In a previous article, we concluded that US equity markets are random. At least that is what was determined based upon our research. I was willing to mark this matter as being solved, however, prior to doing such, a reader of this site sent a message inquiring about the Winner’s Curse, and how this phenomenon might be applied to stock pricing.
Disproving the Winner’s Curse
The winner's curse is a phenomenon that may occur in common value auctions, where all bidders have the same (ex post) value for an item but receive different private (ex ante) signals about this value and wherein the winner is the bidder with the most optimistic evaluation of the asset and therefore will tend to overestimate and overpay.
“Winner’s Curse.” Wikipedia, Wikimedia Foundation, 17 Oct. 2023, en.wikipedia.org/wiki/Winner%27s_curse.
In plain terms, this basically states that the number of bids within an auction, ought to drive up the price of the item being sold. Let’s take a look at this phenomenon as it is applied to the stock market. After all, one probably should expect to observe such a phenomenon within this medium.
To perform the appropriate analysis, I gathered the monthly closing percentage figures for three different stock indices (S&P 500, Nikkei 225, STOXX 600). The months included within this study are November 2003 – September 2023. Data was queried from Yahoo Finance.
I will be utilizing the Pearson's product-moment correlation to test for relationships as it pertains to the index volume for each month, as assessed in comparison to the percentage differentiation of closing price.
I will also test for randomness as it pertains to monthly volume figures through the utilization of the Phillips-Perron Unit Root Test.
Finally, I will test for stationarity amongst monthly volume figures through the application of the Augmented Dicky-Fuller methodology.
###########################################################################
# Getting the Libraries in Order #
library("ggpubr")
library(tseries)
###########################################################################
# S&P 500 (USA) #
###########################################################################
sp_close <- c(0.007, 0.051, 0.017, 0.012, -0.016, -0.017, 0.012, 0.018, -0.034, 0.002, 0.009, 0.014, 0.039, 0.032, -0.025, 0.019, -0.019, -0.02, 0.03, 0, 0.036, -0.011, 0.007, -0.018, 0.035, -0.001, 0.025, 0, 0.011, 0.006, -0.031, 0, 0.005, 0.02, 0.025, 0.032, 0.017, 0.013, 0.014, -0.022, 0.01, 0.043, 0.033, -0.018, -0.033, 0.013, 0.036, 0.014, -0.042, -0.008, -0.061, -0.035, -0.006, 0.045, 0.01, -0.085, -0.007, 0.011, -0.094, -0.168, -0.075, 0.016, -0.085, -0.107, 0.094, 0.1, 0.053, -0.004, 0.072, 0.031, 0.037, -0.018, 0.057, 0.015, -0.038, 0.028, 0.058, 0.013, -0.083, -0.052, 0.068, -0.053, 0.087, 0.035, -0.004, 0.06, 0.023, 0.03, -0.002, 0.026, -0.015, -0.018, -0.021, -0.057, -0.072, 0.108, -0.003, 0.009, 0.043, 0.041, 0.031, -0.007, -0.063, 0.04, 0.012, 0.02, 0.024, -0.02, 0.003, 0.007, 0.05, 0.011, 0.036, 0.018, 0.021, -0.016, 0.047, -0.033, 0.028, 0.044, 0.027, 0.023, -0.034, 0.043, 0.008, 0.005, 0.021, 0.019, -0.016, 0.038, -0.016, 0.024, 0.024, -0.003, -0.031, 0.054, -0.018, 0.009, 0.01, -0.022, 0.018, -0.063, -0.025, 0.083, 0, -0.019, -0.048, -0.002, 0.063, 0.004, 0.014, 0.002, 0.035, -0.001, -0.001, -0.018, 0.033, 0.018, 0.012, 0.034, -0.007, 0.009, 0.01, 0.003, 0.016, -0.002, 0.018, 0.021, 0.025, 0.011, 0.052, -0.036, -0.027, 0.006, 0.024, 0, 0.041, 0.028, 0.006, -0.073, 0.016, -0.102, 0.092, 0.03, 0.013, 0.034, -0.068, 0.069, 0.003, -0.018, 0.023, 0.018, 0.03, 0.028, -0.006, -0.087, -0.131, 0.166, 0.061, 0.02, 0.053, 0.064, -0.041, -0.034, 0.099, 0.03, -0.013, 0.021, 0.034, 0.047, 0.003, 0.019, 0.022, 0.026, -0.049, 0.067, -0.009, 0.035, -0.055, -0.032, 0.038, -0.09, 0, -0.088, 0.092, -0.038, -0.089, 0.073, 0.046, -0.061, 0.058, -0.025, 0.037, 0.016, 0.003, 0.064, 0.031, -0.016, -0.054)
sp_vol <- c(24463220000, 27839130000, 32820000000, 27985600000, 33597900000, 31611900000, 29326400000, 27529500000, 29285600000, 26586800000, 26829870000, 31511000000, 30460280000, 31102500000, 31498800000, 29297410000, 39014150000, 43424270000, 39321990000, 40334040000, 37464670000, 42030090000, 44777510000, 49793790000, 45102870000, 41756130000, 49211650000, 42859940000, 50905040000, 43308430000, 54312830000, 54873260000, 46348220000, 50485620000, 49001440000, 56793620000, 55343930000, 47578780000, 56686200000, 51844990000, 67622250000, 57032470000, 64958050000, 65322800000, 70337430000, 91381760000, 57809700000, 76022580000, 86246950000, 64821670000, 98475340000, 78536130000, 93189170000, 85978630000, 80990480000, 96614040000, 124980570000, 86266010000, 140007320000, 159823030000, 115660210000, 112884470000, 112090640000, 124492210000, 161843640000, 138855320000, 131614940000, 112653150000, 106635790000, 116059270000, 112295490000, 113410990000, 84981530000, 89515330000, 90947580000, 84561340000, 103683550000, 116741910000, 127662780000, 110106750000, 94778110000, 85738250000, 79589450000, 89536270000, 87151070000, 80984530000, 92164940000, 59223660000, 89507640000, 77364810000, 81708980000, 86122730000, 81102170000, 108419170000, 102786820000, 98063670000, 84275050000, 74742430000, 79567560000, 78385710000, 83899660000, 74761710000, 86920490000, 81582440000, 73103810000, 70283810000, 69784280000, 71752320000, 71489310000, 66388180000, 75848510000, 69273480000, 68527110000, 77098000000, 76447250000, 74946790000, 68106820000, 64802810000, 66174410000, 76647400000, 63628190000, 64958820000, 75871910000, 69725590000, 71885030000, 71595810000, 63623630000, 63283380000, 66524690000, 58131140000, 66706000000, 93714040000, 63600190000, 80743820000, 77330040000, 68775560000, 76675850000, 72060940000, 65187730000, 73213980000, 77920590000, 84626790000, 79989370000, 85844900000, 75943590000, 83649260000, 92409770000, 93049560000, 92639420000, 81124990000, 78883600000, 86852700000, 69530250000, 75610310000, 77023620000, 72915530000, 88445380000, 75344550000, 70576420000, 69260940000, 81664010000, 65369860000, 79719460000, 81078810000, 63348090000, 70784900000, 66624120000, 71088550000, 73416960000, 65531700000, 77318690000, 79933970000, 76803890000, 70194700000, 76011820000, 77891360000, 64898300000, 69523070000, 63031510000, 91930980000, 80620020000, 84162180000, 80859870000, 70638770000, 79159660000, 70090370000, 77250740000, 71250630000, 70599470000, 80269220000, 74178980000, 77720640000, 72410620000, 72325540000, 77287980000, 84436590000, 162185380000, 123608160000, 107135190000, 131458880000, 96928130000, 82466520000, 92310780000, 89938980000, 101247180000, 96375680000, 106117800000, 99082320000, 122371150000, 83124090000, 88321860000, 102544180000, 84255620000, 80500760000, 85528860000, 80253600000, 88268840000, 92750180000, 95562890000, 92667710000, 123546260000, 90367840000, 108860390000, 106116710000, 81688320000, 92252350000, 94241020000, 95823760000, 92671910000, 85249330000, 80763810000, 80392280000, 113094800000, 70861260000, 88929200000, 87983140000, 75063200000, 86840820000, 73482980000)
