
           Edge = ifelse(fB > 0, EUB, ifelse(fS > 0, EUS, 0)), 
           PF = ifelse(Point.Forecast >= USDJPY.Low & 
                         Point.Forecast <= USDJPY.High, 
                       Point.Forecast, 0), #if forecasted place-bet price doesn't existing within Hi-Lo price, then the buying action is not stand. Assume there has no web bandwith delay.
           FC = ifelse(forClose >= USDJPY.Low & forClose <= USDJPY.High, 
                       forClose, USDJPY.Close), #if forecasted settle price doesn't existing within Hi-Lo price, then the closing action at closing price. Assume there has no web bandwith delay.
           #'@ Diff = round(forClose - USDJPY.Close, 2),
           ##forecasted closed price minus real close price.

           Buy = ifelse(PF > 0 & FC > PF, 1, 0), ##buy action
           Sell = ifelse(PF > 0 & FC < PF, 1, 0), ##sell action
           BuyS = Edge * Buy * (forClose - PF), 
           SellS = Edge * Sell * (PF - forClose), 
           Profit = BuyS + SellS, Bal = BR + Profit)

  #'@ fitm %>% dplyr::select(Point.Forecast, forClose, Prob, BR, f, EU, Edge, PF, FC, Buy, Sell, SP, Bal)
  #'@ fitm %>% dplyr::select(ProbB, ProbS, BR, fB, fS, EUB, EUS, Edge, PF, USDJPY.Open, FC, Buy, Sell, BuyS, SellS, Profit, Bal) %>% filter(PF > 0, FC > 0)

  ## The garch staking models (Kelly criterion) Adjusted Banl-roll and Balance column.
  for(i in seq(2, nrow(fitm))) {
    fitm$BR[i] = fitm$Bal[i - 1]
    fitm$fB[i] = 2 * fitm$ProbB[i] - 1
    fitm$fS[i] = 2 * fitm$ProbS[i] - 1
    fitm$EUB[i] = fitm$ProbB[i] * log(fitm$BR[i] * (1 + fitm$fB[i])) + 
      (1 - fitm$ProbB[i]) * log(fitm$BR[i] * (1 - fitm$fB[i]))
    fitm$EUS[i] = fitm$ProbS[i] * log(fitm$BR[i] * (1 + fitm$fS[i])) + 
      (1 - fitm$ProbS[i]) * log(fitm$BR[i] * (1 - fitm$fS[i]))
    fitm$Edge[i] = ifelse(fitm$fB[i] > 0, fitm$EUB[i], 
                          ifelse(fitm$fS[i] > 0, fitm$EUS[i], 0)) #For f > 0 need to buy and f <= 0 need to sell.
    #need to study on the risk management on "predicted profit" and "real profit".

    fitm$BuyS[i] = fitm$Edge[i] * fitm$Buy[i] * (fitm$forClose[i] - fitm$PF[i])
    fitm$SellS[i] = fitm$Edge[i] * fitm$Sell[i] * (fitm$PF[i] - fitm$forClose[i])
    fitm$Profit[i] = fitm$BuyS[i] + fitm$SellS[i]
    fitm$Bal[i] = fitm$BR[i] + fitm$Profit[i]
    #'@ if(fitm$Bal[i] <= 0) stop('All invested fund ruined!')
  }; rm(i)

  names(mbase) <- str_replace_all(names(mbase), '^(.*?)+\\.', nm)

  if(.filterBets == TRUE) {
    fitm %<>% filter(PF > 0, FC > 0)
  }

  fitm %<>% mutate(RR = Bal/BR)

  ## convert the log leverage value of fund size and profit into normal digital figure with exp().
  if(.fundLeverageLog == TRUE) fitm %<>% 
    mutate(BR = exp(BR), BuyS = exp(BuyS), SellS = exp(SellS), 
           Profit = exp(Profit), Bal = exp(Profit))

  return(fitm)
```

Source Code：simStakesGarch.R

Reference

- The Kelly Criterion — Does It Work?

- calculate Kelly criterion ratio (leverage or bet size) for a strategy

- The Kelly Criterion in Applied Portfolio Selection

- The Kelly Criterion in Applied Portfolio Selection – Part 2

## Answer by Dave Harris (score 1)

https://quant.stackexchange.com/a/40644

The Kelly Criterion would tend to create very few trades as it is a maximal solution as $t\to\infty$. If you have included the cost of liquidity in your calculations, the drag would minimize trades. That is a good thing though. The Kelly Criterion is equivalent to the logarithmic utility of wealth.

Any code would be specific to you as you know your liabilities. You would maximize log wealth, choosing allocations, subject to any constraints you must meet such as debt payments, collateral obligations and so forth.

You will need to remember that your prospective return will fall as the price increases and raise as it declines.