Before 2008, I reviewed many Monte Carlo simulations showing 4% or more safe-spend rates, increasing annually with inflation. Not only did the assumptions generally ignore expenses, but they also included excess return from alpha. While the efficient market hypothesis can be debated forever, one thing is clear. In its sum, alpha is zero.

This was clearly illustrated back in 1981 by the Nobel laureate William F. Sharpe in his simple paper The Arithmetic of Active Management. Simply stated, these two statements must be true:

• Before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar.
• After costs, the return on the average actively managed dollar will be less than the return on the average passively managed dollar.

This simple arithmetic is perhaps why, as of March 31, 2014, roughly 31% of investments in U.S. stock funds are in index funds, according to Strategic Insight.

The impact of trying to find alpha for clients’ portfolios lowers returns for three mathematically certain reasons. The first is simple: alpha costs more and, in the aggregate, the average return must be equal to the market return minus costs.

The second reason is that alpha is less tax efficient, as more trading must be done, passing through taxable consequences to clients.

The third is a bit more complex: subsets of market securities are more volatile than the market itself, and higher volatility leads to lower return. For instance, the tech sector has recently been more volatile than the total U.S. stock market, both on the upside and the downside. That volatility can result in some interesting mathematics.

As an example, consider Fund A, which gains 30% in one year and loses 10% the next year. The fund’s simple average return is 10% annually, though the geometric return of the investor who owned it for those two years is 8.2% annually. Fund B gains 10% each year and has both an arithmetic and geometric average of 10%. The investor putting \$100 in Fund A has \$117 while the investor in Fund B has \$121.

So unless you’ve found the next Warren Buffett, the quest for alpha has nearly a long-run mathematical certainty of lowering client returns and safe spend rates in retirement.

Allan S. Roth, a Financial Planning contributing writer, is founder of the planning firm Wealth Logic in Colorado Springs, Colo. He also writes for CBS MoneyWatch.com and has taught investing at three universities.

#### Allan S. Roth

Allan S. Roth, a Financial Planning contributing writer, is founder of the planning firm Wealth Logic in Colorado Springs, Colo. He also writes for AARP and has taught investing at three universities.