cor.test(sp_close, sp_vol)
PP.test(sp_vol)
adf.test(sp_vol)
###########################################################################
# Nikkei 225 (JAPAN) #
###########################################################################
nik_vol <- c(2103300000, 1973300000, 1923900000, 2093700000, 1779800000, 1305200000, 1782200000, 1369700000, 1364600000, 1484200000, 1555800000, 1435500000, 1377200000, 1397800000, 1339300000, 1637700000, 1582900000, 1345900000, 1882500000, 1390900000, 1387900000, 1284100000, 1433700000, 1601900000, 1561500000, 1235400000, 1108100000, 1258700000, 1313600000, 1231300000, 1956500000, 1406000000, 1388600000, 1340300000, 1614800000, 1148600000, 1362400000, 1357300000, 1454700000, 1754000000, 1539400000, 1837200000, 3101700000, 1396200000, 1133600000, 1173000000, 1356700000, 1347900000, 1392600000, 1373500000, 1168700000, 1195400000, 1458100000, 1187800000, 1396900000, 1276100000, 1275600000, 1529200000, 1534700000, 1822800000, 1447600000, 1515200000, 1523800000, 1513500000, 1607600000, 1386000000, 1732700000, 1840200000, 1606300000, 1539000000, 1981200000, 1872800000, 1807500000, 1876000000, 1790600000, 2326500000, 2230200000, 2178500000, 2646000000, 2606300000, 2440400000, 3038700000, 3226000000, 2222800000, 2493200000, 2675600000, 2816900000, 3093000000, 2563800000, 3230600000, 3307500000, 4174100000, 3235900000, 2749100000, 2559500000, 2979600000, 3132300000, 3723100000, 3318200000, 3459500000, 3291500000, 3047400000, 3191800000, 2975400000, 2691500000, 2962900000, 3155400000, 3436700000, 2530100000, 2300800000, 2467400000, 2715300000, 2560200000, 2575500000, 3011800000, 3390300000, 3734900000, 3151000000, 3175900000, 3095600000, 2908600000, 3158800000, 4145700000, 4755100000, 7190600000, 6211600000, 4251700000, 5299900000, 4335800000, 3432700000, 2687500000, 2738800000, 2403400000, 2571500000, 2457400000, 2548800000, 2713200000, 2547300000, 3340600000, 3455900000, 2153800000, 2086100000, 2276100000, 2371900000, 2664200000, 3428500000, 2450800000, 2889600000, 2475600000, 2991400000, 4792200000, 3125000000, 2736000000, 2638500000, 2736400000, 2922000000, 2480200000, 2551700000, 2938300000, 2699700000, 3169300000, 3039100000, 2840200000, 2486300000, 3461300000, 3335300000, 2760300000, 3133500000, 2585200000, 2927600000, 3393000000, 3795800000, 3006700000, 3798500000, 3376900000, 2809500000, 2655200000, 2663800000, 2850200000, 4267300000, 2905700000, 2443300000, 2658600000, 2825900000, 2699700000, 2572700000, 2821400000, 2916400000, 3114100000, 2330800000, 3089900000, 2633300000, 2068700000, 3199300000, 2635500000, 2726700000, 2759200000, 2597500000, 3402500000, 3256500000, 2668700000, 2415700000, 2143600000, 2207200000, 2062500000, 2278400000, 2085700000, 2526300000, 2337600000, 2145500000, 2389600000, 2767300000, 2680600000, 3239400000, 3468100000, 3283900000, 3272000000, 2344500000, 1432300000, 1617600000, 1446100000, 1675000000, 2032200000, 1665700000, 1616200000, 1437800000, 1400600000, 1588400000, 1666700000, 1481800000, 1373300000, 1704500000, 1696200000, 2430200000, 2429300000, 1282100000, 1436200000, 1274000000, 1273100000)
nik_close <- c(-0.021, -0.021, -0.01, 0.069, 0.059, 0.023, 0.024, -0.001, 0.055, -0.083, 0.013, 0.066, -0.072, 0.01, 0.048, -0.034, 0.016, -0.029, 0.035, -0.024, -0.078, 0.032, -0.054, -0.012, 0.043, 0.021, -0.057, -0.007, -0.006, -0.022, -0.008, 0.045, 0.003, 0.03, 0.126, -0.009, 0.004, 0.052, -0.029, 0.017, 0.086, 0.075, -0.102, -0.082, -0.005, 0.011, 0.024, 0.048, 0.052, -0.032, -0.002, 0.045, -0.077, 0.034, -0.013, 0.028, 0.054, -0.131, 0.02, -0.103, 0.054, 0.01, 0.014, 0.008, -0.011, 0.046, -0.021, -0.055, 0.001, -0.007, 0.026, 0.073, 0.031, -0.013, -0.007, 0.017, 0.025, 0.011, -0.017, 0.01, -0.014, 0.03, 0.051, 0.049, -0.026, 0.028, 0.053, -0.098, 0.051, -0.003, 0.044, -0.104, -0.074, -0.04, 0.047, 0.084, -0.079, -0.087, 0.014, -0.01, 0.051, 0.02, 0.018, 0.067, 0.02, -0.001, 0.042, 0.015, 0.044, -0.006, 0.028, 0.025, 0.02, -0.04, 0.011, 0.004, -0.083, 0.039, 0.08, -0.013, 0.07, -0.021, -0.006, 0.009, -0.005, 0.107, 0.075, 0.032, 0.048, 0.088, 0.054, 0.013, 0.004, 0.025, -0.047, 0.06, -0.109, -0.067, 0.031, 0.096, 0.029, -0.015, -0.053, 0.047, -0.036, -0.106, -0.005, 0.011, -0.028, 0.009, -0.094, 0.032, -0.011, 0.028, 0.078, -0.026, 0.057, -0.085, 0.025, -0.039, -0.11, -0.011, 0.087, -0.009, -0.04, 0.12, -0.06, -0.004, -0.032, 0.013, 0.045, 0.044, 0.071, 0.074, 0.081, -0.045, -0.125, 0.045, -0.022, -0.329, -0.149, -0.016, -0.01, -0.064, 0.037, 0.095, -0.071, 0.006, -0.115, -0.029, -0.072, -0.002, 0.016, -0.036, -0.052, 0.01, 0.027, 0.003, -0.015, 0.013, 0.004, 0.053, -0.004, 0.014, 0.003, 0.047, -0.008, -0.006, -0.095, -0.013, 0.061, -0.024, 0.021, 0.074, 0.078, 0.003, 0.079, 0.041, 0.027, 0.031, 0.029, -0.053, -0.006, 0.027, -0.006, 0.061, 0.015, -0.011, -0.026, -0.017, -0.054, 0.055, -0.048, 0, 0.051, 0.023, 0, 0.063, -0.059)
cor.test(nik_close, nik_vol)
PP.test(nik_vol)
adf.test(stoxx_vol)
###########################################################################
# STOXX 600 (EUROPE) #
###########################################################################
stoxx_vol <- c(2082064000, 3593140000, 3623085900, 3227490000, 3963845100, 4537933600, 3364175000, 5644136700, 4315542500, 4190288900, 3429359000, 4428634700, 4324893100, 5044459900, 3673166200, 4209030900, 4403288200, 4668497000, 4080039400, 7015693000, 4665939400, 4219964500, 3725329800, 5141114500, 3873973500, 3990773300, 3214970700, 3353233300, 3727672100, 3913126100, 3529714100, 4851670900, 4375370400, 4120573200, 4414589500, 5990354800, 4457050500, 4378642700, 3472143000, 4493206100, 6506693200, 5685330700, 5778662500, 9781539200, 4717665900, 3747876800, 3687903800, 3914857000, 4634906100, 4167228400, 4371274100, 3994185300, 3822333900, 4370401300, 3655958900, 4272524500, 3844484400, 3935024300, 4010016100, 4369953900, 4636643000, 3756703600, 3675091700, 3686458400, 4898417700, 5329248500, 4001420700, 4761109700, 4563697300, 4414670700, 3765308000, 4558362700, 4396511200, 3962271900, 3806938800, 4136701600, 5288574400, 5776592600, 4559447300, 5731696800, 4727016300, 5108929600, 5481488800, 6189735400, 5284539900, 5715861400, 5162109900, 6441906800, 8798906100, 5814206300, 6047662900, 6569684600, 7243086800, 6170797300, 4829569500, 5156214200, 5810022700, 5920225300, 5598217400, 5667279400, 6016609900, 5530892100, 5447295400, 6784088400, 6455256800, 7130308000, 5601864000, 5783571900, 8068259800, 5715514200, 5061411200, 6041303100, 5109740500, 5664157800, 6260120300, 7557556000, 5391112100, 6532452900, 4626036900, 5155068400, 6300416000, 5596521600, 5120640200, 459936200)
