Many will recall Ross Miller's study of Fidelity Magellan fund under Robert Stansky, in which he shows the fund to have been essentially indexing — without adding manager value (however you define that).

This paper appeared circa Feb 2007; shortly after which Mr. Stansky was dismissed.

Here is a check on whether Fidelity Magellan's new manager is real or just a shadow. FMAGX daily returns (cls-cls) were regressed against big-cap SP500 index ETF, SPY. First for an equal 704 day period prior to Ross' study:

Regression Analysis: FMAGX- versus SPY-

The regression equation is
FMAGX- = - 0.000106 + 1.06 SPY-

Predictor        Coef       SE Coef            T      P
Constant   -0.00011  0.00011  -1.01  0.313
SPY-           1.064     0.01640  64.88  0.000

S = 0.00278542   R-Sq = 85.7%   R-Sq(adj) = 85.7%

FMAGX slightly underperformed SPY (NS), with high correlation.

Here is the same regression for the 704 days since the study:

Regression Analysis: FMAGX+ versus SPY+

The regression equation is
FMAGX+ = 0.000011 + 1.07 SPY+

Predictor       Coef         SE Coef      T      P
Constant   0.0000111  0.00023   0.05  0.961
SPY+        1.075         0.01152  93.22  0.000

S = 0.00594187   R-Sq = 92.5%   R-Sq(adj) = 92.5%

Basically identical to SPY, with same beta as before, now with even more correlation.

Eclipsing the shadow.

Alston Mabry continues:

However if one invests in 200+ large cap stocks stocks among 60 subgroups, they are going to likely going to correlate closely with the S&P 500. For example, over the past two years, an equal investment in each the nine stocks he listed would have had a 95% daily correlation with SPY.

Following a similar path, one calculates correlations for the daily log% changes of a few stocks vs SPY, over a 120-day period:
MCD by SPY: +0.36
MSFT by SPY: +0.52
PG by SPY: +0.54

Then, simply add the daily log% changes of one or more stocks together, day by day, and run the correlation against the SPY:

MCD+MSFT by SPY: +0.58
MCD+PG by SPY: +0.55
MCD+MSFT+PG by SPY: +0.67

It doesn't seem surprising that for any combination of components of SPY, one gets a higher R than any of the individual components in the combination.This is just a "back of the envelope" test, and I don't know how it would look for all possible combinations, or taking cap-weighting into account.

Phil McDonnell adds:

If one were to re-do Big Al's study it would be better to use simple percentage changes not logs. Logs are for compounding and are needed for one time period following another if reinvestment is allowed. But since step two in this process is to average the stocks into small 2 & 3 stock portfolios a simple average would be better.

In general building portfolios of positively correlated stocks will tend to move the portfolio toward the average return. However if one searches for negatively correlated investments with positive expectation returns can be achieved with less risk.

Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008

Kim Zussman writes:

MSFT is 2.4% of SP500/SPY; MCD is 0.7%


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