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Modeling the Active versus Passive Debate
By William Rafter
March 9, 2010

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Her experiences are not exclusive to monthly forecasting.  The perfect quarterly portfolio, for example, loses handily to reselection of stocks either every two months or every month.  (Testing annual periods would require either too much data or produce too few results for statistical significance.) 

There are two possible explanations for the increased profitability Cassandra observed.  The least obvious factor would be rebalancing of the entire portfolio every time a new position is taken.  Indeed, rebalancing adds tremendous profitability; the more frequent the better.  In this study, however, there was no rebalancing involved in either strategy.  New positions would have had an equal value allocation, and existing positions were left alone to grow or decline in value, unchanged in size until liquidated.  Thus, with rebalancing absent, there can only be one explanation: that more-frequent forecasting is inherently profitable, even more so than some forms of perfect knowledge. 

Focusing on increasing profits while ignoring risk is foolhardy.  It is worth noting, as an aside, that even perfect knowledge does not always produce profits in every period.  Cassandraís is a long-only strategy in which she is purchasing the top-200 ranked stocks.  There are some periods during which virtually all stocks decline, or at least during which the average return of the top-200 is negative.  Thus we must consider the dark side of investing.

One of the distinct advantages of more-frequent analysis and forecasting is that losses get cut earlier, providing damage control.  Shortened time horizons play an obvious role in risk reduction.  Recasting our 21-day forecast every 15 days produced an annual return of 39 times oneís money, but at the risk of a 30 percent decline in capital.  At 10 days the returns were 138 times, but with a 47 percent drawdown.  At five days, the returns were 56 times, but the maximum drawdown was only 14 percent.  Thus five days had a reward-to-risk ratio of 4 (56/14), compared to 2.9 (138/47) for 10 days and 1.27 (39/30) for 15 days.  The monotone progression makes the point.  A similar finding appears in the quarterly data as well; the risk-adjusted rewards are improved by ever shorter forecasting periods. 

Also of interest were the results of holding beyond the forecasted period.  They were horrible, which underscores that the perfectly selected portfolio is extremely time-specific. 

Here we see a situation in which our investor has perfect future knowledge, and yet she gains a clear advantage by re-evaluating her decisions with increasing frequency.  This is essentially a conflict between two mutually exclusive ideas.  On the one hand, perfect knowledge has to win, and indeed it will over that exact period.† Thatís intuitive.  It is also intuitive, however, that more frequent information proves beneficial, if one is willing to shorten the trading period.  And here we have evidence of the latterís success over a perfectly chosen portfolio.  If active management can improve a portfolio chosen with perfect foresight, surely logic dictates its value over a sub-perfect portfolio.   That would have to be proven, but any of those results would be dependent upon a particular investment or trading program.  The beauty of this particular study is that it is program-independent.  The lesson? If you ignore interim news or market action, you do so at your peril.  The buy-and-ignore strategy is only acceptable if you are unable or unwilling to devote more time to your investment analysis. 

William Rafter has managed hedge funds for over 20 years and has been fully licensed as a securities and financial principal.  He is President of Mathematical Investment Decisions, Inc., a Pennsylvania-based investment consulting firm. ††

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