Besting Dollar Cost Averaging Using A Genetic Algorithm

1
Besting Dollar Cost Averaging Using A Genetic
Algorithm

• Masters Degree Thesis
• James Maxlow
• Christopher Newport University
• November 2003

2
Introduction

• Wealth creating through investment is an
  important goal for fiscally responsible citizens
• Many investors, though, fear or dont understand
  the workings of investment markets, and are
  distrustful of advice given by professionals
• Because of this, they may choose to rely on a
  purely mechanical investing approach known as
  dollar-cost-averaging that absolves then from
  falling prey to bad investment advice
• However, what if there were a mechanical strategy
  that could outperform DCA?

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Purpose

• The purpose of this project was to devise
  mechanical investment strategies that outperform
  dollar-cost-averaging
• If this could be accomplished, then such
  strategies could be made available to investors
  as alternatives to DCA
• These strategies were based solely on the price
  histories of investments and associated fees,
  ignoring any attempts to time the market no
  prediction of future prices or price changes was
  made
• The devising of strategies was left to the
  workings of a genetic algorithm

4
Questions

• Some questions that this project will sought to
  answer are as follows
• Does applying the derived strategies to test data
  sets lead to greater portfolio values than
  dollar-cost averaging over the same data?
• If so, can this result be accepted as a highly
  probable outcome over any general stock data set?
  
• Given that the program will generate multiple
  genomes for each input data set, what can be said
  about the probability of any single strategy
  producing positive results when used on the test
  data set?

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Questions

• Can the results be reliably reproduced, or will
  wild variations in return on investment values
  negate any practical use for the program?
• Will transaction fees and interest on cash
  positions provide an advantage to the derived
  strategy performance?

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Research - DCA

• The use of DCA allows for the acquisition of
  shares at a lower average cost than the average
  share price
• Because DCA is an automatic-buy strategy, there
  are no decisions to be made by the investor, save
  for the investment itself it is a hands-off
  strategy
• This makes it appealing to those that feel they
  have no ability to know when to buy or sell
• It is often used by those on fixed incomes and in
  retirement plans (401k, et. al.)
• But does it actually provide good ROI?

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Research - DCA

• Some research 4 suggests that the use of DCA
  yields no significantly better ROI than random
  buy/sell decisions for a given investment
• If this is true, then the psychological security
  that DCA provides hesitant investors may simply
  hide its relative ineffectiveness
• A strategy that bests DCAs ROI for a given
  investment, then, would serve as a more
  productive alternative to random, time the
  market buy/sell decisions

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Background Genetic Algorithms

• The majority of todays GA research expands on
  the pioneering work done by John Holland in the
  60s
• GAs work by evolving solutions to problems
• More specifically, possible solutions are split,
  recombined and mutated to breed new solutions
  that are more fit or stronger than their
  predecessors
• As the generations of solutions pass by, the
  meta-search for the best or ideal solution is
  focused on promising lineages most weaker
  branches are eventually abandoned

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Background Genetic Algorithms

• Because of this, the initial time of the GA is
  spent weeding out totally unfit solutions, and
  the latter time is spent optimizing very fit
  solutions
• This process can, in many cases, yield greater
  efficiency in finding an ideal solution than
  brute-force search techniques
• Moreover, a GA only needs to know what a solution
  will look like it does not need to have a
  collection of all possible solutions like a
  brute-force technique because it can create
  solutions on its own

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Background Genetic Algorithms

• All of these factors make GAs highly appealing
  for ill-defined problems that feature odd or
  unknown solution spaces
• Three tasks must be completed to run a GA
• First, the structure of the possible solution
  (chromosome) must be designed
• Second, the fitness algorithm for evaluating the
  strength of possible solutions must be designed
• Third, solution population, mating, and mutation
  variables must be set

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Genetic Algorithm Design

• The chromosome for this project consisted of an
  array of 20 integer values between 0 and 2
  inclusive
• The value corresponded to a buy, sell, or hold
  decision
• The position of the value in the array
  corresponded to an interval representing a given
  percentage increase or decrease in stock price

-20, -15)
-5, 0)
0, 5)
5, 10)
10, 15)
15, 20)
25, 30)
-15, -10)
-10, -5)
0
1
1
2
0
0
1
2
2


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Genetic Algorithm Design

• Any possible solution offered direct advice as to
  what action to take when a given stock changes in
  price
• But how could the fitness of this advice be
  judged?
• The GA applied the advice of every possible
  solution it generated to the established
  sequential price history of a stock the higher
  the final ROI for that advice, the stronger the
  solution

