Technical Analysis Compared to Methods Based on Mathematical Models

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• Technical Analysis Compared to Methods Based on
  Mathematical Models
• Under Parameter Mis-specification
• Gunwoo Lim
• Ankit Mangal
• Chao Pan
• Allison Richer

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• Chartist ?!

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(No Transcript)
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Technical Analysis

• Chartists only use stock charts in order to
  predict future movements of stock prices in
  markets!
• why?
• They believe that everything that could
  influence on the stock prices is already
  reflected in the historical stock prices!

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Questions

• Isnt their belief reliable?
• If yes, why is it good? How good?
• If not, Why not good? How bad?

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Our Objective
Provide performance comparisons between technical
analysis and mathematical analysis approaches
under two different conditions
so that Help you invest in stocks at
the right time with right methods
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Math vs. Tech
1. Portfolio Allocation Strategy - Maximize
the expected wealth of trader 2. Model and
Detect Methods - Use stopping rule that
detects the timing at which the drift of
stock changes 3. Moving Average Analysis -
Use the average of the closing prices of the
stock as an indicator that predicts the
future stock movement
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Terminology Utility Function

• Utility function is to measure how much investors
  are satisfied with their investment in terms of
  wealth
• Logarithmic scale will be used to simplify
  functions that evolve according to an exponential
  function

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Under two different worlds
Garbage in, Garbage out!
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Economic setting

• We have two assets traded continuously, one
  riskless bond and one risky asset.
• The bond price is derived from the following
  equation

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Economic setting

• The stock price is derived from the following
  stochastic differential equation
• (Bt)0tT is a one-dimensional Wiener process
• t represents the random time of the drift change
• t is independent of B
• t has an exponential distribution P(t gtt) e-lt,
  t0
• At time t, the instantaneous expected rate of
  return
• changes from µ1 to µ2

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Technical Analysis Focus and Assumptions

• Chartists focus on historical price movements and
  use this historical data to predict future
  activity in the market.
• Assumptions
• Everything is discounted, meaning that the
  underlying factors
• affecting the company and all economic
  factors are reflected in the
• price of the stock.
• (2) Price movements follow trends.
• (3) Patterns in price movements repeat themselves.

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Proposition

• In comparison to Mathematical Analysis,Technical
  Analysis is better at predicting the timing of
  moves in the market

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Process

• Chose Las Vegas Sands Corporation (NYSELVS)
  Stock
• Chose time interval of 1 year with time increment
  (Dt) of 1 day
• Chose the time window used in computing the
  moving average (d) of 0.4 years
• Calculated Mtd using Excel
• Determined the proportion of wealth (?t) invested
  in the stock at time t
• Calculated log Wealth at time t1

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Calculating Mtd

• Take the average of the stock prices for the 146
  days prior to time t (since d0.4 corresponds to
  0.4365 146 days)

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Determining ?t

• We assume the trader has two options
• 1.) Invest all wealth in the stock or
• 2.) Invest all wealth in the riskless bond
• If St gt Mtd, the trader invests in stock (so ?t
  1)
• If St Mtd, the trader invests in bonds (so ?t
  0)

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Graph of Wealth Distribution
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Calculating Wealth at time tn1

• Use the following formula
• Where erDt
• And r 5.06 is the annual risk-free interest
  rate

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Graph of log(W(t))
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Expected logarithmic utility of wealth
where
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Mathematical Analysis

• Outline
• Optimal Portfolio Allocation Strategy under a
  change of drift.
• Two Model and Detect Strategies
• Karatzas Method.
• Shiryaev Method .
• Mis-specified parameters

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Optimal Portfolio Allocation Strategy under a
change of drift.

• Aim
• Characterizing the optimal wealth and portfolio
  allocation of a trader who perfectly knows all
  the parameters mu1, mu2, lambda, r and sigma.
  (unrealistic but used as benchmark)
• for a given non-random initial wealth x.
• where is the proportion of wealth in
  stocks.

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Strategy of Implementation

• In other words,
• Objective is to maximize investors expected
  utility of wealth at the terminal date T.
• Strategy of Implementation
• Find Utility,
• 
  why?
• Find Wealth
• For that we need

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Strategy Contd.

• For that we need Ft , which is the probability
  that change in drift occurred before time t.
• where lambda parameter of exponential
  distribution
• Lt exponential likelihood ratio, which we can
  find
• we need the St

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Model and Detect Methods

• Aim
• To find the stopping rule which
  detects the instant at which the drift of
  the stock return changes.

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Karatzas Method

• To compute the optimal stopping rule that
  minimizes the expected miss
• For which we need to calculate
• where p is the solution to equation
• Where

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Shiryaev Method

• Almost similar method with difference in the
  equation through which it calculates A

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Mis-specified Trading Models

• Why In reality, it is difficult to know the
  parameters characterizing the investment
  opportunity set exactly (e.g. cannot be
  determined a priori and cannot be calibrated
  accurately)
• Assess the impact of estimation risk on the
  performance of the various model-based detection
  strategies.

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Mis-specification of Parameters

• Dynamics of the stock price with estimation error

• Optimal allocation and corresponding wealth

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Model Detect strategies

• Karatzas and corresponding wealth

where satisifies

• Shiryaev and corresponding wealth same as stated
  in the earlier part but the parameters are
  mis-specified

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Setup of Parameters

• Historical parameters

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Matlab Implementation and Results
Optimal allocation method
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Matlab Implementation and Results

• Model Detect strategies
• Astar0.875
• pstar0.875

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Numerical Comparison of Various Strategies
Impact of the change in the volatility
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Numerical Comparison of Various Strategies
Impact of change in time horizon
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Numerical Comparison of Various Strategies
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Reference

• Wilmott on Quantitative Finance and references
  therein. Chapter 20
• Technical analysis compared to mathematical
  models based methods under parameters
  mis-specification. Blanchet-Scalliet et. al.
  Journal of Banking Finance 31 (2007) 1351-1373
• Blanchet-Scalliet, C., Diop, A., Gibson, R.,
  Talay, D., Tanre, E., 2006. Technical analysis
  techniques versusmathematical models boundaries
  of their validity domains. In Niederreiter, H.,
  Talay, D. (Eds.), Monte Carlo and Quasi-Monte
  Carlo Methods 2004. Springer-Verlag, Berlin, pp.
  1530.
• Data from Yahoo Finance