“N” Day Breakout Model on Commodity Market: An Empirical Investigation

Zhenyi Yang
12/12/2012

1. Introduction
There are various strategies to make profits on the commodity markets. The “N” day breakout model is one of the easiest model. However, it is a very effective model and used by many traders. The article uses the “N” day breakout model, combined with the “fixed fractional” risk management scheme, to study the return of the commodity market. The article also compares the different outcomes with different data manipulation method and the potential reasons behind the difference.

2. The “N” Day Break Out Model
The N day break out model utilizes the method that the futures are longed at N day high and shorted at M day low. The rational explanation of the method is that the futures usually continue to rise after a breakout its long-term high. Also, the futures continue to fall after it breaks its short-term low. To simplify the problem, in this article, it chooses the 100 day high as the buying point and the 10 day low as the selling point. The period of study ranges from Dec 2002 to Dec 2012. Moreover, the article also studies the maximum profit one million account balance would make with this strategy with each commodity does not exceed 1% risk.

3. Data Manipulation
Because the commodity future expires after one or two years, for a longer period time, the charts of different futures contracts needs to be connected. Some methods are continuous, which means that the close of the new contract should equal to the expiring contract. Others are not continuous so that there are gaps between different contracts. Moreover, to choose different rolling over periods, the final chart will be quite different, usually we choose the time point that the volume of the expiring contract is less than the new contract as the starting point of the rolling period and the last trading day of the expiring contract as the end day of the rolling period. The paper compares the continuing method with no adjustment with the continuing method. The most profitable market when the unadjusted model is used is the rough rice market, but after adjustment, the copper market exceeds the rough rice market and becomes the most profitable market. Therefore, the selection of rolling over period influences the results dramatically. In the paper, it uses the N day breakout model, so the adjusted continuation chart will be better because it reflects the real price movement of the commodities. The difference of two methods are shown in Table 1 and Table 2.

4. “fixed fractional” risk management scheme
The fixed fractional risk management scheme is not of the simplest risk control method. But it is proved to be effective and used by many traders. The formula of fixed fractional risk management is based on the assumption that the amount of risk on each trade must be less than the fraction of current bankroll the investor is willing to lose. Also, the fraction of the current bankroll one is willing to lose on each trade is found by multiplying it by the allowable risk percent. In the article, I use 1% risk for each commodity. Consequently, the maximum loss of per commodity cannot exceed 1% of the current bankroll. The total risk of the portfolio is determined by the number of commodities multiplied by the risk on each commodity, which is 1%.

5. Results and Interpretation
In Table 1, we can see that the cooper commodity performs best and the lumber market performs worst with the N day breakout model in the past ten years. Likewise, the strategy has a positive Sharpe Ratio compared with the benchmark rate, the 10-year Treasury bond rate. Consequently, the portfolio at least makes money. If we only hold the most profitable commodities and neglect the least profitable commodities, it can even performs better. Moreover, as mentioned before, the result is a little different if we use the unadjusted model. It is reasonable because the commodities like rough rice usually has the highest inventory cost than metal commodities like copper, which reflects a larger difference between the close price of the expiring contract and the new contract. It has to be pointed out that the top performers and bottom performers might change over time. Likewise, if we alter the length of period we study, the story will be quite different, too.

| %Accuracy | Total return of 1m portfolio over 10 years | Annualized Return(260 days) | worst peak to valley drawdown of portfolio | Copper | 48.28% | $122,875.03 | 1.21% | -2.22% | Corn | 35.71% | $35,562.50 | 0.36% | -3.20% | Cotton | 56.25% | $21,540.01 | 0.22% | -2.55% | Crude Oil | 35.71% | -$20,880.00 | -0.22% | -4.15% | Gold | 65.38% | $89,449.96 | 0.89% | -1.67% | Heating Oil | 23.33% | -$23,146.14 | -0.24% | -5.04% | Lean Hogs | 59.09% | $58,362.43 | 0.59% | -1.79% | Lumber | 47.62% | -$3,673.98 | -0.04% | -2.92% | Orange Juice | 46.67% | $22,072.45 | 0.23% | -2.15% | Rough Rice | 43.48% | $57,859.99 | 0.58% | -3.49% | Silver | 57.89% | $67,949.98 | 0.68% | -1.79% | Wheat | 52.94% | $42,125.00 | 0.43% | -2.16% | | | | | | Portfolio | | $470,097.23 | 4.07% | -6.55% |

MAR ratio | sharpe ratio | Rank(Return) | Rank(Sharpe) | Most Profitable | Least Profitable | 0.55 | -1.43 | 1 | 1 | √ | | 0.11 | -3.31 | 7 | 7 | | | 0.09 | -3.87 | 9 | 8 | | | -0.05 | -4.31 | 11 | 10 | | | 0.53 | -3.22 | 2 | 5 | | | -0.05 | -4.15 | 12 | 9 | | | 0.33 | -2.83 | 4 | 4 | | | -0.01 | -4.77 | 10 | 12 | | √ | 0.11 | -4.35 | 8 | 11 | | | 0.17 | -2.09 | 5 | 2 | | | 0.38 | -3.31 | 3 | 6 | | | 0.20 | -2.82 | 6 | 3 | | | | | | | | | 0.62 | 0.36 | | | | |

