Cómo utilizar el criterio de Kelly para colocar una orden en el mercado financiero

Question

Traté de escribir un sistema de comercio en tiempo real, sin embargo, no sé cómo encajar un modelo de Kelly en el sistema. El sistema calculará automáticamente todos los días 12AM mientras que quiero añadir otra función que es auto orden colocada con ciertas apuestas (por el modelo de criterio Kelly aplicado) una vez conseguido el precio de pronóstico calculado.

Código fuente Sistema de negociación en tiempo real (prueba)

A continuación es la codificación que he intentado utilizar looping para calcular el historial de datos, calcular el staking, profit & lose, y también 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)

Código fuente simStakesGarch.R

Referencia

• El criterio de Kelly: ¿funciona?
• calcular el ratio de criterio Kelly (apalancamiento o tamaño de la apuesta) para una estrategia
• El criterio de Kelly en la selección aplicada de carteras
• El criterio de Kelly en la selección aplicada de carteras - Parte 2

Answer 1

El Criterio de Kelly tendería a crear muy pocas operaciones ya que es una solución máxima como $t\to\infty$ . Si ha incluido el coste de la liquidez en sus cálculos, el arrastre minimizaría las operaciones. Pero eso es bueno. El Criterio de Kelly es equivalente a la utilidad logarítmica de la riqueza.

Cualquier código sería específico para ti, ya que conoces tus responsabilidades. Usted maximizaría la riqueza del tronco, eligiendo asignaciones, conforme a cualquier restricción que usted deba resolver por ejemplo pagos de la deuda, obligaciones colaterales y así sucesivamente.

Tendrá que recordar que su rentabilidad prevista disminuirá a medida que aumente el precio y aumentará cuando disminuya.