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L EHRSTUHL FR G ELD , W HRUNG UND I NTERNATIONALE F INANZMRKTE - - PowerPoint PPT Presentation
L EHRSTUHL FR G ELD , W HRUNG UND I NTERNATIONALE F INANZMRKTE - - PowerPoint PPT Presentation
L EHRSTUHL FR G ELD , W HRUNG UND I NTERNATIONALE F INANZMRKTE CHRISTIAN-ALBRECHTS-UNIVERSITT ZU KIEL C HAIR OF M ONETARY E CONOMICS AND I NTERNATIONAL F INANCE UNIVERSITY OF KIEL, GERMANY E FFICIENT M ARKET H YPOTHESIS T HROUGH THE E YES OF
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- 1. INTRODUCTION: EMH VS. TECHNICAL ANALYSIS
FORECAST OF THE PRICE DEVELOPMENT OF FINANCIAL INSTRUMENTS:
- a fundamental analysis (relies on the fundamental attributes of the instrument, such as
price/earning ratio, return on investment and associated economic statistics.) and
- technical analysis (search for psychological component of financial trading, which
manifest in patterns of price and/or volume time series). DEFINITION: The technical analysis is a technique to draw investment decisions for individual financial instruments based on the development of their recent price, traded volume and other quantitative measures. FIRST ENCOUNTER: on the Dojima Rice Exchange in Osaka as early as the 1600s (Homma, futures markets in the 1700s, a link between supply and demand of rice: emotions, a difference between the value and price of rice).1 CONTEMPORARY APPLICATION: wide use by private and professional investors.2 PROBLEM: Weak form of the EMH or the technical analysis.3
1 Nison (2001) and Wong et al (2003). 2 Allen and Taylor (1990) and Taylor (1992). 3 Roberts (1967) and Fama (1991).
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2.1. REVEALED TRANSACTION COSTS Background:
- Roll (1984): an implicit measure of effective bid-ask spread.
- Lesmond et al. (1999): zero returns to estimate TC of a marginal investor.
- Lesmond et al. (2004): latest review of transaction costs.
- Bessembinder et al. (1998): breakeven transaction costs.
Case (i): Expected Increase in the Asset's Price at time 1 + t At time t the budget is
t t t
m c Np Np = + , (1) where 1 < < c is a proportionate transaction cost,
t
m is the initial budget,
t
p is a spot price, and N is a quantity of stock. At time 1 + t the expected profit is
[ ] [ ] ( ) [ ]
t t t t
p p E c p p E N + ⋅ − − =
+ + 1 1
π . (2) The profit is positive if
[ ] [ ]
L t t t t t
c p p E p p E c ≡ + − <
+ + 1 1
, (3) where
L t
c are revealed transaction costs from long position.
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Case (ii): Expected Decrease in the Asset's Price at time 1 + t At time t one has to short N units of the asset at price
t
p , with revenue
t
Np , and to carry the transaction cost of c Npt . At time 1 + t
- ne has to buy N units of the asset at price
[ ]
1 + t
p E , with the total cost of
[ ] [ ]c
p NE p NE
t t 1 1 + + +
, and the expected profit
[ ] [ ] ( ) [ ]
t t t t
p p E c p E p N + ⋅ − − =
+ + 1 1
π . (4) Again looking for the positive profit condition and solving for c we have
[ ] [ ]
S t t t t t
c p p E p E p c ≡ + − <
+ + 1 1
, (5) where
S t
c are revealed transaction costs from short position. 2.2. DECISION-MAKING FUNCTION
( ) [ ] [ ] [ ] [ ]
+ − < + − < =
+ + + + − −
. , , ,... , ,
1 1 1 1 1
- therwise
N p p E p E p c if S p p E p p E c if B p p p c D
t t t t t t t t n t t t t
(6)
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- 3. ARTIFICIAL TECHNICAL ANALYST (ATA)
