L EHRSTUHL FÜR G ELD , W ÄHRUNG UND I NTERNATIONALE F INANZMÄRKTE CHRISTIAN-ALBRECHTS-UNIVERSITÄT 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 A RTIFICIAL T ECHNICAL A NALYST : E MPIRICAL I NVESTIGATION OF THE T OKYO S TOCK E XCHANGE D ATA Timur Yusupov, yusupov@bwl.uni-kiel.de
O UTLINE 1. I NTRODUCTION 2. R EVEALED T RANSACTION C OSTS AND D ECISION -M AKING F UNCTION 3. A RTIFICIAL T ECHNICAL A NALYST 4. B ENCHMARK T RADING S TRATEGIES 4.1. P ERFECT F ORECAST S TRATEGY 4.2. R ANDOM W ALK S TRATEGY 4.3. R ANDOM S TRATEGY 4.4. B UY - AND -H OLD S TRATEGY 5. E MPIRICAL I NVESTIGATION 6. C ONCLUSIONS 7. F UTURE W ORK Slide Page 2 of 30
1. I NTRODUCTION : EMH VS . T ECHNICAL A NALYSIS F ORECAST 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). D EFINITION : 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. F IRST 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 C ONTEMPORARY APPLICATION : wide use by private and professional investors. 2 P ROBLEM : 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). Slide Page 3 of 30
2.1. R EVEALED T RANSACTION C OSTS • Roll (1984): an implicit measure of effective bid-ask spread. Background: • 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 t 1 At time t the budget is + = Np Np c m , (1) t t t < c < where 0 1 is a proportionate transaction cost, m is the initial budget, p is a spot price, t t + and N is a quantity of stock. At time t 1 the expected profit is [ [ ] [ ] ] ( ) π = − − ⋅ + N E p p c E p p . (2) + + t 1 t t 1 t The profit is positive if [ ] − E p p < ≡ + L c t 1 t c , (3) [ ] t + E p p + t 1 t L where c are revealed transaction costs from long position. t Slide Page 4 of 30
+ Case (ii): Expected Decrease in the Asset's Price at time t 1 At time t one has to short N units of the asset at price p , with revenue Np , and to t t + carry the transaction cost of Np t . At time c t 1 one has to buy N units of the asset at price [ ] [ ] [ ] c + + E p , with the total cost of NE p NE p , and the expected profit t + 1 t 1 t + 1 [ [ ] [ ] ] ( ) π = − − ⋅ + N p E p c E p p . (4) t t + 1 t + 1 t Again looking for the positive profit condition and solving for c we have [ ] − p E p < + ≡ S c t t 1 c , (5) [ ] t + E p p + t 1 t S where c are revealed transaction costs from short position. t 2.2. D ECISION -M AKING F UNCTION [ ] − E p p < + B if c t 1 t , [ ] + E p p + t 1 t [ ] − p E p ( ) = < D c , p , p ,... p S if c t t + 1 , (6) [ ] − − t t t 1 t n + E p p + t 1 t N otherwise . Slide Page 5 of 30
3. A RTIFICIAL T ECHNICAL A NALYST (ATA) 3.1. I NTODUCTION 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 condition 1 , condition 2 ,… condition n 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 Slide Page 6 of 30
3.2. ATA C ONTROL W INDOW : L EARNING THE S INE F UNCTION Slide Page 7 of 30
3.3. ATA D ECISION F UNCTION AND A GGREGATE R ETURN D ECISION FUNCTION : T ∏ = A GGREGATE RETURN : R r , where t − p p = t 2 t < ( ) B if c t + 1 , − + p p p c + p p + + t 1 t 1 t if B , t + t 1 p − p p t ( ) ( ) = < − + D I c , p , p ,... p S if c t + , p p p c t 1 ( ) = − − + t t t 1 t n r c , p , p t t 1 t if S , + p p + + t 1 t 1 t + t p t 1 + t 1 1 if N . N otherwise . 4.1. P ERFECT F ORECAST S TRATEGY D ECISION FUNCTION : T ∏ = A GGREGATE RETURN : R r , where t = − t 2 p p < + B if c t 1 t , ( ) − + p p p c + p p + + = t 1 t 1 t if D (...) B , + t 1 t t − p p p ( ) = < t II + ( ) D c , p , p S if c t t 1 , − + p p p c + t t 1 t ( ) + p p = + = r c , p , p t t 1 t if D (...) S , t + 1 t + + t 1 t 1 t t p − p p + t 1 ≥ + t 1 t N if c . + p p = 1 if D (...) N . t + 1 t t Slide Page 8 of 30
4.2. R ANDOM W ALK S TRATEGY 4.3. R ANDOM S TRATEGY = + ε ε σ 2 ˆ p p , where ~ N ( 0 , ) . + t 1 t t t t D ECISION FUNCTION : D ECISION FUNCTION : − p ˆ p < 1 + B if c t 1 t , = B with Pr( B ) , + ˆ p p + 3 t 1 t − ˆ p p ( ) 1 = < D III c , p , p ,... S if c t t + 1 , = = D IV S with Pr( S ) , − t t t 1 + ˆ p p t 3 + t 1 t N if otherwise . 1 = N with Pr( N ) . 3 4.4. B UY - AND -H OLD S TRATEGY A GGREGATE RETURN : T ∏ = A GGREGATE RETURN : R r , where ( ) . t − + p p p c = t 2 = iv T T t R ( ) − + p p p c p + + = t 1 t 1 t if D (...) B , t t p t ( ) − + p p p c ( ) = + = r c , p , p t t 1 t if D (...) S , t + 1 t + 1 t t p + t 1 = 1 if D (...) N . t Slide Page 9 of 30
5. E MPIRICAL I NVESTIGATION 5.1. A SSUMPTIONS (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: ( ) = D c , p , p ,... p { B , S , N }, − − t t 1 t n where c are transaction costs (in fractions); p , p − ,..., p are current and lagged asset prices; t t 1 t − n B denotes the buy transaction; S is the short-sell; and N means to pass up trading. Slide Page 10 of 30
5.2. D IMENSIONS OF E MPIRICAL A NALYSIS (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. D ATA D ESCRIPTION B ACKGROUND : 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 Slide Page 11 of 30
5.4.1. ATA: P OOL OF H IGH -L IQUIDITY S TOCKS Slide Page 12 of 30
5.4.2. ATA: P OOL OF M EDIUM -L IQUIDITY S TOCKS Slide Page 13 of 30
5.4.3. ATA: P OOL OF L OW -L IQUIDITY S TOCKS Slide Page 14 of 30
5.5.1. P ERFECT F ORECAST S TRATEGY : P OOL OF H IGH L IQUIDITY S TOCKS Slide Page 15 of 30
5.5.2. P ERFECT F ORECAST S TRATEGY : P OOL OF M EDIUM -L IQUIDITY S TOCKS Slide Page 16 of 30
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