April Strategy

Profit and Loss

Summary

The following statistics are based on days in which the strategy hold a position in the market. The test ran from 2012-04-02 to 2021-12-28. The number of days in this period was 2356 and the strategy traded on 188 days. All statistics are based on the trading days. All numbers are in EUR if not specified otherwise. The calculations are based on settlement prices from Montel.

The portfolio achieved a daily result of 5,841 (t-statistic of 2.13779) vs. an expected gain of 5,714. The standard deviation of the daily PNL was 37,465. A rough confidence interval for the daily PNL is between -112,394 and 112,394. The best day resulted in a gain of 170,820 and the worst day resulted in a loss of -105,120.

The average long position was 2,571,968 and the average short position was 0. The average amount outstanding (henceforth the “bank account”) was 2,571,968 and the median was 2,531,640.

The daily return is defined as the realized PNL divided by the absolute value of the bank account the day before (e.g., if the value of the net position is -10,000 today and then changes to -9,000 tomorrow the daily return is 10%). The mean daily return 0.27% and the standard deviation is 1.6%, which results in an annualized Sharpe ratio of 2.71. The p-value for the null hypothesis that daily returns were normally distributed was 0 (JB test). The skewness and kurtosis of daily returns were 1.84 and 11.98. The return distribution fit a Skew Student-t distribution.

The energy of the position refers to net MWh (i.e., the sum of # contracts times x hours per contract). The mean and median energy in the position was 87,647 MWh and 87,600 MWh. The corresponding minimum, maximum, and standard deviation were 87,600, 87,840, and 96MWh.

Turnover for one contract is defined as the difference in absolute value between the number of contracts held yesterday and today (e.g., if the short position is -5 yesterday and -4 today, then tunrover is 1.). Portfolio turnover is the sum of contract-specific turnover. For all days with a non-zero position, the average turnover was 10, which includes opening the position each month. Excluding the opening of the position (note that for many strategies we simply roll over the positions so including the opening as part of turnover is too conservative), the turnover was NaN (NaN means no observations).

VaR, CVAR and MDD

The risk assessment is based on daily settlement prices and therefore does not include intra-day fluctuations, which should be analyzed as well. VaR amd CVAR are based on 1/100 event.

In terms of daily returns, the mean VaR and CVAR were -2.93% and -5.13%. The number of trading days that exceed the VaR and CVAR were 4 and 0. The expected number of days with a loss greater than the VaR was 1.9. In terms of daily PNL, the mean CVAR was -130,463. Out of the 188 trading days, 0 days experienced a loss greater than CVAR.

The last table (under “Tables”) shows maximum drawdown (MDD) by calendar month. MDD is defined as the difference between the maximum and the minimum value of the bank account within a month.

The same table also shows which trading day the strategy reaches its maximum and minimum. For example, a strategy that reaches its maximum most often before it reaches its minimum should stop early in the month. The optimal stopping day should be analyzed carefully.

Time-series Analysis

The unconditional probability for a daily GAIN was 53.19% and the unconditional probability for a daily LOSS was 46.81%.

The probability of a GAIN conditional on a GAIN yesterday was 32.48%. The probability of a GAIN conditional on a LOSS yesterday was 26.11%. The probability of a LOSS conditional on a GAIN yesterday was 24.84%. The probability of a LOSS conditional on a LOSS yesterday was 16.56%.

The table presents the results from fitting an ARIMA Model to the daily return series. The ARIMA model as well as the conditional probabilities are informative about optimal risk management (optimal stopping).

## Series: ReaReturn 
## ARIMA(1,1,2) 
## 
## Coefficients:
##          ar1      ma1      ma2
##       -0.367  -0.4010  -0.5719
## s.e.   0.312   0.2776   0.2704
## 
## sigma^2 = 0.0002497:  log likelihood = 507.48
## AIC=-1006.96   AICc=-1006.74   BIC=-994.06
## 
## Training set error measures:
##                       ME       RMSE        MAE MPE MAPE      MASE         ACF1
## Training set 0.001048042 0.01563045 0.01059542 NaN  Inf 0.7292961 -0.003580925

Figures

The figure shows a histogram of daily PNL in EUR thousands. ### Histogram of daily gains and losses

Portfolio Weights

The figure shows the positions in each contract over time. The contracts are “ENOFM1”, “ENOFM2”, “ENOFQ1”, “ENOFQ2”, and “ENOY1”.

## NULL

Tables

Daily Return by Month

The table below presents average daily returns by month.

Maximum Drawdown and Trading Days Before Max and Min PNL

The table below presents maximum drawdown (MDD) as well as the trading day the strategy reaches its maximum and minimum. The statistics are reported by calendar month.