stoxx_close <- c(-0.002, -0.018, -0.028, 0.02, 0.021, -0.034, 0.019, -0.006, 0.016, 0.06, -0.039, 0.061, 0.063, -0.069, -0.054, 0.074, -0.089, -0.011, -0.013, 0.006, -0.038, -0.041, 0.049, -0.028, 0.05, -0.037, 0.018, 0.018, 0.012, 0.02, 0.018, 0.05, 0.02, -0.012, 0.023, 0.119, -0.057, -0.017, 0.028, -0.013, 0.024, 0.033, 0.07, -0.183, -0.094, -0.014, 0.02, 0.025, 0.009, 0.034, -0.014, 0.001, 0.042, -0.061, 0.03, 0.015, 0.037, 0.064, -0.065, -0.012, -0.06, 0.003, -0.025, 0.033, -0.009, -0.006, 0.041, -0.021, -0.044, 0.016, 0.006, -0.024, 0.017, 0.035, -0.012, -0.006, -0.027, 0.008, 0.013, 0.025, 0.024, -0.003, 0.053, 0.006, -0.009, -0.004, 0.003, 0.033, -0.052, 0.017, 0.016, 0.011, -0.029, -0.068, -0.056, 0.029, 0.069, -0.035, -0.095, 0.034, -0.052, 0.012, -0.002, 0.014, 0.064, 0.063, -0.009, 0.03, -0.018, 0.002, 0.018, -0.019, -0.008, 0.019, 0.009, -0.005, 0.047, -0.02, 0.008, 0.008, 0.036, 0.037, -0.01, 0.043)
cor.test(stoxx_close, stoxx_vol)
PP.test(stoxx_vol)
adf.test(stoxx_vol)
###########################################################################
# Visual Creation Output #
###########################################################################
# S&P 500 (USA) #
my_data <- data.frame(sp_close, sp_vol)
ggscatter(my_data, x = "sp_vol", y = "sp_close",
add = "reg.line", conf.int = TRUE,
cor.coef = TRUE, cor.method = "pearson",
xlab = "S&P 500 Monthly Volume", ylab = "S&P 500 Monthly Close")
# Nikkei 225 (JAPAN) #
my_data <- data.frame(nik_close, nik_vol)
ggscatter(my_data, x = "nik_vol", y = "nik_close",
add = "reg.line", conf.int = TRUE,
cor.coef = TRUE, cor.method = "pearson",
xlab = "Nikkei 225 Monthly Volume", ylab = "Nikkei 225 Monthly Close")
# STOXX 600 (EUROPE) #
my_data <- data.frame(stoxx_close, stoxx_vol)
ggscatter(my_data, x = "stoxx_vol", y = "stoxx_close",
add = "reg.line", conf.int = TRUE,
cor.coef = TRUE, cor.method = "pearson",
xlab = "STOXX 600 Monthly Volume", ylab = "STOXX 600 Monthly Close")
###########################################################################
Initial Findings
There was a negative correlation between the two variables: S&P 500 Monthly Close (n = 239) and S&P 500 Monthly Volume (n = 239). S&P 500 Monthly Close (M = .006, SD = .043), S&P 500 Monthly Volume (M = 77899674812, SD = 24642426931), Conditions; t(237) = -2.1245, p = .03. Pearson Product-Moment Correlation Coefficient: r = -.14.
There was a negative correlation between the two variables: Nikkei 225 Monthly Close (n = 239) and Nikkei 225 Monthly Volume (n = 239). Nikkei 225 Monthly Close (M = .003, SD = .055), Nikkei 225 Monthly Volume (M = 2400008787, SD = 912823479), Conditions; t(237) = -0.48111, p = .63. Pearson Product-Moment Correlation Coefficient: r = -.03.
There was a negative correlation between the two variables: STOXX 600 Monthly Close (n = 124)* and STOXX 600 Monthly Volume (n = 124). STOXX 600 Monthly Close (M = .002, SD = .041), STOXX 600 Monthly Volume (M = 4885890780, SD = 1260418703), Conditions; t(122) = -2.0375, p = .04. Pearson Product-Moment Correlation Coefficient: r = -.18.
* - Only limited historical data was available for the STOXX 600 index.
Initial Conclusions
The results of this analysis indicates that there is a correlative relationship as it pertains to volume and closing price; at least, as it pertains to the S&P 500 and the STOXX 600. These indexes are of American, and European origin, respectively. However, this phenomenon was not evident in the results of the analysis as it pertains to the Nikkei 225, a Japanese stock market index. There is an old adage in the field of economics, which is typically some variation of: treat the Japanese economy as a singular non-universalized phenomenon, in which, observations related to such cannot be applied to other instances within the field as whole. This truism seems to hold merit as it relates to these findings.
Interestingly, each analytical outcome demonstrates a weak modeling potential. The Pearson Product-Moment Correlation Coefficient as it pertains to each index is negative, with the Japanese Nikkei 225 possessing the lowest coefficient figure: - .03.
This would seemingly indicate the inverse conclusion inferred by, “The Winner’s Curse”.
Initial Conclusions
The results of this analysis indicates that there is a correlative relationship as it pertains to volume and closing price; at least, as it pertains to the S&P 500 and the STOXX 600. These indexes are of American, and European origin, respectively. However, this phenomenon was not evident in the results of the analysis as it pertains to the Nikkei 225, a Japanese stock market index. There is an old adage in the field of economics, which is typically some variation of: treat the Japanese economy as a singular non-universalized phenomenon, in which, observations related to such cannot be applied to other instances within the field as whole. This truism seems to hold merit as it relates to these findings.
Interestingly, each analytical outcome demonstrates a weak modeling potential. The Pearson Product-Moment Correlation Coefficient as it pertains to each index is negative, with the Japanese Nikkei 225 possessing the lowest coefficient figure: - .03.
This would seemingly indicate the inverse conclusion inferred by, “The Winner’s Curse”.
As is observed within the above graphics, the volume which exists within each market, appears to drive down market pricing. Even if the effect is marginal and inconsistent, it exists nevertheless.
Though this really ought to fly in the face of fundamental economic theory, we must ask ourselves, does it really? According to Say’s Law, supply creates its own demand. Therefore, would it stand to reason that the inverse ought to be true? Does demand create its own supply?
Additional Research
With this in mind, I decided to perform some additional analysis in order to either support or disprove the initial findings.
Utilizing my favorite outlier function, I searched for potential outlier values within the volume variables for each individual index.
OutlierFunction <- function(t){
q1 <- fivenum(t)
q1 <- q1[2] #Q1
q3 <- fivenum(t)
q3 <- q3[4] #Q3
iqrange <- q3 - q1
out1 <<- (q1 - (iqrange * 1.5))
out2 <<- (q3 + (iqrange * 1.5))
lowout <<- subset(t, t < out1, na.rm = TRUE)
highout <<- subset(t, t > out2, na.rm = TRUE)
}
OutlierFunction()
This turned up the following values as it pertains to each index.
S&P 500 – 124980570000, 140007320000, 159823030000, 124492210000, 161843640000, 138855320000, 131614940000, 127662780000, 162185380000, 131458880000, 24463220000, 27839130000, 27985600000, 29326400000, 27529500000, 29285600000, 26586800000, 26829870000, 30460280000, 31102500000, 29297410000
Nikkei 225 – 7190600000, 6211600000, 5299900000
STOXX 600 – 9781539200, 8798906100, 459936200
I then matched these volume values to their corresponding closing figures.
S&P 500
Nikkei 225
STOXX 600
Next, I ran additional analysis on the data vectors with outlier values removed.
