YOUR LOGO Repetitiveness of Daily Trading Behavior and Price Directions for Canola Futures: A Discriminant Analysis Approach SANGHOON LEE SENIOR ECONOMIST, GYEONGGI RESEARCH INSTITUTE, KOREA

YOUR LOGO Three Basic Techniques to Forecast Price Movement in Futures Market 1.Fundamental analysis: study of supply and demand factors affecting the price of a commodity - current stock of a commodity - the condition of the new crop in the field - the growing environment for the new crop - the present consumption rate

YOUR LOGO 2. Technical analysis: prices can be projected based on historical price movement and current market activity. - generally assume that all fundamental factors are reflected in the day-to-day prices and their parameters. - charts, trends, oscillators, volume, open interest, etc.

YOUR LOGO 3. Sentiment Analysis: the actions of market participants power the market and determine prices - sentiment is a measure of the traders ’ degree of bullishness or bearishness toward a given futures market. - Bullish Consensus(a weekly market letter published by Market Vane Corporation)

YOUR LOGO Introduction  HYPOTHESIS: MARKET EFFICIENCY -The changes of futures prices are independent overtime and price series and market activities are random walk.  Forecasting futures price through past price series are not efficient. -Market is not perfect  some range to forecast futures price by past data series. -Common Technique to detect market efficiency  Estimate the degree of serial correlation  Test the homogeneity of pricing behavior

YOUR LOGO Review of Literature  Failed to Reject Market Efficiency Hypothesis -Goldenberg(89) -Fung and Lo(93)  Composite Results -Kamara(82) -Kawaller and others(94) -Corazza and others(97)  Rejected Market Efficiency Hypothesis - Helms and others(84) - Martell and Trevino(90) - DeCoster and others(92) - Chowdhury(91) - Schroeder and Goodwin(91) - Bessler and Covey(91) - Olszewski(98)

YOUR LOGO Objective of This Paper  To estimate the repetitiveness of daily market behavior and directions of closing prices - price moves in futures market  results of market participant ’ s activities - find some repetitive rules of market participant

YOUR LOGO Testable Hypothesis 1. Daily trading behaviors are repetitive  the direction of closing prices can be forecasted 2. This repetitiveness is homogeneous across the contracts and years

YOUR LOGO Discriminant Analysis  Predict class membership of an individual observation based on a set of predictor variable From known information  develop DCR(discriminant classification rule)  DCR assign new observation into one of several population groups

YOUR LOGO Developed DCR and Assignment Decline Group Canola Trading Data Declining Constant Rising Constant Group Rising Group Develop DCR New entry

YOUR LOGO Discriminant Rules  Likelihood Rule  Mahalanobis Distance Rule  Posterior probability Rule  Bays Rule  Nonparametric Nearest Neighbor Rule

YOUR LOGO Likelihood Rule -Suppose populations are multivariate normal distributions  i ~  (  i,  i ) Choose  i if L(x;  i,  i ) > L(x;  j,  j ) for i  j = 1, 2, 3. where,  i : mean vector of i th population  i : variance-covariance matrix of i th population L(x;  i,  i ): the likelihood function for the ith population evaluated at x, i=1, 2, 3

YOUR LOGO Mahalanobis Distance Rule -Suppose three populations (declining, rising, and constant) have equal variance-covariance matrices(  1 =  2 =  3 ), then the likelihood rule is also equivalent to: Choose  i when d i 2 < d j 2 where d i 2 = (x-  i )´  ˉ 1 (x –  i ) for i  j =1, 2, 3. The Mahalannobis squared distance rule classifies an observation into the population to whose mean it is closest.

YOUR LOGO Posterior Probability Rule -When the variance-covariance matrices are equal, the quantity P(  i | x) defined by k P(  i | x) = exp[(- ½ )d i 2 ] /  exp[(- ½ )d i 2 ] j=1 is called the posterior probability of population  I given x, for i = 1, 2, 3. Then a discriminant rule of posterior probability is: Choose  i if P(  i | x) > P(  j | x) for i  j = 1, 2, 3.

YOUR LOGO Bayes Rule for Discriminant -Pi: the prior probability for group i, the probability that a randomly selected observation comes from  i, for i=1, 2, 3. -C(i/j): cost of misclassifying an observation from  j into  i - P(i/j): probability of misclassifying an observation from  j into  i. Than the average cost of the misclassification of a randomly selected observation is Pi · C(j/i) · P(j/i) + Pj · C(i/j) · P(i/j) for i  j = 1, 2, 3.

