PerryKaufmanAsignacionDeCarterasParaTraders

7/29/2019 PerryKaufmanAsignacionDeCarterasParaTraders

1/17

PORTFOLIO ALLOCATIONPORTFOLIO ALLOCATION

FOR THE ACTIVE TRADERFOR THE ACTIVE TRADERUsing Genetic Algorithm TechnologyUsing Genetic Algorithm Technology

PERRY J . KAUFMANPERRY J . KAUFMAN

SpecialistSpecialist ininproductproduct developmentdevelopmentandandfinancialfinancial engineeringengineering


2/17

Proper Allocation is ImportantProper Allocation is Important

The amount allocated can change failure toThe amount allocated can change failure to

successsuccess or success to failureor success to failure

It considers the risk of each marketIt considers the risk of each market

It considers the correlation in returnsIt considers the correlation in returnsbetween each pair of marketsbetween each pair of markets

20%

Microsoft

25%

U.S.

notes

15%

Crude oil

5%

Gold

stocks

35%

Cisco


3/17

Allocation ObjectivesAllocation Objectives

In general, equalizing the risk of eachIn general, equalizing the risk of each

market maximizes diversificationmarket maximizes diversification

In general, allocating equally acrossIn general, allocating equally across

correlated groups maximizes diversificationcorrelated groups maximizes diversification


4/17

Everyone Uses MarkowitzEveryone Uses Markowitz Markowitz is the creator of MPTMarkowitz is the creator of MPT

Modern Portfolio TheoryModern Portfolio Theory

Expected risk is the portfolio varianceExpected risk is the portfolio variance

RR

22 = = wwii22ii

22 + + wwiiwwjjCCijij

Note thatNote thatis theis thestandard deviation (risk)standard deviation (risk)

Note thatNote thatCCijij

are theare thecrosscross--correlationscorrelations

Note thatNote that wwii are theare theweighting factorsweighting factors


5/17

Most Traders Have Disjoint ReturnsMost Traders Have Disjoint Returns MPT is intended to use continuous returns, such as stockMPT is intended to use continuous returns, such as stock

prices expressed as a percentage return seriesprices expressed as a percentage return series

Real trading is not always in the market; returns areReal trading is not always in the market; returns aredisjointdisjoint separated by periods of zero (no activity)separated by periods of zero (no activity)

Periods of zero returns artificially makePeriods of zero returns artificially make smaller andsmaller andcreate suspicious covariance valuescreate suspicious covariance values

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

%Returns

No market positions

Risk is grea ter w hen

there are positions

in both markets

Risk is less

whe n only one

market has an

oen position


6/17

The Genetic AlgorithmThe Genetic Algorithm

If MPT does not show the true risk ofIf MPT does not show the true risk of

trading, then another method is neededtrading, then another method is needed

A Genetic Algorithm solves this problemA Genetic Algorithm solves this problem

It is a very powerful search method that isIt is a very powerful search method that isbased on the concepts ofbased on the concepts ofreproductionreproduction andand

survival of the fittestsurvival of the fittest


7/17

Genetic Algorithm ProcessGenetic Algorithm Process1.1. Start with aStart with agene poolgene pool

2.2. RankRank the best attributesthe best attributes

3.3. PropagatePropagatethethesurvival of the fittestsurvival of the fittest

4.4. MateMate5.5. IntroduceIntroducemutationsmutations

6.6. Cycle into step 2Cycle into step 2


8/17

Gene PoolGene Pool Create of GeneCreate of Gene

Pool using randomPool using randomnumbers betweennumbers between0 and 1.00 and 1.0

Each line is a newEach line is a newportfolioportfolio

Scale betweenScale between

0 and 1.0,0 and 1.0,sum = 1.0sum = 1.0

Portfolio 1 2 3 4 5

1 0.65 0.33 0.59 0.94 0.08 2 0.42 0.87 0.17 0.01 0.66

3 0.30 0.09 0.98 0.97 0.44

4 0.13 0.27 0.57 0.99 0.22

5 0.08 0.61 0.16 0.51 0.41

6 0.82 0.98 0.60 0.76 0.97

7 0.52 0.93 0.61 0.45 0.86

8 0.25 0.39 0.41 0.45 0.75

9 0.76 0.61 0.89 0.59 0.33

10 0.58 0.76 0.14 0.14 0.86

11 0.70 0.69 0.77 0.57 0.17

12 0.53 0.69 0.24 0.20 0.85

. 0.93 0.80 0.16 0.35 0.23

. 0.50 0.29 0.27 0.92 0.99

. 0.97 0.28 0.38 0.57 0.66

ASSET (RANDOM ALLOCATION)


9/17

Scaling the Pool into Weighting FactorsScaling the Pool into Weighting Factors

Total each row and divide by the totalTotal each row and divide by the total

2.860.660.570.380.280.97.