3.1. INTODUCTION The core of the ATA is TiCS, an implementation of Learning Classifier Systems (LCS). LCS is a rule-based evolutionary learning systems proposed by John Holland (Holland, 1975; Holland, 1976; Holland, 1977): IF condition1, condition2,… conditionn THEN action ⇔ 001#0#01#:001 … 0#01#001#:010 The ATA is designed to replicate the technical analysis Trading rules are bundles of conditions (some past observations should belong to a set) and interval estimates of next period values in a time series Rules are dynamically derived from data With each new observation the ATA performs following steps:
- 1. Data preprocessing: Local normalization
- 2. Data preprocessing: Piece-wise linearization
- 3. Data preprocessing: Encoding of nodes to binary alphabet
- 4. Data analysis: TiCS forms the expectation of the next period value
- 5. Data post-processing: Decoding of binary value to decimal intervals
- 6. Data post-processing: De-normalization of the interval values
- 7. Trading and feedback: Form the trading decision. Send a feedback to TiCS
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3.2. ATA CONTROL WINDOW: LEARNING THE SINE FUNCTION
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3.3. ATA DECISION FUNCTION AND AGGREGATE RETURN DECISION FUNCTION:
( )
+ − < + − < =
+ + + + − −
. , , ,... , ,
1 1 1 1 1
- therwise
N p p p p c if S p p p p c if B p p p c D
t t t t t t t t n t t t I t
AGGREGATE RETURN: ,
2
∏
=
=
T t t
r R where
( ) ( ) ( )
+ − + − =
+ + + + + +
. 1 , , , ,
1 1 1 1 1 1
N if S if p c p p p B if p c p p p p p c r
t t t t t t t t t t t
4.1. PERFECT FORECAST STRATEGY DECISION FUNCTION:
( )
+ − ≥ + − < + − < =
+ + + + + + +
. , , , ,
1 1 1 1 1 1 1 t t t t t t t t t t t t t t II t
p p p p c if N p p p p c if S p p p p c if B p p c D AGGREGATE RETURN: ,
2
∏
=
=
T t t
r R where
( ) ( ) ( )
= = + − = + − =
+ + + + + +
. (...) 1 , (...) , (...) , ,
1 1 1 1 1 1
N D if S D if p c p p p B D if p c p p p p p c r
t t t t t t t t t t t t t t
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4.2. RANDOM WALK STRATEGY 4.3. RANDOM STRATEGY , ˆ
1 t t t
p p ε + =
+
where ) , ( ~
2 t t
N σ ε . DECISION FUNCTION:
( )
+ − < + − < =
+ + + + −
. , ˆ ˆ , ˆ ˆ ,... , ,
1 1 1 1 1
- therwise
if N p p p p c if S p p p p c if B p p c D
t t t t t t t t t t III t
DECISION FUNCTION: = = = = . 3 1 ) Pr( , 3 1 ) Pr( , 3 1 ) Pr( N with N S with S B with B DIV
t
4.4. BUY-AND-HOLD STRATEGY AGGREGATE RETURN:
( ) .
t t T T iv
p c p p p R + − = AGGREGATE RETURN: ,
2
∏
=
=
T t t
r R where
( ) ( ) ( )
= = + − = + − =
+ + + + + +
. (...) 1 , (...) , (...) , ,
1 1 1 1 1 1
N D if S D if p c p p p B D if p c p p p p p c r
t t t t t t t t t t t t t t
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- 5. EMPIRICAL INVESTIGATION
5.1. ASSUMPTIONS (i) We disregard the impact of inflation, dividends and splits. At high frequency their impact is negligible. (ii) The aggregate return is computed separately for every time series in the study. (iii) The trading strategy is applied at every period, i.e. at the beginning of each period the previous position should be closed. Correspondingly the aggregate return is a product of returns for every time period. (iv) Returns from buying or short selling are adjusted for round-trip TC. (v) The decision-making function
( )
D maps the arguments into the space of actions:
( )
}, , , { ,... , ,
1
N S B p p p c D
n t t t
=
− −
where c are transaction costs (in fractions);
n t t t
p p p
− − ,...,
,
1
are current and lagged asset prices; B denotes the buy transaction; S is the short-sell; and N means to pass up trading.