-20, -15)
-5, 0)
0, 5)
5, 10)
10, 15)
15, 20)
25, 30)
-15, -10)
-10, -5)
0
1
1
2
0
0
1
2
2


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Genetic Algorithm Design

• At this point it can be seen that the GA tried to
  form advice based on past stock prices but that
  in itself does nothing for the investor
• It was hoped that there is a hidden structure to
  stock price fluctuations such that what worked
  well in the past will likely work well again in
  the future
• That is to say that if buying when a stocks
  price rose 12 in the past produced positive
  results, so should repeating that action in the
  future, in most cases

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Genetic Algorithm Design

• The next phase, then, was to apply the strongest
  solutions to a new data set the current stock
  price values over 3 years and see how the
  solutions ROI compared with DCA over the same
  time period
• If the solutions ROI was higher, then it will
  have been established that GA generated advice
  based solely on price histories can be a better
  alternative to DCA
• If, however, applying the solutions to new data
  sets failed to produce significantly better
  results than DCA, then it will have been
  established that price histories alone are
  insufficient on which to base decisions

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Methodology

• Stocks were chosen and price histories acquired
• The Dow 30 was cut down to 15 sample stocks based
  on available data, adjusted prices, and
  correlation values
• Chromosome was implemented in code
• Fitness algorithm was implemented in code
• Program structure was finalized to allow for
  robust input and output
• Testing was done with various GA parameters to
  find a good performance compromise

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Methodology

• For each sample stock and fee/interest variable,
  the GA was set to work devising 20 strategies
  from the stocks price history
• Each of these strategies was then be applied to
  its relevant test data set to determine ROI
• 15 stocks, 2 fees, 2 interest rates 60 program
  runs resulting in 1200 strategies
• DCAs ROI for each stock was calculated on the
  test data sets (accounting for fees and interest
  rates)

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Methodology

• The results of the devised strategies were
  statistically analyzed to determine if they
  indeed offer any benefit over DCA, and if the GA
  can devise consistently better strategies
• This analysis covered mean ROI, minimum ROI,
  standard deviations, mean/DCA ROI differential,
  standard deviation distance to DCA ROI, and fee
  and interest rate effects

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Program Operation
x 20
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A Note on GA Parameters

• Tweaking of GA parameters was performed to
  increase the mean ROI of the genomes and increase
  the speed of run completion
• Pop 50 Mut 0.002 Cross 0.6 Gen 5000
• Crossover type single point (no apparent benefit
  otherwise the others slowed the program)
• Populations Deme wherein populations are
  evolved in parallel, joined at certain points,
  then segregated again good for diversity

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A Note on GA Parameters

• Selection method rank selection was chosen
  wherein the top n genomes are allowed to mate
• Every other selection method I tested failed to
  produce higher mean ROI values
• Speed an evolution-terminating condition was set
  to reduce the time spent on the GA
• This conditioned checked to see if the ratio of
  the current 200th highest genome fitness score
  to the current highest genome fitness score was
  0.999 or higher

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A Note on Fees and Interest

• Fixed-rate transaction fees were set at 1.5 and
  3
• These represented discount and full-service
  brokerage fees, respectively
• Interest rates on cash positions were set at 0
  and 2
• The 2 value is somewhat arbitrary since there is
  no universal savings account or money market
  interest rate
• Each stock was run through the program 4 times to
  account for the permutations of these values

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Results Mean and Minimum ROI

• 55 of 60 program runs produced genomes whose mean
  ROI over the test data set was higher than the
  DCA ROI over the same data set
• Of the 5 failed runs, 1 mean was lower by approx.
  1 4 means were significantly lower (all from PG
  runs)
• 46 of 60 runs produced no genome whose ROI was
  lower than DCA ROI
• 1028 out of 1200 total genomes (86) had ROI
  higher than DCA
• PG contributed 80 of the 172 failing genomes
  excluding PG would yield a 92 success rate

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Results Standard Deviations

• The mean ROI/DCA ROI differential standard
  deviation multiple can give insight into the
  probability that any random genome generated
  could best DCA

2.25 std dev multiple yields better than a 95
confidence interval
Differential
1 std dev
1 std dev
Mean ROI
DCA ROI
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Results Standard Deviations