###########################################################################
# S&P 500 (USA) OUTLIERS! #
###########################################################################
sp_close <- c(0.166, 0.038, 0.034, 0.013, 0.031, -0.075, -0.018, 0.037, 0.016, -0.004, 0.037, -0.085, -0.052, 0, -0.057, 0.061, 0.072, -0.013, -0.088, 0.058, -0.072, 0.019, 0.099, 0.021, -0.061, 0.108, 0.053, -0.085, 0.03, 0.073, -0.055, 0.068, -0.089, 0.024, -0.006, -0.002, 0.035, 0.046, -0.032, 0.063, -0.048, -0.041, -0.038, 0.023, -0.073, 0.013, -0.038, -0.09, -0.034, 0.035, 0.015, -0.002, 0.003, 0.033, 0.003, -0.009, 0.064, -0.004, -0.063, 0.002, -0.016, 0.011, -0.042, -0.018, 0.045, 0.083, -0.053, -0.049, -0.061, 0.057, -0.063, 0.028, -0.087, -0.003, 0.022, -0.102, 0.031, -0.019, 0.047, 0.064, -0.015, 0.092, -0.007, 0.04, 0.004, -0.021, 0.003, 0.01, 0.06, 0.092, 0.058, -0.003, 0.016, 0.026, -0.025, -0.018, 0.067, -0.025, -0.036, 0.01, 0.087, 0.043, 0.013, 0.014, -0.035, 0.041, 0.018, 0, 0.018, 0.026, -0.031, 0.052, -0.006, -0.068, 0.018, -0.001, -0.027, -0.018, 0.044, 0.021, 0.014, 0.024, 0, -0.034, 0.05, -0.001, 0.018, 0.031, -0.016, -0.007, 0.009, 0.023, -0.054, 0.025, -0.022, 0.012, -0.018, 0.03, 0.028, 0.009, 0.008, -0.02, 0.005, 0.003, 0.069, 0.021, 0.016, -0.002, 0.03, 0.003, 0.012, -0.033, 0.02, 0.006, 0.034, 0.024, 0.043, 0.035, 0.028, 0.011, 0.034, 0.054, 0.036, 0.047, 0.01, -0.016, 0.018, -0.016, 0.007, 0.028, 0.011, 0.009, -0.018, 0.01, 0.023, 0.033, 0.041, -0.008, -0.033, 0.027, 0.021, 0.024, 0.016, 0.019, 0.006, 0.03, 0.038, 0.036, 0.043, 0.032, 0.014, 0.017, 0, -0.031, -0.022, 0.011, 0.02, -0.018, 0.025, 0.025, 0.013, 0.005, 0.035, 0.007, -0.02, 0.006, 0, -0.011, -0.001, 0, 0.03, -0.019, 0.036, -0.016, 0.017, -0.017, 0.014, -0.025)
sp_vol <- c(123608160000, 123546260000, 122371150000, 116741910000, 116059270000, 115660210000, 113410990000, 113094800000, 112884470000, 112653150000, 112295490000, 112090640000, 110106750000, 108860390000, 108419170000, 107135190000, 106635790000, 106117800000, 106116710000, 103683550000, 102786820000, 102544180000, 101247180000, 99082320000, 98475340000, 98063670000, 96928130000, 96614040000, 96375680000, 95823760000, 95562890000, 94778110000, 94241020000, 93714040000, 93189170000, 93049560000, 92750180000, 92671910000, 92667710000, 92639420000, 92409770000, 92310780000, 92252350000, 92164940000, 91930980000, 91381760000, 90947580000, 90367840000, 89938980000, 89536270000, 89515330000, 89507640000, 88929200000, 88445380000, 88321860000, 88268840000, 87983140000, 87151070000, 86920490000, 86852700000, 86840820000, 86266010000, 86246950000, 86122730000, 85978630000, 85844900000, 85738250000, 85528860000, 85249330000, 84981530000, 84626790000, 84561340000, 84436590000, 84275050000, 84255620000, 84162180000, 83899660000, 83649260000, 83124090000, 82466520000, 81708980000, 81688320000, 81664010000, 81582440000, 81124990000, 81102170000, 81078810000, 80990480000, 80984530000, 80859870000, 80763810000, 80743820000, 80620020000, 80500760000, 80392280000, 80269220000, 80253600000, 79989370000, 79933970000, 79719460000, 79589450000, 79567560000, 79159660000, 78883600000, 78536130000, 78385710000, 77920590000, 77891360000, 77720640000, 77364810000, 77330040000, 77318690000, 77287980000, 77250740000, 77098000000, 77023620000, 76803890000, 76675850000, 76647400000, 76447250000, 76022580000, 76011820000, 75943590000, 75871910000, 75848510000, 75610310000, 75344550000, 75063200000, 74946790000, 74761710000, 74742430000, 74178980000, 73482980000, 73416960000, 73213980000, 73103810000, 72915530000, 72410620000, 72325540000, 72060940000, 71885030000, 71752320000, 71595810000, 71489310000, 71250630000, 71088550000, 70861260000, 70784900000, 70638770000, 70599470000, 70576420000, 70337430000, 70283810000, 70194700000, 70090370000, 69784280000, 69725590000, 69530250000, 69523070000, 69273480000, 69260940000, 68775560000, 68527110000, 68106820000, 67622250000, 66706000000, 66624120000, 66524690000, 66388180000, 66174410000, 65531700000, 65369860000, 65322800000, 65187730000, 64958820000, 64958050000, 64898300000, 64821670000, 64802810000, 63628190000, 63623630000, 63600190000, 63348090000, 63283380000, 63031510000, 59223660000, 58131140000, 57809700000, 57032470000, 56793620000, 56686200000, 55343930000, 54873260000, 54312830000, 51844990000, 50905040000, 50485620000, 49793790000, 49211650000, 49001440000, 47578780000, 46348220000, 45102870000, 44777510000, 43424270000, 43308430000, 42859940000, 42030090000, 41756130000, 40334040000, 39321990000, 39014150000, 37464670000, 33597900000, 32820000000, 31611900000, 31511000000, 31498800000)
cor.test(sp_close, sp_vol)
###########################################################################
# Nikkei 225 (JAPAN) OUTLIERS! #
###########################################################################
nik_vol <- c(-0.094, 0.009, 0.048, -0.329, 0.075, -0.104, -0.006, 0.074, 0.044, -0.083, -0.087, 0.078, -0.04, -0.01, 0.096, 0.015, 0.088, -0.106, -0.015, 0.045, 0.004, 0.081, 0.031, 0.12, 0.014, 0.044, 0.051, 0.003, 0.079, 0.013, 0.074, -0.074, -0.003, 0.051, -0.036, 0.018, 0.08, -0.11, -0.021, 0.042, 0.039, -0.004, -0.079, 0.032, -0.115, -0.102, -0.013, -0.098, -0.072, 0.02, -0.011, 0.03, 0.011, 0.071, 0.009, 0.084, 0.067, -0.001, 0.025, 0.013, -0.026, 0.006, 0.07, -0.149, 0.011, -0.022, 0.087, -0.064, -0.071, 0.053, -0.045, -0.024, -0.06, 0.027, -0.04, 0.013, 0.078, -0.011, 0.01, 0.025, -0.109, -0.039, 0.037, 0.02, 0.054, 0.021, 0.028, 0.004, -0.036, 0.045, -0.01, -0.125, -0.017, 0.028, -0.052, -0.002, 0.01, 0.003, -0.032, -0.04, 0.095, 0.025, 0.051, 0.02, 0.047, -0.085, 0.06, -0.067, 0.044, -0.006, -0.026, -0.009, 0.057, -0.028, 0.028, -0.047, -0.005, -0.016, -0.014, 0, 0.051, 0.053, 0.004, 0.061, 0.047, 0.041, -0.095, -0.029, 0.017, -0.006, 0.047, -0.053, 0.025, 0.049, 0.014, 0.011, 0.029, -0.013, -0.004, -0.021, 0.069, -0.015, -0.008, 0.016, 0.003, -0.006, 0.026, -0.021, -0.008, -0.01, 0.035, -0.013, 0.073, -0.055, 0.075, -0.103, 0.031, -0.007, 0.024, 0.059, 0.017, -0.021, 0.055, -0.048, -0.053, -0.026, 0.027, -0.034, 0.031, -0.006, 0.126, -0.011, 0.001, -0.012, -0.011, 0.016, 0.043, 0.013, 0.086, -0.007, 0.02, -0.131, 0.014, 0.01, 0.008, -0.083, -0.017, -0.077, -0.029, 0.054, 0.029, 0.061, 0, 0.066, -0.054, 0.027, 0.045, 0.015, 0.01, -0.013, -0.082, 0.052, -0.024, 0.003, -0.078, 0.046, -0.072, -0.032, -0.054, -0.001, 0.055, 0.004, 0.052, 0.024, 0.048, -0.029, 0.03, 0.048, -0.006, 0.023, 0.032, 0.023, 0.028, 0.054, 0.063, -0.059, -0.007, 0.021, -0.022, 0.045, 0.034, 0.011, -0.002, -0.009, -0.005, -0.057)