2.970.990.920.270.290.50.

2.470.230.350.160.800.93.

2.510.850.200.240.690.5312

2.900.170.570.770.690.7011

2.480.860.140.140.760.5810

3.180.330.590.890.610.769

2.250.750.450.410.390.258

3.370.860.450.610.930.527

4.130.970.760.600.980.826

1.770.410.510.160.610.085

2.180.220.990.570.270.134

2.780.440.970.980.090.303

2.130.660.010.170.870.422

2.590.080.940.590.330.651

Total54321Portfolio

ASSET (RANDOM ALLOCATION)

1.000.230.200.130.100.34.

1.000.330.310.090.100.17.

1.000.090.140.060.320.38.

1.000.340.080.100.270.2112

1.000.060.200.270.240.2411

1.000.350.060.060.310.2310

1.000.100.190.280.190.249

1.000.330.200.180.170.118

1.000.260.130.180.280.157

1.000.230.180.150.240.206

1.000.230.290.090.340.055

1.000.100.450.260.120.064

1.000.160.350.350.030.113

1.000.310.000.080.410.202

1.000.030.360.230.130.251

Total54321Portfolio

ASSET (RESCALED VALUES)


10/17

Gene Pool RescalingGene Pool Rescaling

with Whole Numberswith Whole Numbers100

Portfolio 1 2 3 4 5 Total 1 2 3 4 5

1 0.07 0.74 0.87 0.13 0.47 2.28 3 33 38 6 212 0.20 0.62 0.77 0.30 0.70 2.59 8 24 30 11 27

3 0.41 0.22 0.04 0.50 0.54 1.71 24 13 2 29 31

4 0.60 0.52 0.79 0.10 0.26 2.27 27 23 35 4 11

5 0.72 0.66 0.53 0.70 0.04 2.65 27 25 20 27 1

6 0.75 0.77 0.60 0.99 0.77 3.87 19 20 15 26 20 7 0.41 0.70 0.62 0.83 0.45 3.01 14 23 21 27 15

8 0.54 0.15 0.30 0.09 0.66 1.74 31 8 17 5 38

9 0.13 0.07 0.59 0.89 0.00 1.68 8 4 35 53 0

10 0.02 0.80 0.49 0.17 0.47 1.94 1 41 25 9 24

11 0.61 0.53 0.89 0.83 0.32 3.18 19 17 28 26 10 12 0.02 0.21 0.63 0.25 0.41 1.53 2 14 41 16 27

. 0.15 0.88 0.96 0.22 0.06 2.27 7 39 42 10 3

. 0.91 0.91 0.44 0.47 0.12 2.86 32 32 16 17 4

. 0.04 0.80 0.57 0.77 0.70 2.88 1 28 20 27 24

ASSET (RANDOM ALLOCATION) SCALE BETWEEN 0 AND 100


11/17

PropagationPropagation Using portfolio 1Using portfolio 1

allocations,allocations,calculate returns,calculate returns,

risk, and ratio ofrisk, and ratio of

return/riskreturn/risk

Find all ratiosFind all ratios

Sort by ratioSort by ratio

1 2 3 4 5 Daily Total

0.19 0.07 0.20 0.39 0.14 Return Return

19990104 0 0 -0.241 0 -0.018 -0.050 -0.050

19990105 0 0 0.184 0 0.120 0.054 0.004

19990106 0 0 0.084 0 0.190 0.044 0.048

19990107 0 0.008 0.182 0 0 0.036 0.084

19990108 0 0.041 0.011 0 0 0.005 0.089

19990111 0 0.142 0.166 0.198 0 0.121 0.210

19990112 0 0 0 0.040 0.023 0.019 0.229

19990113 -0.029 0.028 0 0.010 - 0.070 -0.010 0.219

19990114 0.048 0.128 0 -0.373 0.460 -0.062 0.157

19990115 0.012 0.034 0 0.100 0 0.044 0.201

19990119 0.003 0 0 0.417 0

0.165 0.36619990120 0.097 0.103 0 0.050 0 0.046 0.412

19990121 -0.179 -0.102 0 0.710 0 0.238 0.649

19990122 -0.064 -0.107 0 0.057 0 0.003 0.652

19990125 0 0.121 -0.008 0.040 - 0.018 0.020 0.672

19990126 -0.017 0.052 -0.011 -0.733 -0.150 -0.312 0.360

19990127 -0.088 -0.098 -0.145 0.057 -0.020 -0.033 0.327

19990128 0 - 0.002 - 0.065 - 0.462 - 0.208 -0.225 0.102

19990129 0 -0.078 0.159 0 0 0.026 0.127

19990201 0 0.117 0.063 0 0 0.021 0.14819990202 -0.026 0.02 -0.142 0 0 -0.032 0.116