• 3 stocks had 3 multiples (99 confidence int.)
• 5 stocks had 2-3 multiples (95 confidence int.)
• 1 stock had 1.53-2 multiples (80 confidence
  int.)
• 3 stocks had an average multiple of 0.86-1.27
• CAT established a good multiple on 1 of 4 runs
• Overall 15 of 60 runs were at 99, 32 of 60
  were at 95, 41 of 60 were at 68
• EK, UTX, CAT and C had acceptable but not great
  results
• PG failed completely

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Results Fees and Interest Rates

• 1.5 fee runs produced a mean ROI that was 0.55
  higher than the 3 fee runs
• 13 of the 30 paired runs were higher by 1 or
  more, yet 11 of the 30 paired runs actually
  yielded a lower ROI with the 1.5 fee
• This can be explained by noting that many of
  these 11 cases had a relatively high number of
  hold actions advised in the 3 runs, which incur
  no fee

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Results Fees and Interest Rates

• 2 interest runs produced a mean ROI that was
  1.25 higher than the 0 interest runs
• 8 of the 30 paired runs were higher by 2 or more
• Only 4 of the 30 paired runs actually yielded a
  lower ROI with the 2 fee
• This can be explained by noting that most of
  these 4 cases had a relatively high number of buy
  actions advised in the 2 runs, which would
  reduce the benefit associated with interest on a
  large cash position perhaps enough to push the
  results into the insignificant benefit category

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Results The Loser (PG)

• The question remains Why does the GA perform so
  poorly when applied to PGs data?
• The mean ROI values of the PG runs were 10-15
  below the DCA ROI values
• The maximum genome ROI values were 3-9 below the
  DCA ROI values
• The minimum genome ROI values were 15-19 below
  the DCA ROI values
• In short, every genome of every run of PG was a
  complete failure

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Results The Loser (PG)

• Note that for any descending price trend,
  repeated buying will lead to negative ROI any
  combination of buy, sell, and hold would perform
  better (though not necessarily yielding a
  positive ROI)
• Yet for any ascending price trend, repeated
  buying will maximize ROI any combination of buy,
  sell, and hold cannot keep pace
• To see how this might apply to PG, we examine the
  PG test data set price graph

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Results The Loser (PG)

• Here we see a short descent, and then a long
  sustained upward trend (after one spike)
• The GAs repeated buy, sell, and hold techniques
  cannot beat DCA in this specific case!

• Testing shows that the genomes can beat DCA on
  the downward slope (-8 vs. -25) but they lost
  on the much longer upward slope (-6 vs. 11)

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Results The Loser (PG)

• It is this downward slope followed by a long
  upward slope that causes the genomes to fail
  any stock that exhibits this behavior shows the
  programs weakness
• In contrast, the two best performers (GM and DIS)
  showed high variability in prices, despite slight
  overall downward trends

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Conclusion

• The genomes of investment advice generated by the
  program have no difficulty in besting DCA ROI
  results in the vast majority of cases
• The singular failure of the genome advice is
  revealed when it is applied to any sustained, low
  variability upward price trend for nothing can
  top repeated buying on such a trend
• This effect is compounded when preceded by a
  sustained low variability downward trend

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Conclusion

• Failure on such trends can be mitigated, however
• If the investor monitors the performance of the
  stock to which he or she is applying the genome
  advice, the beginnings of any sustained upward
  trend can be noted at which point the investor
  can abandon the genome advice, switching to
  repeated buying, until the trend appears to
  falter (vary significantly)
• The genome advice, which thrives on variability,
  can then be enacted again

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Conclusion

• The ability to notice situations in which the
  genomes would produce weak ROI, combined with
  their great performance on all other tested
  situations, leads me to conclude that this
  project was a success
• These genomes can best DCA in the majority of
  cases, and further refinement of the algorithm
  may lead to even greater success

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References

• 1 Edleson, M. E. Value Averaging The Safe and
  Easy Investment Strategy. Chicago International
  Publishing Corporation, 1991.
• 2 GAlib documentation http//lancet.mit.edu/ga/
  
• 3 Liscio, J. Portfolio Discipline The Rewards
  of Dollar Cost Averaging. Barrons, Aug. 8,
  1988, pp. 57-58.
• 4 Marshall, Paul S. A Statistical Comparison of
  Value Averaging vs. Dollar Cost Averaging and
  Random Investing Techniques. Journal of
  Financial and Strategic Decisions Vol. 13 No.
  1, Spring 2000.
• 5 Mitchell, Melanie. An Introduction to Genetic
  Algorithms. Cambridge The MIT Press, 2002.
• 6 The Vanguard Group of Investment Companies.
  The Dollar Cost Averaging Advantage. Valley
  Forge Brochure 0888-5, BDCA, 1988.