nik_close <- c(4792200000, 4755100000, 4335800000, 4267300000, 4251700000, 4174100000, 4145700000, 3798500000, 3795800000, 3734900000, 3723100000, 3468100000, 3461300000, 3459500000, 3455900000, 3436700000, 3432700000, 3428500000, 3402500000, 3393000000, 3390300000, 3376900000, 3340600000, 3335300000, 3318200000, 3307500000, 3291500000, 3283900000, 3272000000, 3256500000, 3239400000, 3235900000, 3230600000, 3226000000, 3199300000, 3191800000, 3175900000, 3169300000, 3158800000, 3155400000, 3151000000, 3133500000, 3132300000, 3125000000, 3114100000, 3101700000, 3095600000, 3093000000, 3089900000, 3047400000, 3039100000, 3038700000, 3011800000, 3006700000, 2991400000, 2979600000, 2975400000, 2962900000, 2938300000, 2927600000, 2922000000, 2916400000, 2908600000, 2905700000, 2889600000, 2850200000, 2840200000, 2825900000, 2821400000, 2816900000, 2809500000, 2767300000, 2760300000, 2759200000, 2749100000, 2738800000, 2736400000, 2736000000, 2726700000, 2715300000, 2713200000, 2699700000, 2699700000, 2691500000, 2687500000, 2680600000, 2675600000, 2668700000, 2664200000, 2663800000, 2658600000, 2655200000, 2646000000, 2638500000, 2635500000, 2633300000, 2606300000, 2597500000, 2585200000, 2575500000, 2572700000, 2571500000, 2563800000, 2560200000, 2559500000, 2551700000, 2548800000, 2547300000, 2530100000, 2526300000, 2493200000, 2486300000, 2480200000, 2475600000, 2467400000, 2457400000, 2450800000, 2443300000, 2440400000, 2430200000, 2429300000, 2415700000, 2403400000, 2389600000, 2371900000, 2344500000, 2337600000, 2330800000, 2326500000, 2300800000, 2278400000, 2276100000, 2230200000, 2222800000, 2207200000, 2178500000, 2153800000, 2145500000, 2143600000, 2103300000, 2093700000, 2086100000, 2085700000, 2068700000, 2062500000, 2032200000, 1981200000, 1973300000, 1956500000, 1923900000, 1882500000, 1876000000, 1872800000, 1840200000, 1837200000, 1822800000, 1807500000, 1790600000, 1782200000, 1779800000, 1754000000, 1732700000, 1704500000, 1696200000, 1675000000, 1666700000, 1665700000, 1637700000, 1617600000, 1616200000, 1614800000, 1607600000, 1606300000, 1601900000, 1588400000, 1582900000, 1561500000, 1555800000, 1539400000, 1539000000, 1534700000, 1529200000, 1523800000, 1515200000, 1513500000, 1484200000, 1481800000, 1458100000, 1454700000, 1447600000, 1446100000, 1437800000, 1436200000, 1435500000, 1433700000, 1432300000, 1406000000, 1400600000, 1397800000, 1396900000, 1396200000, 1392600000, 1390900000, 1388600000, 1387900000, 1386000000, 1377200000, 1373500000, 1373300000, 1369700000, 1364600000, 1362400000, 1357300000, 1356700000, 1347900000, 1345900000, 1340300000, 1339300000, 1313600000, 1305200000, 1284100000, 1282100000, 1276100000, 1275600000, 1274000000, 1273100000, 1258700000, 1235400000, 1231300000, 1195400000, 1187800000, 1173000000, 1168700000, 1148600000, 1133600000, 1108100000)
cor.test(nik_close, nik_vol)
###########################################################################
# STOXX 600 (EUROPE) OUTLIERS #
###########################################################################
stoxx_vol <- c(8068259800, 7557556000, 7243086800, 7130308000, 7015693000, 6784088400, 6569684600, 6532452900, 6506693200, 6455256800, 6441906800, 6300416000, 6260120300, 6189735400, 6170797300, 6047662900, 6041303100, 6016609900, 5990354800, 5920225300, 5814206300, 5810022700, 5783571900, 5778662500, 5776592600, 5731696800, 5715861400, 5715514200, 5685330700, 5667279400, 5664157800, 5644136700, 5601864000, 5598217400, 5596521600, 5530892100, 5481488800, 5447295400, 5391112100, 5329248500, 5288574400, 5284539900, 5162109900, 5156214200, 5155068400, 5141114500, 5120640200, 5109740500, 5108929600, 5061411200, 5044459900, 4898417700, 4851670900, 4829569500, 4761109700, 4727016300, 4717665900, 4668497000, 4665939400, 4636643000, 4634906100, 4626036900, 4563697300, 4559447300, 4558362700, 4537933600, 4493206100, 4457050500, 4428634700, 4414670700, 4414589500, 4403288200, 4396511200, 4378642700, 4375370400, 4371274100, 4370401300, 4369953900, 4324893100, 4315542500, 4272524500, 4219964500, 4209030900, 4190288900, 4167228400, 4136701600, 4120573200, 4080039400, 4010016100, 4001420700, 3994185300, 3990773300, 3963845100, 3962271900, 3935024300, 3914857000, 3913126100, 3873973500, 3844484400, 3822333900, 3806938800, 3765308000, 3756703600, 3747876800, 3727672100, 3725329800, 3687903800, 3686458400, 3675091700, 3673166200, 3655958900, 3623085900, 3593140000, 3529714100, 3472143000, 3429359000, 3364175000, 3353233300, 3227490000, 3214970700)
stoxx_close <- c(-0.018, -0.005, -0.029, 0.063, 0.006, 0.014, 0.011, -0.02, 0.024, 0.064, 0.033, 0.036, 0.009, 0.006, -0.068, 0.016, -0.019, -0.052, 0.119, -0.035, 0.017, 0.069, 0.03, 0.07, 0.008, 0.025, -0.004, 0.002, 0.033, 0.034, 0.019, -0.006, -0.009, -0.095, 0.037, 0.012, 0.053, -0.002, 0.047, -0.006, -0.027, -0.009, 0.003, 0.029, 0.008, -0.028, -0.01, -0.008, -0.003, 0.018, -0.069, -0.009, 0.05, -0.056, -0.021, 0.024, -0.094, -0.011, -0.038, -0.06, 0.009, 0.008, -0.044, 0.013, -0.024, -0.034, -0.013, -0.057, 0.061, 0.016, 0.023, -0.089, 0.017, -0.017, 0.02, -0.014, -0.061, -0.012, 0.063, 0.016, 0.015, -0.041, 0.074, 0.06, 0.034, -0.006, -0.012, -0.013, -0.065, 0.041, 0.001, -0.037, 0.021, 0.035, 0.064, 0.025, 0.02, 0.05, 0.037, 0.042, -0.012, 0.006, 0.003, -0.014, 0.012, 0.049, 0.02, 0.033, -0.025, -0.054, 0.03, -0.028, -0.018, 0.018, 0.028, -0.039, 0.019, 0.018, 0.02, 0.018)
cor.test(stoxx_close, stoxx_vol)
###########################################################################
Additional Findings
There was a negative correlation between the two variables: S&P 500 Monthly Close (n = 218) and S&P 500 Monthly Volume (n = 218). S&P 500 Monthly Close (M = .007, SD = .039), S&P 500 Monthly Volume (M = 77543082110, SD = 18749895626), Conditions; t(216) = -0.34354, p = .73. Pearson Product-Moment Correlation Coefficient: r = -.02.
There was a negative correlation between the two variables: Nikkei 225 Monthly Close (n = 236) and Nikkei 225 Monthly Volume (n = 236). Nikkei 225 Monthly Close (M = .002, SD = .055), Nikkei 225 Monthly Volume (M = 2351271186, SD = 803886229), Conditions; t(234) = -1.2234, p = .22. Pearson Product-Moment Correlation Coefficient: r = -.08.
There was a positive correlation between the two variables: STOXX 600 Monthly Close (n = 120) and STOXX 600 Monthly Volume (n = 120). STOXX 600 Monthly Close (M = .004, SD = .038), STOXX 600 Monthly Volume (M = 4872733427, SD = 1039773116), Conditions; t(118) = 0.31681, p = .75. Pearson Product-Moment Correlation Coefficient: r = .03.
