Serial Correlation

If you toss a coin and it comes up Heads, do you think that'll influence the next toss?

>Of course not! They're independent! Even if I toss a hundred heads, the next toss ...
Okay. Now do you think that today's stock return will influence tomorrow's return?

>Uh ... maybe momentum works or maybe ...
Okay, now consider Monte Carlo simulation.
There are (at least!) two Monte Carlo rituals:

1. You select returns at random from some assumed distribution of returns.   (Example: a lognormal distribution.)
2. You select returns at random from a list of historical returns.
Now there's an implicit assumption that the randomly selected return has no influence on the next selection.
>Does it?
Aah, that's the question, eh?
We're talking correlation between successive returns .. so let's play with that.
We'll look at the annual retrurns listed here and calculate the return-correlation between successive years:

Recently I played with a spreadsheet (described here) that calculated serial correlation between successive daily returns.
In particular, the XIU Index and its components and the DOW and its components and ...

>And can you just give the results without all the verbal paraphernalia, because I think ...
Okay. Here's what I got for correlation between successive daily returns.

 Asset Correlation LgCap/Gwt -1.3% LgCap/Val -8.2% SmlCap/Gwt 4.0% SmlCap/Val 7.8% T-bills 91.9% 5 yr Treasury 14.6% Gov Lng Bnd -5.7% S&P 500 -2.0%
 Asset Correlation ROGERS COMMUNICAT(RCI-B.TO) 64.0% 22.7% 0.57 2.17 PENN WEST PETROLE(PWT-UN.TO) -10.5% 32.7% 1.38 -0.28 LOBLAW COMPANIES (L.TO) -15.6% 16.8% 0.21 -1.24 CANADIAN NATURAL (CNQ.TO) -6.4% 34.1% 1.95 -0.08 IMPERIAL OIL LTD(IMO.TO) 10.2% 28.5% 1.36 0.44 CANADIAN OIL SAND(COS-UN.TO) -9.1% 40.8% 1.86 -0.11 FORDING INC(FDG-UN.TO) -37.5% 38.0% 1.12 -1.15 NEXEN INC(NXY.TO) 5.8% 36.5% 2.04 0.29 HUSKY ENERGY INC(HSE.TO) 7.9% 25.6% 1.18 0.30 Tim Hortons Inc(THI.TO) 13.9% 20.0% -0.03 0.57 TECK COMINCO LIMI(TCK-B.TO) 17.3% 39.8% 1.80 0.47 SUNCOR ENERGY INC(SU.TO) -4.1% 32.6% 1.85 -0.03 PETRO-CANADA(PCA.TO) -19.7% 28.2% 1.55 -0.69 BIOVAIL CORPORATI(BVF.TO) -14.9% 41.3% 0.74 -0.22 TALISMAN ENERGY I(TLM.TO) -4.5% 36.3% 1.99 0.02 CAMECO CORPORATIO(CCO.TO) 5.8% 39.1% 2.01 0.33 CANADIAN IMPERIAL(CM.TO) 26.6% 13.9% 0.39 1.44 ENCANA CORP(ECA.TO) 10.4% 29.6% 1.59 0.41 YAMANA RESOURCES (YRI.TO) 57.8% 53.0% 2.44 1.05 GOLDCORP INC(G.TO) -6.9% 43.3% 2.17 -0.01 LUNDIN MINING COR(LUN.TO) -43.5% 88.3% 2.21 -0.02 BCE INC(BCE.TO) 11.3% 22.7% 0.25 0.42 CANADIAN NATIONAL(CNR.TO) 0.3% 20.9% 0.83 -0.04 AGNICO-EAGLE MINE(AEM.TO) 53.9% 47.4% 2.39 1.01 AGRIUM INC(AGU.TO) 55.3% 32.3% 1.23 1.45 ACE AVIATION HOLD(ACE-B.TO) 14.0% 32.9% 0.34 0.45 POTASH CORPORATIO(POT.TO) 86.5% 33.5% 1.21 1.88 IUNITS