Seeking Alpha

Are you tracking the performance of your portfolio and measuring the Internal Rate of Return (IRR) with respect to the IRR of an appropriate benchmark? If not, why not? Investors not engaged in this level of measurement will likely find this discussion of little use. Shall we say, ignorance is bliss.

Serious investors take the time and make the effort to know if they are adding alpha or value to the portfolio based on their investment decisions. If the portfolio lags the benchmark, and this is the case for the vast majority of investors who build their portfolios through the selection of individual stocks, what are some possible reasons for under-performing the benchmark? We are going to approach this mathematically, so hang on and see this argument through to the end.

Posit that you are using 10 metrics to determine which stock to purchase. Ten metrics can easily end up with 10 strategies. But it does not end there as the statistics of combination come into play. Granted, not all metrics are of equal importance. Let's begin with the problem of combining two metrics from the 10 available for analysis. How many strategies arise when we combine two of the 10 metrics.

Using the mathematics from the link show above we have the following.

Combinations = n!/[r!*(n - r)!]

where n = number of metrics or strategies.

r = options taken at a time. Two in this example.

Combinations = 10!/[2!*(10 - 2)!] = 10!/[2!*8!] = 45

Example of 10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10

Using three characteristics or metrics we have the following number of combinations.

Combinations = 10!/[3!*(10 - 3)!] = 10!/[3!*7!] = 120

The complexity quickly ramps up to where it becomes exceedingly difficult for any investor to get their arms around all the variables wrapped up in an individual stock.

Let me quote extensively from William J. Bernstein's "Investor's Manifesto" book – beginning on page 40.

"The reason why 90 percent of investors and fund managers cannot pick stocks is simple: Whenever you buy or sell a stock or bond, there is someone on the other side of that trade, and that someone most likely has a name like Goldman Sachs, PIMCO, or Warren Buffett."

"There is even something worse than trading with Buffett, and that is trading with a top executive of the company whose stock you are buying or selling, and who likely knows more about its condition and prospects than even the smartest and best-informed security analyst. Trading individual stocks is like playing tennis against an invisible opponent; what you don't realize is that you are volleying with the Williams sisters."

Other than the very occasional stock we might add to a larger portfolio, we are going to turn stock picking over to those wishing to participate in "the losers game" or the true experts. For those who do not have a clue as to how well their portfolio is performing with respect to a benchmark, index investing is highly recommended. Portfolio performance ignorance is no excuse to continue playing the stock picking game.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.