Additional Conclusions
When outliers are removed and the analysis is performed, there is a slight shift in the correlation coefficient values amongst the various indices. S&P 500 (-.14; -.02), Nikkei 225 (-.03; -.08), STOXX 600 (-.18; .03). There also was a shift in correlation significance. S&P 500 (.03; .73), Nikkei 225 (.63; .22), STOXX 600 (.04; .75).
With the removal of outliers, every index had a decline in correlation significance (p), with the exception being the Nikkei 225. Oddly, as it pertains to correlation coefficient values, the S&P 500 rose and remained negative, the Nikkei 225 declined and remained negative, while the STOXX 600 value became positive.
In almost instance, increases in volume equates for decreases in price. It would seem that the most massive volume increases are the largest contributors to price decline. Seemily, disproportionately so, the Nikkei 500 continues to be an odd duck, in that, it seems to be in a perpetual state of stasis, with smaller upward shifts of volume being more impactful on price than comparatively larger shifts.
Tests for Randomness / Stationarity
Phillips-Perron Unit Root Test
data: sp_vol
Dickey-Fuller = -4.7548, Truncation lag parameter = 4, p-value = 0.01
Phillips-Perron Unit Root Test
data: nik_vol
Dickey-Fuller = -4.2136, Truncation lag parameter = 4, p-value = 0.01
Phillips-Perron Unit Root Test
data: stoxx_vol
Dickey-Fuller = -6.906, Truncation lag parameter = 4, p-value = 0.01
Augmented Dickey-Fuller Test
data: sp_vol
Dickey-Fuller = -2.2459, Lag order = 6, p-value = 0.4725
alternative hypothesis: stationary
Augmented Dickey-Fuller Test
data: nik_vol
Dickey-Fuller = -2.3522, Lag order = 6, p-value = 0.4277
alternative hypothesis: stationary
Augmented Dickey-Fuller Test
data: stoxx_vol
Dickey-Fuller = -2.6845, Lag order = 4, p-value = 0.2921
alternative hypothesis: stationary
Final Thoughts and Conclusions
In every instance, the volume measurements for each index were non-stationary, and non-random. Thus, I suppose that it should be expected, that volume figures should typically increase over time. As was demonstrated by the correlation analysis both as it relates to index/volume assessments (with and without outliers), large unanticipated upward shifts in volume, typically should be expected to cause price decline.
Thus, it might be said, that demand creates its own supply. Or at the very least, impacts supply price in a deflationary manner. Or perhaps some combination of the two.
As it relates to volume’s long term impact on pricing, it would seem that the stationary / random walk analysis that was performed for a prior article, holds true. In that, like a tiny pill bug walking haphazardly across graphing paper, a small push by a human hand here and there may alter the insect’s course, but will otherwise not prove to be impactful, other than demonstrating some significance in the present moment.
In a similar manner, as with a stretched slinky, outside gyrations obviously cause disruption, but only temporarily. Once the interference ceases, the stationarity is maintained.
Markets outside of the United States continue to remain mysterious in comparison to their state side counterparts while comparing growth patterns. Perhaps the limbic bounces of a market’s price have much to do with the culture of an economy. Though, the bounces themselves do remain very much human in origin, regardless.
Though this really ought to fly in the face of fundamental economic theory, we must ask ourselves, does it really? According to Say’s Law, supply creates its own demand. Therefore, would it stand to reason that the inverse ought to be true? Does demand create its own supply?
Additional Research
With this in mind, I decided to perform some additional analysis in order to either support or disprove the initial findings.
Utilizing my favorite outlier function, I searched for potential outlier values within the volume variables for each individual index.
OutlierFunction <- function(t){
q1 <- fivenum(t)
q1 <- q1[2] #Q1
q3 <- fivenum(t)
q3 <- q3[4] #Q3
iqrange <- q3 - q1
out1 <<- (q1 - (iqrange * 1.5))
out2 <<- (q3 + (iqrange * 1.5))
lowout <<- subset(t, t < out1, na.rm = TRUE)
highout <<- subset(t, t > out2, na.rm = TRUE)
}
OutlierFunction()
This turned up the following values as it pertains to each index.
S&P 500 – 124980570000, 140007320000, 159823030000, 124492210000, 161843640000, 138855320000, 131614940000, 127662780000, 162185380000, 131458880000, 24463220000, 27839130000, 27985600000, 29326400000, 27529500000, 29285600000, 26586800000, 26829870000, 30460280000, 31102500000, 29297410000
Nikkei 225 – 7190600000, 6211600000, 5299900000
STOXX 600 – 9781539200, 8798906100, 459936200
I then matched these volume values to their corresponding closing figures.
S&P 500
Nikkei 225
STOXX 600
Next, I ran additional analysis on the data vectors with outlier values removed.
###########################################################################
# S&P 500 (USA) OUTLIERS! #
###########################################################################
sp_close <- c(0.166, 0.038, 0.034, 0.013, 0.031, -0.075, -0.018, 0.037, 0.016, -0.004, 0.037, -0.085, -0.052, 0, -0.057, 0.061, 0.072, -0.013, -0.088, 0.058, -0.072, 0.019, 0.099, 0.021, -0.061, 0.108, 0.053, -0.085, 0.03, 0.073, -0.055, 0.068, -0.089, 0.024, -0.006, -0.002, 0.035, 0.046, -0.032, 0.063, -0.048, -0.041, -0.038, 0.023, -0.073, 0.013, -0.038, -0.09, -0.034, 0.035, 0.015, -0.002, 0.003, 0.033, 0.003, -0.009, 0.064, -0.004, -0.063, 0.002, -0.016, 0.011, -0.042, -0.018, 0.045, 0.083, -0.053, -0.049, -0.061, 0.057, -0.063, 0.028, -0.087, -0.003, 0.022, -0.102, 0.031, -0.019, 0.047, 0.064, -0.015, 0.092, -0.007, 0.04, 0.004, -0.021, 0.003, 0.01, 0.06, 0.092, 0.058, -0.003, 0.016, 0.026, -0.025, -0.018, 0.067, -0.025, -0.036, 0.01, 0.087, 0.043, 0.013, 0.014, -0.035, 0.041, 0.018, 0, 0.018, 0.026, -0.031, 0.052, -0.006, -0.068, 0.018, -0.001, -0.027, -0.018, 0.044, 0.021, 0.014, 0.024, 0, -0.034, 0.05, -0.001, 0.018, 0.031, -0.016, -0.007, 0.009, 0.023, -0.054, 0.025, -0.022, 0.012, -0.018, 0.03, 0.028, 0.009, 0.008, -0.02, 0.005, 0.003, 0.069, 0.021, 0.016, -0.002, 0.03, 0.003, 0.012, -0.033, 0.02, 0.006, 0.034, 0.024, 0.043, 0.035, 0.028, 0.011, 0.034, 0.054, 0.036, 0.047, 0.01, -0.016, 0.018, -0.016, 0.007, 0.028, 0.011, 0.009, -0.018, 0.01, 0.023, 0.033, 0.041, -0.008, -0.033, 0.027, 0.021, 0.024, 0.016, 0.019, 0.006, 0.03, 0.038, 0.036, 0.043, 0.032, 0.014, 0.017, 0, -0.031, -0.022, 0.011, 0.02, -0.018, 0.025, 0.025, 0.013, 0.005, 0.035, 0.007, -0.02, 0.006, 0, -0.011, -0.001, 0, 0.03, -0.019, 0.036, -0.016, 0.017, -0.017, 0.014, -0.025)
