Prices and Volumes on the Stock Market

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Marek Adamski
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1 Prices and Volumes on the Stock Market Krzysztof Karpio Piotr Łukasiewicz Arkadiusz Orłowski Warszawa, listopada

2 Data selection Warsaw Stock Exchange WIG index assets most important for investors different sectors content: every 3 months (volume, capitalization) to >= 27 assets 3961 trading days ~ 15 years. Warszawa, listopada

3 WIG: prices and volumes Warszawa, listopada

4 WIG: prices and volumes Warszawa, listopada

5 WIG: prices and volumes Prices 3-7 times larger Volumes 45 times larger! greater fluctuations than for prices some spikes Prices & volumes seem to go together. Warszawa, listopada

6 Questions How to compare prices/volumes to themselves? 15 years of history How to define a big/small? differences: few orders of magnitude. Warszawa, listopada

7 Current value vs history small price Not so small 45 days 300 days Warszawa, listopada

8 Current value vs history If you can not look forward. just look backward! How far? We don t know. Lets look k - days. Warszawa, listopada

9 Warszawa, listopada Variables: current value vs average p t, v t - daily closure price, trading volume k - investor memory (k<=401). ) ( k t t t t k t p p p k p P = K ) ( k t t t t k t v v v k v V = K

10 P k distribution ln(p k ) Warszawa, listopada

11 ln(p 11t ) Warszawa, listopada

12 ln(p 51t ) Warszawa, listopada

13 ln(p 101t ) Warszawa, listopada

14 ln(p 201t ) Warszawa, listopada

15 ln(p 301t ) Warszawa, listopada

16 ln(p 401t ) Warszawa, listopada

17 ln(p k ) Gaussian fit f ( x) = a exp( ( x μ) σ 2 2 ), μ = (0.032 ; ) σ = (0.131 ; ) R 2 = 0.93 Warszawa, listopada

18 ln(p k ) Gaussian fit parameters f ( x) = a exp( ( x μ) σ 2 2 ), Warszawa, listopada

19 Autocorrelations No autocorrelations -> R 2 = 0.99 b = 0.55±0.01 σ ( k) k σ ( k) = a k b small positive autocorrelations. Warszawa, listopada

20 V k distribution f ( x) = a x exp( (ln( x) μ) σ 2 2 ) μ = (0.042 ;; 0.065) σ = (0.550 ;; 0.579) R 2 =0.988 Warszawa, listopada

21 ln(v 11t ) Warszawa, listopada

22 ln(v 51t ) Warszawa, listopada

23 ln(v 101t ) Warszawa, listopada

24 ln(v 201t ) Warszawa, listopada

25 ln(v 301t ) Warszawa, listopada

26 ln(v 401t ) Warszawa, listopada

27 ln(v k ) - Gaussian fit parameters f ( x) = a exp( ( x μ) σ 2 2 ), Warszawa, listopada

28 Autocorrelations No autocorrelations -> R 2 = 0.96 b = ± σ ( k) k big negative autocorrelations. Warszawa, listopada

29 Autocorrelations: prices vs volumes Prices Small positive Trend to keep changes Prices are unlimited Volumes Big negative Counteraction against changes Volume is limited Demand is restrained by the price growth Suppply is restrained by the price descrease. Warszawa, listopada

30 Correlations ln(p k ) vs ln(v k ) local localmaximum at at75 75 days days daily dailylogarithmic return return rates rates Warszawa, listopada

31 Correlation plot, k=101 Warszawa, listopada

Warszawa, 25-27 listopada 2010 32 Parametrization of correlation plots, 2 exp ), ( 2 2 2 2 2 1 2 1 2 1 2 1 2 2 2 1 ) ( ) )( ( ) ( ) 2(1

32 Warszawa, listopada Parametrization of correlation plots, 2 exp ), ( ) ( ) )( ( ) ( ) 2( = σ μ σ σ μ μ σ μ ρ ρ σ πσ ρ v v p p A v p f 2-dim Gauss Weighted χ 2 error = sqrt(bin content) χ 2 /ndf slightly bigger than 1

33 Correlations ln(p k ) vs ln(v k ) wide widelocal localmaximum around days days local localminimum days days Warszawa, listopada

34 ln(p k ) - ln(v k ), k=1 Warszawa, listopada

35 ln(p k ) - ln(v k ), k=5 Warszawa, listopada

36 ln(p k ) - ln(v k ), k=11 Warszawa, listopada

37 ln(p k ) - ln(v k ), k=21 Warszawa, listopada

38 ln(p k ) - ln(v k ), k=51 Warszawa, listopada

39 ln(p k ) - ln(v k ), k=81 Warszawa, listopada

40 ln(p k ) - ln(v k ), k=101 Warszawa, listopada

41 ln(p k ) - ln(v k ), k=151 Warszawa, listopada

42 ln(p k ) - ln(v k ), k=201 Warszawa, listopada

43 ln(p k ) - ln(v k ), k=251 Warszawa, listopada

44 ln(p k ) - ln(v k ), k=301 Warszawa, listopada

45 ln(p k ) - ln(v k ), k=351 Warszawa, listopada

46 ln(p k ) - ln(v k ), k=401. Warszawa, listopada

47 Slope coefficient vs k stabilization Warszawa, listopada

48 Causality Correlations exist What s the direction? ln(p k ) -> ln(v k ) ln(v k ) -> ln(p k ) ln(v k ) <->ln(p k ) Granger test. Warszawa, listopada

49 Granger test What is better forecasted based on the past data? prices volumes ln( V t ), ln( P t ) = B l l 0 + αi ln( Vt i ) + βi ln( Pt i ) i= 1 i= 1 How far to look backward? What is the range l. Warszawa, listopada

50 Granger test: range Very clear direction prices -> volumes stabilization around 10 range 12 for future analysis. Warszawa, listopada

51 Granger test Warszawa, listopada

52 Granger Prices -> Volumes Result independent on k Two directional relation for some k? Other studies Latin America emerging: vol -> prices Mexico, US: prices -> vol Some evidence on Polish market maturity? Warszawa, listopada

53 Overall glance again Warszawa, listopada

54 Distribution of price/volume f ( x) = a x exp( (ln( x) μ) 2 ) σ 2 R 2 = 0.95 μ = ± 0.05 σ = 1.04 ± 0.06 Warszawa, listopada

55 Companies (σ) U.S. (NYSE) Poland (GPW) Solvay: Pekao: DaimlerChysler: Budimex: Microsoft: Rafako: Warszawa, listopada

56 P k /V k vs k Warszawa, listopada

57 Final remarks Event prices & volumes signifitantly changed over time: P kt & V kt are stationary P kt & V kt are log-normal distributed P kt - small positive autocorrelations V kt - big negative autocorrelations Moderate correlations P kt -V kt local maximum (100) & minimum (210) 2dim plots tend to rotate: some stabilization at 250. Warszawa, listopada

58 Final remarks (cont.) Strong Granger causality P -> V similarity to mature markets opposite behavious than for emerging ones at least in Latin America Simply P/V values conform log-normal distribution Width of ln(p k /V k ) exchibites local maximum & minimum. Warszawa, listopada

59 Thank You! Warszawa, listopada

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