YOUR LOGO Bayes Rule Minimizes the average cost of misclassification with respect to prior probabilities P 1, P 2, and P 3. Choose  i which minimizes d i 2 d i 2 = (x -  i ) ´  -1 (x -  i ) + log   i  -2 log  Pi  C(j/i)], for i  j = 1, 2, 3.

YOUR LOGO Data and Empirical Procedure -Data: canola futures data(1982 – 2000) from WCE - Contracts: Nov., Jan., Mar., Sept. -Daily Trading Behavior: open, high, low, closing, open interest, volume of trade -Three directions: declining, rising, constant in closing price

YOUR LOGO Variable Selection Procedure  Stepwise method was applied to select subsets of variables that might have chances at being good discriminators. -11variables(before stepwise): previous day ’ s open (t-1), high (t-1), low (t-1), closing (t-1), open interest (t-1), volume (t-1) and current day ’ s open (t), high (t), low (t), open interest (t), and volume (t). -8 variables(after stepwise): previous day ’ s open (t-1) closing (t-1), open interest (t-1), volume of trade (t-1), current day ’ s open (t), high (t), low (t), volume (t) (t-1)

YOUR LOGO Discriminant Classification Rule ( DCR i (t) )  DCR i(t) will determine the group i, which minimizes di 2 d i 2 = (x -  i ) ´  -1 (x -  i ) - log   i  -2 log  Pi  C(j/i)], for i  j = 1, 2, 3. - where, x: observation vector,open (t-1), closing (t-1), - volume (t-1), open interest (t-1), open (t), - high (t), low (t), volume (t) -  i : mean vector of x in population i - Pi: prior probability of population i

YOUR LOGO Results of Bayes DCR( ) Contract Declining Forecasted/ Real,day,(%) Rising Forecasted/ Real,day, (%) Constant Forecasted/ Real,day, (%) Total day Nov. Jan. Sept. Mar. Total 1,695/1,870 (90.6) 1,199/1,377 (87.1) 1,076/1,213 (88.7) 960/1,083 (88.6) 4,930/5,543 (88.9) 1,655/1,853 (89.3) 1,111/1,294 (85.9) 924/1,137 (81.3) 902/1,007 (89.5) 4,592/5,291 (86.8) 0/57 (0.0) 1/40 (2.5) 6/48 (12.5) 1/38 (2.6) 8/183 (4.4) 3,780 2,711 2,398 2,128 11,017

YOUR LOGO Results of Nonparametric DCR( ) Contract Declining Forecasted/ Real,day,(%) Rising Forecasted/ Real,day, (%) Constant Forecasted/ Real,day, (%) Total day Nov. Jan. Sept. Mar. Total 1,634/1,870 (87.4) 1,195/1,377 (86.8) 1,050/1,213 (86.6) 957/1,083 (88.4) 4,836/5,543 (87.2) 1,638/1,853 (88.3) 1,106/1,294 (85.5) 966/1,137 (84.0) 889/1,007 (88.3) 4,599/5,291 (86.9) 0/57 (0.0) 0/40 (0.0) 0/48 (0.0) 0/38 (0.0) 0/183 (0.0) 3,780 2,711 2,398 2,128 11,017

YOUR LOGO Rate of Correct Forecasting across the Year ( ) Rate of Correct Forecasting by Bayes DCR ( )

YOUR LOGO Rate of Correct Forecasting by Nonparametric DCR ( )

YOUR LOGO Repetitiveness across the Year, Contracts, and Directions  A GLM model was used to test homogeneity of the results Bayes DCR Results - DCR results across the year is not different at 95% significant level - DCR results across the contracts is not different at 95% significant level - repetitiveness across directions is different at 95% significant level

YOUR LOGO  Nonparametric DCR Results -DCR results across the year is not different at 95% significant level -DCR results across the contracts is different at 95% significant level -repetitiveness across directions is different at 95% significant level  Bayes and Nonparametric - DCR results are different at 95% significant level

YOUR LOGO Summary  The results showed existence of repetitiveness of daily trading behavior of canola futures  Repetitiveness were homogeneous across the year and contract except directions in Bayes DCR  Repetitiveness were homogeneous across the year but different in contracts and directions for nonparametric DCR.  Repetitiveness of Bayes and Nonparametric DCR were different.

YOUR LOGO General Conclusions  Futures prices can be predictable with the past data series.  Emphasize the existence of repetitiveness as efficient forecasting tools, and technical systems could work in canola futures market.

YOUR LOGO THE END Thank You