sp_vol <- c(123608160000, 123546260000, 122371150000, 116741910000, 116059270000, 115660210000, 113410990000, 113094800000, 112884470000, 112653150000, 112295490000, 112090640000, 110106750000, 108860390000, 108419170000, 107135190000, 106635790000, 106117800000, 106116710000, 103683550000, 102786820000, 102544180000, 101247180000, 99082320000, 98475340000, 98063670000, 96928130000, 96614040000, 96375680000, 95823760000, 95562890000, 94778110000, 94241020000, 93714040000, 93189170000, 93049560000, 92750180000, 92671910000, 92667710000, 92639420000, 92409770000, 92310780000, 92252350000, 92164940000, 91930980000, 91381760000, 90947580000, 90367840000, 89938980000, 89536270000, 89515330000, 89507640000, 88929200000, 88445380000, 88321860000, 88268840000, 87983140000, 87151070000, 86920490000, 86852700000, 86840820000, 86266010000, 86246950000, 86122730000, 85978630000, 85844900000, 85738250000, 85528860000, 85249330000, 84981530000, 84626790000, 84561340000, 84436590000, 84275050000, 84255620000, 84162180000, 83899660000, 83649260000, 83124090000, 82466520000, 81708980000, 81688320000, 81664010000, 81582440000, 81124990000, 81102170000, 81078810000, 80990480000, 80984530000, 80859870000, 80763810000, 80743820000, 80620020000, 80500760000, 80392280000, 80269220000, 80253600000, 79989370000, 79933970000, 79719460000, 79589450000, 79567560000, 79159660000, 78883600000, 78536130000, 78385710000, 77920590000, 77891360000, 77720640000, 77364810000, 77330040000, 77318690000, 77287980000, 77250740000, 77098000000, 77023620000, 76803890000, 76675850000, 76647400000, 76447250000, 76022580000, 76011820000, 75943590000, 75871910000, 75848510000, 75610310000, 75344550000, 75063200000, 74946790000, 74761710000, 74742430000, 74178980000, 73482980000, 73416960000, 73213980000, 73103810000, 72915530000, 72410620000, 72325540000, 72060940000, 71885030000, 71752320000, 71595810000, 71489310000, 71250630000, 71088550000, 70861260000, 70784900000, 70638770000, 70599470000, 70576420000, 70337430000, 70283810000, 70194700000, 70090370000, 69784280000, 69725590000, 69530250000, 69523070000, 69273480000, 69260940000, 68775560000, 68527110000, 68106820000, 67622250000, 66706000000, 66624120000, 66524690000, 66388180000, 66174410000, 65531700000, 65369860000, 65322800000, 65187730000, 64958820000, 64958050000, 64898300000, 64821670000, 64802810000, 63628190000, 63623630000, 63600190000, 63348090000, 63283380000, 63031510000, 59223660000, 58131140000, 57809700000, 57032470000, 56793620000, 56686200000, 55343930000, 54873260000, 54312830000, 51844990000, 50905040000, 50485620000, 49793790000, 49211650000, 49001440000, 47578780000, 46348220000, 45102870000, 44777510000, 43424270000, 43308430000, 42859940000, 42030090000, 41756130000, 40334040000, 39321990000, 39014150000, 37464670000, 33597900000, 32820000000, 31611900000, 31511000000, 31498800000)
cor.test(sp_close, sp_vol)
###########################################################################
# Nikkei 225 (JAPAN) OUTLIERS! #
###########################################################################
nik_vol <- c(-0.094, 0.009, 0.048, -0.329, 0.075, -0.104, -0.006, 0.074, 0.044, -0.083, -0.087, 0.078, -0.04, -0.01, 0.096, 0.015, 0.088, -0.106, -0.015, 0.045, 0.004, 0.081, 0.031, 0.12, 0.014, 0.044, 0.051, 0.003, 0.079, 0.013, 0.074, -0.074, -0.003, 0.051, -0.036, 0.018, 0.08, -0.11, -0.021, 0.042, 0.039, -0.004, -0.079, 0.032, -0.115, -0.102, -0.013, -0.098, -0.072, 0.02, -0.011, 0.03, 0.011, 0.071, 0.009, 0.084, 0.067, -0.001, 0.025, 0.013, -0.026, 0.006, 0.07, -0.149, 0.011, -0.022, 0.087, -0.064, -0.071, 0.053, -0.045, -0.024, -0.06, 0.027, -0.04, 0.013, 0.078, -0.011, 0.01, 0.025, -0.109, -0.039, 0.037, 0.02, 0.054, 0.021, 0.028, 0.004, -0.036, 0.045, -0.01, -0.125, -0.017, 0.028, -0.052, -0.002, 0.01, 0.003, -0.032, -0.04, 0.095, 0.025, 0.051, 0.02, 0.047, -0.085, 0.06, -0.067, 0.044, -0.006, -0.026, -0.009, 0.057, -0.028, 0.028, -0.047, -0.005, -0.016, -0.014, 0, 0.051, 0.053, 0.004, 0.061, 0.047, 0.041, -0.095, -0.029, 0.017, -0.006, 0.047, -0.053, 0.025, 0.049, 0.014, 0.011, 0.029, -0.013, -0.004, -0.021, 0.069, -0.015, -0.008, 0.016, 0.003, -0.006, 0.026, -0.021, -0.008, -0.01, 0.035, -0.013, 0.073, -0.055, 0.075, -0.103, 0.031, -0.007, 0.024, 0.059, 0.017, -0.021, 0.055, -0.048, -0.053, -0.026, 0.027, -0.034, 0.031, -0.006, 0.126, -0.011, 0.001, -0.012, -0.011, 0.016, 0.043, 0.013, 0.086, -0.007, 0.02, -0.131, 0.014, 0.01, 0.008, -0.083, -0.017, -0.077, -0.029, 0.054, 0.029, 0.061, 0, 0.066, -0.054, 0.027, 0.045, 0.015, 0.01, -0.013, -0.082, 0.052, -0.024, 0.003, -0.078, 0.046, -0.072, -0.032, -0.054, -0.001, 0.055, 0.004, 0.052, 0.024, 0.048, -0.029, 0.03, 0.048, -0.006, 0.023, 0.032, 0.023, 0.028, 0.054, 0.063, -0.059, -0.007, 0.021, -0.022, 0.045, 0.034, 0.011, -0.002, -0.009, -0.005, -0.057)
nik_close <- c(4792200000, 4755100000, 4335800000, 4267300000, 4251700000, 4174100000, 4145700000, 3798500000, 3795800000, 3734900000, 3723100000, 3468100000, 3461300000, 3459500000, 3455900000, 3436700000, 3432700000, 3428500000, 3402500000, 3393000000, 3390300000, 3376900000, 3340600000, 3335300000, 3318200000, 3307500000, 3291500000, 3283900000, 3272000000, 3256500000, 3239400000, 3235900000, 3230600000, 3226000000, 3199300000, 3191800000, 3175900000, 3169300000, 3158800000, 3155400000, 3151000000, 3133500000, 3132300000, 3125000000, 3114100000, 3101700000, 3095600000, 3093000000, 3089900000, 3047400000, 3039100000, 3038700000, 3011800000, 3006700000, 2991400000, 2979600000, 2975400000, 2962900000, 2938300000, 2927600000, 2922000000, 2916400000, 2908600000, 2905700000, 2889600000, 2850200000, 2840200000, 2825900000, 2821400000, 2816900000, 2809500000, 2767300000, 2760300000, 2759200000, 2749100000, 2738800000, 2736400000, 2736000000, 2726700000, 2715300000, 2713200000, 2699700000, 2699700000, 2691500000, 2687500000, 2680600000, 2675600000, 2668700000, 2664200000, 2663800000, 2658600000, 2655200000, 2646000000, 2638500000, 2635500000, 2633300000, 2606300000, 2597500000, 2585200000, 2575500000, 2572700000, 2571500000, 2563800000, 2560200000, 2559500000, 2551700000, 2548800000, 2547300000, 2530100000, 2526300000, 2493200000, 2486300000, 2480200000, 2475600000, 2467400000, 2457400000, 2450800000, 2443300000, 2440400000, 2430200000, 2429300000, 2415700000, 2403400000, 2389600000, 2371900000, 2344500000, 2337600000, 2330800000, 2326500000, 2300800000, 2278400000, 2276100000, 2230200000, 2222800000, 2207200000, 2178500000, 2153800000, 2145500000, 2143600000, 2103300000, 2093700000, 2086100000, 2085700000, 2068700000, 2062500000, 2032200000, 1981200000, 1973300000, 1956500000, 1923900000, 1882500000, 1876000000, 1872800000, 1840200000, 1837200000, 1822800000, 1807500000, 1790600000, 1782200000, 1779800000, 1754000000, 1732700000, 1704500000, 1696200000, 1675000000, 1666700000, 1665700000, 1637700000, 1617600000, 1616200000, 1614800000, 1607600000, 1606300000, 1601900000, 1588400000, 1582900000, 1561500000, 1555800000, 1539400000, 1539000000, 1534700000, 1529200000, 1523800000, 1515200000, 1513500000, 1484200000, 1481800000, 1458100000, 1454700000, 1447600000, 1446100000, 1437800000, 1436200000, 1435500000, 1433700000, 1432300000, 1406000000, 1400600000, 1397800000, 1396900000, 1396200000, 1392600000, 1390900000, 1388600000, 1387900000, 1386000000, 1377200000, 1373500000, 1373300000, 1369700000, 1364600000, 1362400000, 1357300000, 1356700000, 1347900000, 1345900000, 1340300000, 1339300000, 1313600000, 1305200000, 1284100000, 1282100000, 1276100000, 1275600000, 1274000000, 1273100000, 1258700000, 1235400000, 1231300000, 1195400000, 1187800000, 1173000000, 1168700000, 1148600000, 1133600000, 1108100000)