Table 1: The summary of the futures under ADC with rolling over

| %Accuracy | total return of 1m portfolio | worst peak to valley drawdown of portfolio | Copper | 42.9% | 85075 | -8150 | Corn | 35.3% | 45300 | -8175 | Cotton | 50.0% | 47375 | -7860 | Crude Oil | 44.4% | -9100 | -8850 | Gold | 71.4% | 101110 | -9000 | Heating Oil | 36.4% | -11033 | -8022 | Lean Hogs | 60.9% | 59250 | -8600 | Lumber | 42.3% | -20108 | -8844 | Natural Gas | 52.2% | 30110 | -7395 | Orange Juice | 39.3% | 8520 | -5550 | Rough Rice | 46.7% | 124430 | -8280 | Silver | 52.2% | 86625 | -7075 | Wheat | 57.9% | 66088 | -4425 | sharpe ratio | Rank(Return) | Rank(Sharpe) | Most Profitable | Least Profitable | -3.84 | 4 | 8 | | | -2.86 | 8 | 4 | | | -3.53 | 7 | 7 | | | -3.84 | 11 | 8 | | | -2.92 | 2 | 6 | | | -3.85 | 12 | 10 | | | -2.49 | 6 | 2 | | | -4.61 | 13 | 12 | | √ | -4.03 | 9 | 11 | | | -4.61 | 10 | 13 | | | -1.58 | 1 | 1 | √ | | -2.91 | 3 | 5 | | | -2.83 | 5 | 3 | | |

Table 2: The summary of the futures under ADC without rolling over

6. Appendix
Codes needed to generate results
LeanHogs = read.csv("Wheat.csv", header = TRUE ) size <- length(LeanHogs$Date) sizeOfContract <- 5000 pCurrent <- size - 100 minSize <- 0.25 minChange <- 12.5 bankroll <- vector(mode = "numeric", length = size ) bankroll[pCurrent] <- 1000000
NumOfContracts <- vector(mode = "numeric", length = size )
NumOfContracts[pCurrent] <- 0 changed = F for( i in 1:(size-101))
{
changed = F pCurrent <- pCurrent - 1 if( LeanHogs$High[pCurrent] > max(LeanHogs$High[(pCurrent+1):(pCurrent+100)])) { if(NumOfContracts[pCurrent+1] == 0) { NumOfContracts[pCurrent] <- floor(bankroll[pCurrent+1]*0.01/(minChange*(LeanHogs$High[pCurrent]-min(LeanHogs$Low[(pCurrent+1):(pCurrent+10)]))/minSize)) bankroll[pCurrent] <- bankroll[pCurrent+1]+NumOfContracts[pCurrent]*minChange*(LeanHogs$Last[pCurrent]-max(LeanHogs$High[(pCurrent+1):(pCurrent+100)]))/minSize changed = T } } else if(LeanHogs$Low[pCurrent] < min(LeanHogs$Low[(pCurrent+1):(pCurrent+10)])) { if( NumOfContracts[pCurrent+1] != 0) { bankroll[pCurrent] <- bankroll[pCurrent+1]+NumOfContracts[pCurrent+1]*minChange*(min(LeanHogs$Low[(pCurrent+1):(pCurrent+10)])-LeanHogs$Last[pCurrent+1])/minSize NumOfContracts[pCurrent] <- 0 changed = T } } if( changed == F) { NumOfContracts[pCurrent] <- NumOfContracts[pCurrent+1] bankroll[pCurrent] <- bankroll[pCurrent+1]+NumOfContracts[pCurrent+1]*minChange*(LeanHogs$Last[pCurrent]-LeanHogs$Last[pCurrent+1])/minSize }
}
write.csv(cbind(LeanHogs, NumOfContracts, bankroll),file = "Wheat_Result.csv")

Corn = read.csv("Wheat_Result2.csv", header = TRUE ) numRow <- length(Corn$Date) sigBuy <- integer() sigSell <- integer() ran <- integer() acc <- integer() chg <- numeric() ptfChg <- numeric() numOfSig <- 1 for(i in 101:(numRow-1))
{
if(Corn$NumOfContracts[i]!=0) { if(Corn$NumOfContracts[i-1]==0) { sigBuy <- c(sigBuy, i); } else if(Corn$NumOfContracts[i+1]==0) { sigSell <- c(sigSell, i+1) ran <- c(ran, (sigSell[numOfSig] - sigBuy[numOfSig])) if(min(Corn$Low[(sigSell[numOfSig]-10):(sigSell[numOfSig]-1)]) > max(Corn$High[(sigBuy[numOfSig]-100):(sigBuy[numOfSig]-1)])) { acc <- c(acc, 1) } else { acc <- c(acc, 0) } chg <- c(chg,(min(Corn$Low[(sigSell[numOfSig]-10):(sigSell[numOfSig]-1)]) - max(Corn$High[(sigBuy[numOfSig]-100):(sigBuy[numOfSig]-1)]))) ptfChg <- c(ptfChg,Corn$bankroll[sigSell[numOfSig]] - Corn$bankroll[sigBuy[numOfSig]-1]) numOfSig <- numOfSig + 1 } else if(i==numRow-1) { sigSell <- c(sigSell, i+1) ran <- c(ran, (sigSell[numOfSig] - sigBuy[numOfSig])) if(Corn$Last[sigSell[numOfSig]] > max(Corn$High[(sigBuy[numOfSig]-100):(sigBuy[numOfSig]-1)])) { acc <- c(acc, 1) } else { acc <- c(acc, 0) } chg <- c(chg,(Corn$Last[sigSell[numOfSig]] - max(Corn$High[(sigBuy[numOfSig]-100):(sigBuy[numOfSig]-1)]))) ptfChg <- c(ptfChg,Corn$bankroll[sigSell[numOfSig]] - Corn$bankroll[sigBuy[numOfSig]-1]) numOfSig <- numOfSig + 1 } }
}
colName <- c("Buy","Sell","Range","Accuracy","Change", "Portfolio Change")
DF <- data.frame(Corn$Date[sigBuy],Corn$Date[sigSell], ran, acc, chg, ptfChg) names(DF) <- colName

write.csv(DF, file = "WheatSignal.csv")