S&P/TSX 60(XIU.TO) 12.7% 13.4% 1.00 0.73 GEORGE WESTON LTD(WN.TO) -15.4% 17.7% 0.36 -1.10 ALCAN INC(AL.TO) 28.3% 34.2% 1.74 0.78 ROYAL BANK OF CAN(RY.TO) 19.2% 15.1% 0.53 1.00 IPSCO INC(IPS.TO) 8.6% 35.5% 1.60 0.24 COGNOS INC(CSN.TO) 2.6% 36.1% 0.43 0.16 BANK OF NOVA SCOT(BNS.TO) 13.9% 13.6% 0.44 0.75 BARRICK GOLD CORP(ABX.TO) 8.2% 29.7% 1.48 0.30 THOMSON CORP (THE(TOC.TO) 14.3% 15.1% 0.35 0.73 BANK OF MONTREAL(BMO.TO) 9.0% 12.1% 0.35 0.42 ENBRIDGE INC(ENB.TO) 11.4% 16.1% 0.56 0.52 BOMBARDIER INC CL(BBD-B.TO) 61.3% 46.8% 1.02 1.22 CELESTICA INC. SV(CLS.TO) -41.8% 46.1% 0.66 -1.03 KINROSS GOLD CORP(K.TO) 43.5% 45.4% 2.20 0.95 TORONTO-DOMINION (TD.TO) 8.3% 13.8% 0.44 0.35 NATIONAL BANK OF (NA.TO) 4.5% 14.2% 0.42 0.06 SUN LIFE FINANCIA(SLF.TO) 6.3% 16.4% 0.56 0.21 CANADIAN PACIFIC (CP.TO) 11.3% 23.2% 0.95 0.40 NOVA CHEMICALS CO(NCX.TO) 4.9% 30.4% 0.73 0.08 RESEARCH IN MOTIO(RIM.TO) 67.8% 41.9% 0.78 1.36 YELLOW PAGES INCO(YLO-UN.TO) -13.7% 26.3% 0.54 -0.56 TELUS CORP(T.TO) 23.5% 26.8% 0.55 0.82 TRANSCANADA PIPEL(TRP.TO) 15.2% 16.8% 0.52 0.77 COTT CORPORATION(BCB.TO) 0.8% 33.2% 0.14 0.06 TRANSALTA CORPORA(TA.TO) 8.4% 19.6% 0.30 0.33 NORTEL NETWORKS C(NT.TO) -4.8% 43.2% 0.42 0.08 MDS INC(MDS.TO) -1.3% 20.5% 0.46 -0.13 SHOPPERS DRUG MAR(SC.TO) 15.9% 15.6% 0.25 0.79 NOVELIS INC(NVL.TO) 79.8% 38.3% 0.02 1.94 MANULIFE FINL COR(MFC.TO) 10.4% 15.6% 0.60 0.48
 Asset Correlation UNITED TECH(UTX) 18.4% COCA COLA CO THE(KO) 13.0% JOHNSON AND JOHNS(JNJ) 11.3% AT&T INC.(T) 10.8% WAL MART STORES(WMT) 10.8% GEN MOTORS(GM) 10.4% GEN ELECTRIC CO(GE) 8.9% DU PONT E I DE NE(DD) 8.9% PFIZER INC(PFE) 8.8% ALCOA INC(AA) 7.9% CATERPILLAR INC(CAT) 7.8% HONEYWELL INTL IN(HON) 7.5% AMER INTL GROUP I(AIG) 7.1% CITIGROUP INC(C) 5.5% BOEING CO(BA) 5.5% DOW JONES INDUSTR(^DJI) 5.2% HOME DEPOT INC(HD) 5.0% INTEL CP(INTC) 4.2% JP MORGAN CHASE C(JPM) 3.9% 3M COMPANY(MMM) 2.8% EXXON MOBIL CP(XOM) 1.7% INTL BUSINESS MAC(IBM) 0.8% MCDONALDS CP(MCD) -2.2% HEWLETT PACKARD C(HPQ) -3.1% MICROSOFT CP(MSFT) -5.2% WALT DISNEY-DISNE(DIS) -5.3% PROCTER GAMBLE (PG) -6.3% VERIZON COMMUN(VZ) -6.7% AMER EXPRESS INC(AXP) -6.8% MERCK CO INC(MRK) -11.3% ALTRIA GROUP INC(MO) -11.4%
You can even stare with awe at the daily stuff for the S&P500.

>And what does that prove?
Uh ... nothing, but it's interesting, no? The Index itself is roughly in the middle. That's interesting, no?
>No.
Well, I'd be wary of using Monte Carlo and random, independent returns with stocks that have a high serial correlation, wouldn't you?
>No. I never actually believe what Monte says, anyway. It's a game, a rough estimate, some hand waving, a "what if" scenario not to be taken too seriously, something to gaze at, cogitate and ...
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