OMETIMES PICTURES CAN BE EXTREMELY helpful in conveying information and making a point. Pictures can be worth a thousand words.

But they have to be taken in context as they can oftentimes be misleading. In the end, pictures are just a way of viewing reality at a specific place and time.

The same hold true for charts. Quants love to use charts to confirm relationships and test theories. Like a picture, a chart provides a way to view reality. Yet no matter how simple to interpret, when taken in isolation a chart may distort the very reality it's designed to measure.

Short-Term Shapes the Long-Term

But if you compare its returns to those of the S&P 500, you might wonder why we'd have to wait that long. As you can see from the nearby chart, P3 has handily trailed the benchmark almost from its very inception. Does it really take a rocket scientist to see it's not working?

Chart 1 Not a Pretty Picture

Despite a fine start, Portfolio 3 has not done a good job tracking the S&P 500. By the end of February 2002, the difference between the two was over 35%.

The cumulative picture certainly doesn't look good, but you have to be careful as to what you read into it. Yes, P3 does lag over the measurement period. Yes, the disparities can be quite large over small periods. Just consider the first quarter of 2001 when the majority of the overall difference occurred.

Yet that's the weakness of a cumulative performance chart. Short periods of under (or over) performance shape the overall results. They may not be indicative of the correlation between the two series yet they have a disproportionate effect on the end result.

That's why mutual fund companies love cumulative charts: one or two good years at the outset will mask a number of mediocre or down years. Most firms carefully pick the starting point of their illustrations to maximize this effect.

As you'd expect, the exact opposite effect occurs if performance lags at the beginning of the measurement period. That's precisely the situation in regard to Portfolio 3 and the S&P 500. Just as the mutual funds' apparent outperformance really isn't indicative of ongoing expectations, neither is P3's early underperformance.

What If?

Like Portfolio 4, P3 has a growth bent. Investors' transition to value left it behind. It also didn't help that the shift was as abrupt as it was broad. P3 was only reformulated twice during the period, the first time relying heavily on investors' earlier growth bent.

Chart 2 Without Winter 2000-2001

Without the four month period of November 16, 2000 - March 14, 2001, P3 would be tracking right with the S&P 500.

As they often do, investors overreacted in those four months, sending previously undervalued issues into the stratosphere. By March 2001, many value stocks were as overvalued as the now forsaken growth issues. From that point through February 2002, the S&P 500 went nowhere, grinding back and forth in profitless sector rotation.

So what would the comparison with the index look like if that dreadful four month period hadn't occurred? To find out, we extracted the November 16, 2000 - March 14, 2001 period and replotted the daily returns. The results appear on Chart 2.

What a difference four months make! If it weren't for them, we'd probably be wearing our arms out patting ourselves on the back for devising such a reliable model. Despite minor fluctuations, the two series would be tracking right on top of one another.

With the adjusted timeframe, the correlation between the two is a quite respectable .8735. Oddly enough, correlation over the total measurement period is even higher: .9455. On that basis alone, the model has achieved part of its original mission.

Our Quant Portfolios

Portfolio 3 Top 30 Stocks Based on Stepwise Regression Across All Stocks of the S&P 500 No Attempt is Made to Sector-Weight this Portfolio Rebalanced Every 60 Days Stocks Remain in the Portfolio Until Falling Below the Top 40 The Highest Rated Stocks Not Already in the Portfolio are Added When Existing Constituents are Removed Portfolio 4 Top Stocks of Each Sector Based on Stepwise Regression of Each Individual Sector of the S&P 500 Number of Stocks Selected in Each Sector Determined by Current Sector-Weightings of the S&P 500 Rebalanced Every June Stocks Remain in the Portfolio for 12 Months Unless Deleted for Special Circumstance e.g. Acquisition Stocks Removed for Mergers and Acquisitions are Replaced by the Next Highest Rated Stocks in Their Specific Sector

(Correlation measures how two series track together. Perfect positive correlation is 1.000 and indicates the two series move in perfect tandem. Perfect negative correlation is -1.000 and occurs when each series moves in the exact opposite direction from the other at all times. Correlations around 0 indicate no relation between the two.)

So What?

Sure it's bad statistics, but it still illustrates a point: The model's considerable underperformance in its first twenty months is not sufficient reason to abandon it and move on to the next.

In fact it clearly illustrates that the underperformance was concentrated in one relatively short period of time. It also suggests that a similar period of outperformance is not completely out of the question, either. After all, remember reversion to the mean?

And a recovery might be more likely than you'd think. As you're probably painfully aware, the S&P has been in a decline since September 2000 -- just two months after P3 came into existence. In other words, so far it's been tested in a down market.

Chart 3 A Bullish Model

P3 is reformulated every two months. In comparing each formulation's performance to the S&P 500 (bars), P3 outperforms when the market is up and lags when it's down. The line shows the difference between the results.

Yet P3 tends to outperform in up markets. This is illustrated in Chart 3. The bars compare P3 and the S&P 500 over two month periods representing the various formulations of the portfolio. In those periods when the market was up, P3 leads the index. This is highlighted by the red line showing the difference between the two series.

Sixteen months remain in the testing period. Most economists believe the economy will soon emerge from recession. A return to growth will definitely benefit the equity markets. If P3 continues to outperform the index in up markets, it certainly has the potential to close the gap opened in late 2000.

That's why you don't write off a model when it stumbles out of the gate. The best test is one that considers as many different market conditions as possible. So far P3 has experienced a bear market. Hopefully the full three year measurement period will allow it to function in a bull market, too.

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