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Investing Insights

Active Management, Anti-Vaxxers and the Flat-Earth Society

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Jim Steel, CFA, CFPActive Management, Anti-Vaxxers and the Flat-Earth Society

by Jim Steel, CFA, CFP

What do active managers, anti-vaxxers and flat-Earthers have in common? 

They all ignore the evidence. 

Anti-vaxxers ignore the evidence that vaccinations save lives. Flat-Earthers ignore the evidence that the Earth is round. Active managers ignore the evidence that they are destined to underperform.  

To explore this further, what follows is an explanation of the mathematics that provides a simple “proof” that active management will underperform its relative benchmark after fees, using real-world data as evidence. 

For an example of this simple proof, we turn to Nobel laureate William Sharpe and his article “The Arithmetic of Active Management”. Sharpe points out that there are only two types of returns available for investors:  

  1. returns generated through active management  
  2. returns generated through passive management. 

He also explains that the total market return MUST equal a weighted average of the returns of the passive and active segments of the market. 

If we assume 90% of the market is active and 10% is passive, we end up with this simplified equation (the percentages do not matter – the result would be the same even if the numbers were reversed): 

                                                                           M = 90%*A + 10%*P

 where:           M = return of the entire market

                         A  = average return of all active managers

                         P  = average return of all passive managers

Recalling your Grade 10 math, there is always an implied “1” in front of everything; and remembering that 1=100% when dealing with percentages; and that the multiplication symbol * is the same as the word “of”, we can express the equation above as:

                                                                100%*M = 90%*A + 10%*P

 In other words, 100% of the total market return is equal to 90% of active managers’ return plus 10% of passive managers’ return. 

However, passive managers, by definition, capture the return of the total market, therefore:

                                                      market return = passive return

                                                                             M = P

 Since M = P we can substitute M for P in the initial equation:

                                                                        100%*M = 90%*A + 10%*P    (initial equation)

                                  100%*M = 90%*A + 10%*M   (sub M for P on the right side)

 Rearrange by subtracting 10%*M from both sides (Grade 10 math):

                                                                  100%*M = 90%*A + 10%*M

                                                         100%*M - 10%*M = 90%*A + 10%*M – 10%*M 

                                                                          90%*M = 90%*A

                                                                          90%*M = 90%*A

                                                                                   M = A

                                                                   But:  M = P (from above)   

                                                        Therefore:  M = A = P

This means that mathematically, the return of all active managers MUST equal the return of the market and of all passive managers. It is as concrete as 1+1=2. 

However, this conveniently ignores fees charged by active managers. 

Fees for active management are many times greater than passive management. Therefore the smartest and best course of action for investors is to adopt a passive approach and minimize fees. 

What does the data show? 

To analyze this further, we need data that tracks the performance of a large group of active managers and then compare their returns to a relative index. Standard & Poor’s does this in its semi-annual report SPIVA Canada Scorecard. This report analyzes data from thousands of active managers; makes adjustments to account for various tricks used by the mutual fund industry; and compares the results to those of comparable benchmark indexes. The following is a summary of the most recent SPIVA Canada Scorecard (data up to mid-2019. 

SPIVA Canada Mid-year 2019 Summary: 

  • Over 88% of Canadian equity managers underperformed the S&P/TSX Composite over the 10-year period ending in June 2019. 
  • Results were particularly bleak for the dividend & income equity fund category, as no manager was able to outperform the benchmark over the 10-year period. 
  • Over 98% of U.S. equity managers underperformed the S&P 500 Index over the 10-year period ending in June 2019.
  • Over 87% of International equity managers underperformed the S&P EPAC LargeMidCap Index over the 10-year period ending in June 2019.
  • Over 95% of global equity managers underperformed the S&P Developed LargeMidCap Index over the 10-year period ending in June 2019.
  • Over 97% of Canadian Focused Equity (a mix of Canadian, U.S. and International managers) underperformed the relative blended index over the 10-year period ending in June 2019. 

How much was this underperformance? 

                                           Canada (equity):  0.76%

      Canada (dividend & income equity):  2.33%

                                                                   US:  2.92%

                                                International:  2.28%

                                                            Global:  3.08%

Canada (focused equity incl US & Intl):  3.94%

  Average active underperformance:  2.55%

  Average mutual fund fee in Canada:  2.35%

(source: Morningstar 2016)


William Sharpe and Grade 10 mathematics proves that active managers are destined to underperform their relative benchmark indexes by at least the amount of fees they charge. Real world data supports this evidence. Investors should choose wisely, and opt for passive management and minimize the fees they pay. Vaccinations save lives. The Earth is not flat. Active managers do not beat the market. Do the math.

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