290 THE HANDBOOK OF PORTFOLIO MATHEMATICS
Additionally, since I am speaking here of, say, market A making the large
move, and its correlation to B, then too can I expect A and C to see an
increase in their correlation coefficient in those time periods of the large
move, and hence between B and C during those periods where I see a large
move in A.
In short, when the big moves come, things tend to line up and move
together (to a far greater degree than the correlation coefficient implies).
In incidental time periods, which are most time periods, the correlation
coefficients tend back toward zero.
To see this, consider the following study. Here, I tried to choose ran-
dom and disparate markets. Surely, everyone may have picked a different
basket than the random one I drew here, but this basket will illustrate the
effect as well as any other. I took three commodities—crude oil (CL), gold
(GC), and corn (C)—using continuous back-adjusted contracts, the use of
which I devised while working with Bruce Babcock in 1985. I also put in the
S&P 500 Cash Stock Index (SPX) and the prices of four individual stocks,
Exxon (XOM), Ford (F), Microsoft (MSFT), and Pfizer (PFE). The data
used were from the beginning of January 1986 through May 2006—nearly
20 years.
I used daily data, which required some alignment for days where some
exchanges were closed and others were not. Particularly troublesome here
was the mid-September 2001 period.
However, despite this unavoidable slop (which, ultimately, has little
bearing on these results), the study bears out this dangerous characteris-
tic of using correlation coefficients for market-traded pairwise price se-
quences.
Each market was reduced to a daily percentage of the previous day
merely by converting the daily prices for each day as divided by the price
of that item on the previous day. Afterward, for each market, I calculated
the standard deviation in these daily price percentage changes.
Taking these eight different markets, I first ran their correlation coeffi-
cients over the daily percentage price data in question. This is shown in the
“All days,” section, andisthe benchmark, as it is typically whatwouldbe
used in constructing the classical portfolio of these components.
Next, I took each component and ran a study wherein the correlations
of all components in the portfolio were looked at, but only on those days
where the distinguishing component moved beyond 3 standard deviations
that day. This was also done for days where the distinguishing component
moved less than one standard deviation that day (the “Incidental days”).
This can be seen as follows. The section titled “CL beyond 3 sigma”
shows the correlation of all components in the study period on those days
where crude oil had a move in excess of 3 standard deviations.