cor.test(nik_close, nik_vol)
###########################################################################
# STOXX 600 (EUROPE) OUTLIERS #
###########################################################################
stoxx_vol <- c(8068259800, 7557556000, 7243086800, 7130308000, 7015693000, 6784088400, 6569684600, 6532452900, 6506693200, 6455256800, 6441906800, 6300416000, 6260120300, 6189735400, 6170797300, 6047662900, 6041303100, 6016609900, 5990354800, 5920225300, 5814206300, 5810022700, 5783571900, 5778662500, 5776592600, 5731696800, 5715861400, 5715514200, 5685330700, 5667279400, 5664157800, 5644136700, 5601864000, 5598217400, 5596521600, 5530892100, 5481488800, 5447295400, 5391112100, 5329248500, 5288574400, 5284539900, 5162109900, 5156214200, 5155068400, 5141114500, 5120640200, 5109740500, 5108929600, 5061411200, 5044459900, 4898417700, 4851670900, 4829569500, 4761109700, 4727016300, 4717665900, 4668497000, 4665939400, 4636643000, 4634906100, 4626036900, 4563697300, 4559447300, 4558362700, 4537933600, 4493206100, 4457050500, 4428634700, 4414670700, 4414589500, 4403288200, 4396511200, 4378642700, 4375370400, 4371274100, 4370401300, 4369953900, 4324893100, 4315542500, 4272524500, 4219964500, 4209030900, 4190288900, 4167228400, 4136701600, 4120573200, 4080039400, 4010016100, 4001420700, 3994185300, 3990773300, 3963845100, 3962271900, 3935024300, 3914857000, 3913126100, 3873973500, 3844484400, 3822333900, 3806938800, 3765308000, 3756703600, 3747876800, 3727672100, 3725329800, 3687903800, 3686458400, 3675091700, 3673166200, 3655958900, 3623085900, 3593140000, 3529714100, 3472143000, 3429359000, 3364175000, 3353233300, 3227490000, 3214970700)
stoxx_close <- c(-0.018, -0.005, -0.029, 0.063, 0.006, 0.014, 0.011, -0.02, 0.024, 0.064, 0.033, 0.036, 0.009, 0.006, -0.068, 0.016, -0.019, -0.052, 0.119, -0.035, 0.017, 0.069, 0.03, 0.07, 0.008, 0.025, -0.004, 0.002, 0.033, 0.034, 0.019, -0.006, -0.009, -0.095, 0.037, 0.012, 0.053, -0.002, 0.047, -0.006, -0.027, -0.009, 0.003, 0.029, 0.008, -0.028, -0.01, -0.008, -0.003, 0.018, -0.069, -0.009, 0.05, -0.056, -0.021, 0.024, -0.094, -0.011, -0.038, -0.06, 0.009, 0.008, -0.044, 0.013, -0.024, -0.034, -0.013, -0.057, 0.061, 0.016, 0.023, -0.089, 0.017, -0.017, 0.02, -0.014, -0.061, -0.012, 0.063, 0.016, 0.015, -0.041, 0.074, 0.06, 0.034, -0.006, -0.012, -0.013, -0.065, 0.041, 0.001, -0.037, 0.021, 0.035, 0.064, 0.025, 0.02, 0.05, 0.037, 0.042, -0.012, 0.006, 0.003, -0.014, 0.012, 0.049, 0.02, 0.033, -0.025, -0.054, 0.03, -0.028, -0.018, 0.018, 0.028, -0.039, 0.019, 0.018, 0.02, 0.018)
cor.test(stoxx_close, stoxx_vol)
###########################################################################
Additional Findings
There was a negative correlation between the two variables: S&P 500 Monthly Close (n = 218) and S&P 500 Monthly Volume (n = 218). S&P 500 Monthly Close (M = .007, SD = .039), S&P 500 Monthly Volume (M = 77543082110, SD = 18749895626), Conditions; t(216) = -0.34354, p = .73. Pearson Product-Moment Correlation Coefficient: r = -.02.
There was a negative correlation between the two variables: Nikkei 225 Monthly Close (n = 236) and Nikkei 225 Monthly Volume (n = 236). Nikkei 225 Monthly Close (M = .002, SD = .055), Nikkei 225 Monthly Volume (M = 2351271186, SD = 803886229), Conditions; t(234) = -1.2234, p = .22. Pearson Product-Moment Correlation Coefficient: r = -.08.
There was a positive correlation between the two variables: STOXX 600 Monthly Close (n = 120) and STOXX 600 Monthly Volume (n = 120). STOXX 600 Monthly Close (M = .004, SD = .038), STOXX 600 Monthly Volume (M = 4872733427, SD = 1039773116), Conditions; t(118) = 0.31681, p = .75. Pearson Product-Moment Correlation Coefficient: r = .03.
Additional Conclusions
When outliers are removed and the analysis is performed, there is a slight shift in the correlation coefficient values amongst the various indices. S&P 500 (-.14; -.02), Nikkei 225 (-.03; -.08), STOXX 600 (-.18; .03). There also was a shift in correlation significance. S&P 500 (.03; .73), Nikkei 225 (.63; .22), STOXX 600 (.04; .75).
With the removal of outliers, every index had a decline in correlation significance (p), with the exception being the Nikkei 225. Oddly, as it pertains to correlation coefficient values, the S&P 500 rose and remained negative, the Nikkei 225 declined and remained negative, while the STOXX 600 value became positive.
In almost instance, increases in volume equates for decreases in price. It would seem that the most massive volume increases are the largest contributors to price decline. Seemily, disproportionately so, the Nikkei 500 continues to be an odd duck, in that, it seems to be in a perpetual state of stasis, with smaller upward shifts of volume being more impactful on price than comparatively larger shifts.
Tests for Randomness / Stationarity
Phillips-Perron Unit Root Test
data: sp_vol
Dickey-Fuller = -4.7548, Truncation lag parameter = 4, p-value = 0.01
Phillips-Perron Unit Root Test
data: nik_vol
Dickey-Fuller = -4.2136, Truncation lag parameter = 4, p-value = 0.01
Phillips-Perron Unit Root Test
data: stoxx_vol
Dickey-Fuller = -6.906, Truncation lag parameter = 4, p-value = 0.01
Augmented Dickey-Fuller Test
data: sp_vol
Dickey-Fuller = -2.2459, Lag order = 6, p-value = 0.4725
alternative hypothesis: stationary
Augmented Dickey-Fuller Test
data: nik_vol
Dickey-Fuller = -2.3522, Lag order = 6, p-value = 0.4277
alternative hypothesis: stationary
Augmented Dickey-Fuller Test
data: stoxx_vol
Dickey-Fuller = -2.6845, Lag order = 4, p-value = 0.2921
alternative hypothesis: stationary
Final Thoughts and Conclusions
In every instance, the volume measurements for each index were non-stationary, and non-random. Thus, I suppose that it should be expected, that volume figures should typically increase over time. As was demonstrated by the correlation analysis both as it relates to index/volume assessments (with and without outliers), large unanticipated upward shifts in volume, typically should be expected to cause price decline.
Thus, it might be said, that demand creates its own supply. Or at the very least, impacts supply price in a deflationary manner. Or perhaps some combination of the two.
As it relates to volume’s long term impact on pricing, it would seem that the stationary / random walk analysis that was performed for a prior article, holds true. In that, like a tiny pill bug walking haphazardly across graphing paper, a small push by a human hand here and there may alter the insect’s course, but will otherwise not prove to be impactful, other than demonstrating some significance in the present moment.
In a similar manner, as with a stretched slinky, outside gyrations obviously cause disruption, but only temporarily. Once the interference ceases, the stationarity is maintained.
Markets outside of the United States continue to remain mysterious in comparison to their state side counterparts while comparing growth patterns. Perhaps the limbic bounces of a market’s price have much to do with the culture of an economy. Though, the bounces themselves do remain very much human in origin, regardless.
