Correlation Coefficients
"Where you lead I will follow"
One overlooked danger of our Workshop strategies is correlation. Because many strategies choose similar types of stocks, they tend to track each other. By calculating the correlation coefficients between strategies, you can build a Workshop portfolio with complementary strategies. End result: higher returns, lower volatility.
By Todd Beaird (TMF Synchronicity)
December 6, 2000
Remember the old saying "As General Motors <% if gsSubBrand = "aolsnapshot" then Response.Write("(NYSE:GM)") else Response.Write("(NYSE:GM)") end if %> goes, so goes the nation"? People didn't really think that GM controlled the economy, so what did that phrase mean?
For many years, GM was one of the preeminent companies in the United States. (Heck, with total revenues of more than 176 billion dollars last year, it's not too shabby today.) There was always a demand to buy vehicles, and GM was always there to sell them. When the U.S. economy was going well, car sales were great, but as the economy slowed down, so would vehicle purchases. Because GM was so large and its products were so pervasive, any slowdown in the economy would affect GM. This meant that GM's stock tended to track the U.S. economy. So, as GM went, so went the nation.
The mathematical phrase for that phenomenon is that GM's performance was strongly correlated with the performance of the U.S. economy. Any two (or more) stocks that tend to track each other can be said to have correlated returns. Stocks that are in the same industry, such as GM and Ford <% if gsSubBrand = "aolsnapshot" then Response.Write("(NYSE: F)") else Response.Write("(NYSE: F)") end if %>, are often strongly correlated.
There is a way to calculate the degree of this correlation. Given two sets of returns, we can calculate the correlation coefficient for those returns. As I wrote earlier this summer: "A correlation coefficient is a value between -1 and +1. A value of +1 would reflect a perfect positive correlation (Screen A goes up 10% when Screen B goes up 10%). A value of -1 would indicate a perfect negative correlation (Screen A goes down 10% when screen B goes up 10%). A coefficient of zero would mean that there is no apparent relation between the two (Screen B goes up 10%, and Screen A does something completely random)."
The correlation coefficient is easy to calculate in Excel, using the "CORREL" function. (For more help with CORREL and other Excel issues, check out the "Spreadsheet advice" board.) Here are the annual returns for General Motors and Ford since 1977:
Year GM Ford
1977 -11.5% -6.6%
1978 -5.6% -7.9%
1979 2.1% -24.0%
1980 -4.6% -37.5%
1981 -9.9% -16.2%
1982 71.1% 132.1%
1983 24.1% 63.5%
1984 12.6% 7.7%
1985 -3.7% 27.1%
1986 0.3% 45.5%
1987 -0.8% 34.0%
1988 45.5% 34.0%
1989 8.4% -13.6%
1990 -12.5% -39.0%
1991 -13.3% 5.6%
1992 16.1% 52.5%
1993 73.4% 50.4%
1994 -22.0% -13.6%
1995 28.7% 3.6%
1996 8.7% 11.7%
1997 19.4% 50.6%
1998 21.3% 20.9%
1999 26.1% -9.2%
2000* -28.7% -19.7%
*results through 12/1/00
The returns appear to "track" each other closely, although there are some exceptions (1999, for example). Sure enough, the correlation coefficient is 0.7073. That's a pretty high positive correlation.
Correlation coefficients can help in building your Workshop portfolio. We often use multiple strategies in order to reduce volatility. Unfortunately, many of our Workshop screens are growth screens, and they are highly correlated. By using coefficients, we can see how closely our Workshop screens have tracked each other historically.
Let's take a look at the correlation coefficients (or "CCs," not to be confused with covered calls) for six tentative strategies that have been proposed for the official Workshop Portfolio. All data is courtesy of Jamie Gritton's backtest engines. You can download a spreadsheet showing the calculations behind these results here. Remember that "1" means the screens track each other perfectly, and zero means they have no relation at all.
LowPB Key100 Plbk PEG26 CAPRS RS13
LowPB --- 0.36 0.24 0.39 0.33 0.46
Key100 --- 0.61 0.21 0.58 0.57
Plbk --- 0.16 0.54 0.47
PEG26 --- 0.21 0.28
CAPRS --- 0.57
RS13 ---
(Note: "LowPB" is Low Price/Book Value, "Key100" is Keystone 100, and "Plbk" is Plowback.)
First, note that all of the correlations are positive. We don't have anything that we can count on to go up when everything else goes down. The next best thing would be low positive correlations.
The most likely candidate for a low positive correlation is our "value" strategy, Low Price/Book Value. Value strategies traditionally move in opposite directions from "growth" strategies. The chart above confirms this, with all of the LowPB screens coefficients less than 0.5. Also, the PEG26 strategy tends to go its own way. PEG26 and Plowback have almost no relation: their CC is a lowly 0.16. PEG26 comes closest to tracking LowPB, but not much, with a CC of only 0.39. This indicates that PEG and LowPB will add a lot of diversity to our portfolio.
Looking at the entire chart, we can see that the strongest relation is between Keystone100 and Plowback. They have a CC of 0.61. This isn't as bad as GM and Ford, but indicates that these screens may move in tandem more than we'd like.
Why do you care about correlation coefficients? Two reasons: diversification and risk management. You can select several strategies with excellent returns and Sharpe Ratios. However, if two of those screens "track" each other closely, then it's almost like buying the same strategy twice. When Gateway <% if gsSubBrand = "aolsnapshot" then Response.Write("(NYSE: GTW)") else Response.Write("(NYSE: GTW)") end if %> dropped last week after warning that earnings would be poor, Dell <% if gsSubBrand = "aolsnapshot" then Response.Write("(Nasdaq: DELL)") else Response.Write("(Nasdaq: DELL)") end if %> and Compaq <% if gsSubBrand = "aolsnapshot" then Response.Write("(NYSE: CPQ)") else Response.Write("(NYSE: CPQ)") end if %> followed it down. So much for diversification. On the other hand, two complementary strategies should reduce volatility, if one does well when the other doesn't.
For more on Workshop strategy correlation coefficients, you can check this post from "littlebob" (yet another example of the great work done by our community). I urge you to consider correlations between strategies when developing your own Workshop portfolio. To reiterate what Ann Coleman said last Thursday, please don't mimic our strategy. Build your own Workshop strategy, tailored to your own needs and risk tolerance.
See you next week -- same Fool Time, same Fool Channel.