19990203 -0.055 -0.006 0.101 0 0 0.009 0.125

19990204 0.056 0.132 -0.122 0 0 -0.004 0.121

19990205 0.067 0.045 0.056 -0.013 0 0.022 0.143

19990208 0.039 0 -0.034 -0.212 0 -0.083 0.061

19990209 -0.003 0 -0.038 0 0.122 0.010 0.070

19990210 -0.021 0 0.121 0 -0.080 0.008 0.078

19990211 -0.03 0 -0.119 0 0.220 0.003 0.081

19990212 -0.009 0 0.057 0.017 0 0.016 0.09719990216 0.145 - 0.014 0.023 -0.205 0 -0.049 0.048

19990217 -0.045 -0.046 0.036 0.420 0.103 0.176 0.224

Standard deviation = 0.1011

Rate of return = 0.224

Annua lize d standard devia tion = 0.8218

Annua lize d rate of return = 1.8181

RETURN RATIO 2.2123

RETURNS OF PORTFOLIO 1


12/17

How Much to Propagate?How Much to Propagate?

(Make more copies of the best)(Make more copies of the best)

Sort portfolios by rankSort portfolios by rank

Get a random number between 3.5 and 5.2Get a random number between 3.5 and 5.2 Create as many copies as the closest rank toCreate as many copies as the closest rank to

the random numberthe random number

(if random number is 4.9, make 5 copies)(if random number is 4.9, make 5 copies)

Put the copies into a new poolPut the copies into a new pool

5.2 4.5 4.1 3.8 3.6 3.5 3.5


13/17

MatingMating

Pick 2 portfolios at random from the poolPick 2 portfolios at random from the pool

Pick a random point from 0 to 5 assetsPick a random point from 0 to 5 assets

Switch the left allocationsSwitch the left allocations

Mate all of the portfolios in the poolMate all of the portfolios in the pool

1 2 3 4 5

A B C D E

A B 3 4 5

1 2 C D E

RANDOM POINT

SWITCH LEFT ASSETS


14/17

Mutating Creates New PossibilitiesMutating Creates New Possibilities

Choose a portfolio atChoose a portfolio at

randomrandom Choose an asset atChoose an asset at

randomrandom

Choose a newChoose a newallocation at randomallocation at random

Rescale portfolioRescale portfolio

Mutate 1 asset in 10%Mutate 1 asset in 10%

of all portfoliosof all portfolios

Portfolio 1 2 3 4 5

1

2

3

4

5

67

8

9

10

1112

.

.

.

ASSET


15/17

Why Mutate?Why Mutate? If you donIf you dont mutate, then you can only findt mutate, then you can only find

the best result from combinations in thethe best result from combinations in theoriginal pool. The bigger the pool, the moreoriginal pool. The bigger the pool, the more

combinations. This is calledcombinations. This is called prematurepremature

convergence.convergence.

Too much mutation may change all the bestToo much mutation may change all the best

combinations and you may lose the bestcombinations and you may lose the bestresults. We may getresults. We may get no convergence.no convergence.


16/17

Cycle Back to RankingCycle Back to Ranking Are We Done?Are We Done?

If there are noIf there are no

portfolios withportfolios withhigher ratios,higher ratios,

then we are done.then we are done.

Create pool

Calculate ratios

Are we done?

Propagate best

Mate

Mutate

yes


17/17

More About Genetic AlgorithmsMore About Genetic Algorithms A GA searches for the global maximumA GA searches for the global maximum

50 x 50 x50 x 50 x

x 50 (100 times) combinationsx 50 (100 times) combinations

It may find a local maximumIt may find a local maximum

Repeat the search 5 times for a better chanceRepeat the search 5 times for a better chance

Each search takes about 10 minutesEach search takes about 10 minutes

1 . Assets . 50

Returns

Global maximum

Local maximum

CONTOUR MAP OFPOSSIBLE RETURNS

Weights

1% to100%

PerryKaufmanAsignacionDeCarterasParaTraders

Documents

Transcript of PerryKaufmanAsignacionDeCarterasParaTraders