A Brief Note on Monte Carlo

When we back-test a strategy against the historical prices of an instrument, say, the NIFTY 50 index, we have to keep in mind that historical values are just one path of the many paths that the instrument could have taken.

For example, 10 tosses of a fair coin can result in TTTTTFFFFF and TFTFTFTFTF with equal probability. If your strategy is path dependent (as most strategies are,) then just because it was successful in one trial (historical prices) doesn’t mean that it would have been successful in all (or majority) of them.

The simple thing to do after a successful back-test against historical prices is to run a Monte Carlo simulation to check if the strategy comes out ahead in most of them. This can be setup by assuming returns are normally distributed and running a simulation using the mean and standard deviation of the sample.

For instance, in the recent past, daily NIFTY 50 returns have exhibited a mean of -0.0003742873 and std. dev. of 0.01079387. When you run a simulation and plot the results over the actual closing prices of the index, you get the resulting chart:

monte-carlo.NIFTY

How many of these paths will result in a total equity wipeout of the back-tested strategy?

Theme: Low Volatility Update 09.05.2016

held since returns (%)
WIPRO
2014-May-02
+3.59
ACC
2015-Dec-31
+6.69
HDFCBANK
2015-Dec-31
+5.40
INDUSINDBK
2015-Dec-31
+8.78
CIPLA
2015-Dec-31
-14.43
PIDILITIND
2015-Dec-31
+7.10
COLPAL
2016-Feb-01
-1.47
CASTROLIND
2016-Feb-01
+2.75
CRISIL
2016-Mar-04
+11.96
HDFC
2016-Mar-04
+6.80
ASIANPAINT
2016-Mar-04
+5.00
HINDUNILVR
2016-Mar-04
-0.37
DABUR
2016-Mar-04
+14.18
POWERGRID
2016-Mar-04
+3.96
INFY
2016-Apr-05
-2.25
RELIANCE
2016-Apr-05
-4.65
HCLTECH
2016-Apr-05
-14.83
BIOCON
2016-Apr-05
+14.86
TATACHEM
2016-Apr-05
+11.53
OIL
2016-Apr-05
+5.43
Since the last rebalance on 2016-Apr-05 till 2016-May-06, this strategy has returned +3.97%

You can find more details about the Low Volatility Theme here.

Theme: HighIR Momentum Update 09.05.2016

held since returns (%)
KAJARIACER
2015-Dec-31
+8.49
HINDPETRO
2015-Dec-31
+0.26
RAJESHEXPO
2015-Dec-31
-15.97
ASHOKLEY
2015-Dec-31
+17.54
RELIANCE
2016-Feb-01
-4.52
TORNTPOWER
2016-Feb-01
-2.19
VAKRANGEE
2016-Feb-01
+0.83
NHPC
2016-Feb-01
+0.24
TATAELXSI
2016-Mar-04
-1.30
ASIANPAINT
2016-Mar-04
+5.01
WELSPUNIND
2016-Mar-04
+10.30
ZEEL
2016-Mar-04
+6.81
KANSAINER
2016-Mar-04
+4.08
GODREJCP
2016-Apr-05
+0.07
AUROPHARMA
2016-Apr-05
+7.56
RELINFRA
2016-Apr-05
+0.73
JUBILANT
2016-Apr-05
-3.16
TATASTEEL
2016-Apr-05
+5.07
APOLLOTYRE
2016-Apr-05
-5.70
TV18BRDCST
2016-Apr-05
-3.59
Since the last rebalance on 2016-Apr-05 till 2016-May-06, this strategy has returned -0.93%

You can find more details about the HighIR Momentum Theme here.

Theme: High Sharpe Update 09.05.2016

held since returns (%)
RAJESHEXPO
2015-Dec-23
-15.86
CHOLAFIN
2015-Dec-23
+40.41
MPHASIS
2015-Dec-23
-2.75
PETRONET
2015-Dec-23
+12.15
MARICO
2015-Dec-23
+8.69
ASHOKLEY
2015-Dec-23
+17.54
IGL
2016-Feb-01
+1.84
TATAELXSI
2016-Mar-04
-1.33
JSWSTEEL
2016-Mar-04
+11.66
WELSPUNIND
2016-Mar-04
+10.18
APLLTD
2016-Mar-04
-7.26
KANSAINER
2016-Mar-04
+4.10
TORNTPOWER
2016-Mar-04
+2.44
VAKRANGEE
2016-Mar-04
-13.55
BAJAJFINSV
2016-Apr-05
+7.21
GODREJCP
2016-Apr-05
-0.37
INFY
2016-Apr-05
-2.09
JUBILANT
2016-Apr-05
-3.96
RAMCOCEM
2016-Apr-05
+22.85
TVSMOTOR
2016-Apr-05
-4.89
Since the last rebalance on 2016-Apr-05 till 2016-May-06, this strategy has returned +1.70%

You can find more details about the High Sharpe Theme here.

Theme: High Alpha Update 09.05.2016

held since returns (%)
SRF
2015-Dec-23
+11.22
AUROPHARMA
2015-Dec-23
-5.71
HINDPETRO
2015-Dec-23
-1.06
APLLTD
2015-Dec-23
-15.23
RAJESHEXPO
2015-Dec-23
-15.77
VAKRANGEE
2015-Dec-23
+6.97
ASHOKLEY
2015-Dec-23
+17.23
TORNTPOWER
2016-Feb-01
-2.08
TATAELXSI
2016-Mar-04
-1.37
JSWSTEEL
2016-Mar-04
+11.45
WELSPUNIND
2016-Mar-04
+10.24
SKSMICRO
2016-Mar-04
+12.43
PETRONET
2016-Mar-04
+14.10
IGL
2016-Apr-05
+1.65
RELINFRA
2016-Apr-05
+0.61
MPHASIS
2016-Apr-05
+3.60
JUBILANT
2016-Apr-05
-2.99
RAMCOCEM
2016-Apr-05
+22.67
KANSAINER
2016-Apr-05
+5.11
TV18BRDCST
2016-Apr-05
-3.72
Since the last rebalance on 2016-Apr-05 till 2016-May-06, this strategy has returned +2.20%

You can find more details about the High Alpha Theme here.