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5.2. DIMENSIONS OF EMPIRICAL ANALYSIS (ii) the range of frequencies at which the trading decisions are made: 1:10 min, (iii) the schedule of transaction costs (TC): from 0 to 10% with 0.01% increment, (iv) the schedule of subsample sizes, n : from 50 to 250 price observations with an increment of 10 price observations. 5.3. DATA DESCRIPTION BACKGROUND: The study of the quote-driven activity of the TSE did not reveal significant differences from NYSE, or over stock markets with designated market-makers (Lehman et al., 1994; Bauwens, 2005). 2273 TSE stocks were sorted into 3 groups based on liquidity: a high, medium and low liquidity pools of stocks In each pool 10 random stocks were selected Corresponding time series of prices are used in the empirical analysis Raw data was homogenized with previous tick interpolation algorithm
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5.4.1. ATA: POOL OF HIGH-LIQUIDITY STOCKS
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5.4.2. ATA: POOL OF MEDIUM-LIQUIDITY STOCKS
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5.4.3. ATA: POOL OF LOW-LIQUIDITY STOCKS
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5.5.1. PERFECT FORECAST STRATEGY: POOL OF HIGH LIQUIDITY STOCKS
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5.5.2. PERFECT FORECAST STRATEGY: POOL OF MEDIUM-LIQUIDITY STOCKS
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5.5.3. PERFECT FORECAST STRATEGY: POOL OF LOW-LIQUIDITY STOCKS
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5.6.1. RANDOM WALK STRATEGY: POOL OF HIGH-LIQUIDITY STOCKS
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5.6.2. RANDOM WALK STRATEGY: POOL OF MEDIUM-LIQUIDITY STOCKS
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5.6.3. RANDOM WALK STRATEGY: POOL OF LOW-LIQUIDITY STOCKS
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5.7.1. RANDOM STRATEGY: POOL OF HIGH-LIQUIDITY STOCKS
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5.7.2. RANDOM STRATEGY: POOL OF MEDIUM-LIQUIDITY STOCKS
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5.7.3. RANDOM STRATEGY: POOL OF LOW-LIQUIDITY STOCKS
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5.8.1. BUY-AND-HOLD STRATEGY: POOL OF HIGH-LIQUIDITY STOCKS
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5.8.2. BUY-AND-HOLD STRATEGY: POOL OF MEDIUM-LIQUIDITY STOCKS
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5.8.3. BUY-AND-HOLD STRATEGY: POOL OF LOW-LIQUIDITY STOCKS
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5.9.1. BREAK-EVEN TRANSACTION COSTS: A COMPARATIVE TABLE Strategy ATA PF RW Rand B&H T Liq.pool H M L H M L H M L H M L H M L RTC, % .28
.32 .25 >2 >2 >2 .01 .01 .01 0 .01 .01 >2 >2 >2 0
@, obs.
50 50 50 1
∀ @, min.
3 4 4 2
RTC, % .15
.20 .25 >2 >2 >2 .01 .01 .01 .01 .01 .02 >2 >2 >2 3
@, obs.
50 50 50 4
#1 @, min.
4 6 4 5
RTC, % .20
.37 .31 >2 >2 >2 0 .01 .01 .01 .01 .01 >2 >2 >2 6
@, obs.
50 60 50 7
#2 @, min.
4 3 4 8
RTC, % .33
.51 .32 >2 >2 >2 0 .01 .02 0 .01 0 >2 >2 >2 9
@, obs.
50 60 50 10
#3 @, min.
3 3 2 11 a b c d e f g h i j k l m n
- p
q r s t u Note:
- 1. The table uses the following notations: T – Time span; H – High, M – Medium and L – Low liquidity
pool of stocks; PF – Perfect Forecast, RW – Random Walk, Rand – Random and B&H – Buy-and-Hold trading strategy; “>2” – the value of RTC is more than 2.00%.
- 2. Subsample sizes (@, obs.) and decision-making frequencies (@, min.) are recorded when the
maximum break-even revealed transaction costs (RTC, %) were observed.
- 3. For the benchmark strategies the values of break-even revealed transaction costs are recorded at the
same frequencies as for the ATA trading strategy.
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5.9.2. BUY-AND-HOLD VS. ATA TRADING STRATEGY
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- 6. CONCLUSIONS
At the ultra-high frequency of trading a technical trader (like the ATA) can get substantial aggregate returns adjusted for transaction costs. Analysis of individual time spans indicate the learning progress of the ATA. The liquidity criterion to pool the stocks has little effect on results. Even though the ATA has lower break-even revealed transaction costs then the Buy-and- Hold strategy, the intensity of the ATA returns are much higher. Hypothetical results for the TSE data indicate a case-dependent violation of the weak form of market efficiency, reflected in positive market returns: market participants with low transaction costs may perceive the market as inefficient, while a participant with high transaction costs observes the efficiency of the market.
- 7. FUTURE WORK
□ Include in the analysis order book records and past volumes. □ Analyze stock market data from the US and Europe. □ Develop theoretical model and simulation framework for studying the impact of the population of ATA on financial market stability and prevention of financial crises.
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