The simple math of investment returns and expenses

David Peartree, The Daily Record Newswire

Some of the most fundamental truths about investing revolve around very basic math. The concepts are obvious once stated but the implications for investors can be profound if they learn to accept and act on the obvious.

Last year, William Sharpe, a Nobel Laureate in Economics, and more recently John Bogle, the founder and former CEO of The Vanguard Group, published separate articles in the Financial Analysts Journal addressing the arithmetic of investment returns and expenses.

The arguments they make are apparently not so obvious that this prestigious journal thought their analyses a waste of time. Very likely, too many investors and their advisors are ignoring the obvious because of their own biases and overconfidence.

Market return = Average return. Start with the idea that investors as a group can earn no more than the market return. As Bogle might say, “duh.” The gross market return equals the average weighted return of all securities held by investors.

This is true no matter what market we consider: the S&P 500, the total U.S. stock market, the international stock market, or any of the bond markets. This is pretty straightforward stuff, except that the market return, the average, is what investors get before any expenses are considered. Nobody invests for free and investors tend to overlook or minimize the total costs and other frictions associated with investing.

Actual returns = Gross returns — Costs of investing. There are costs to buy, costs to hold, costs to sell, management and administrative charges, taxes and other potential expenses or drags on performance. The actual returns experienced by investors on average are necessarily something less than the market returns.

Much ink has been spilt over the years discussing a facet of portfolio theory known as the “Efficient Market Hypothesis,” a theory concerning the degree to which the markets are efficient or inefficient. Bogle does not dismiss the Efficient Market Hypothesis; it’s backed by strong evidence and it appears largely true even if it does not fully explain market performance.

He does, however, propose a simpler, more practical theory that should animate investors’ thinking and actions, what he calls the Cost Matters Hypothesis. “No matter how efficient or inefficient markets may be, the returns earned by investors as a group must fall short of the market returns by precisely the amount of the aggregate costs they incur.”

It turns out that investors have no control over market returns (another obvious but ignored reality) but they can control their investment expenses. Expenses have a direct impact on the actual returns experienced by investors and this makes it critically important to understand the scope and nature of investment expenses.

What are the all-in expenses of investing? More than most investors think. Sharpe’s study (“The Arithmetic of Investment Expenses”) focuses on fund expense ratios, while Bogle’s analysis (“The Arithmetic of ‘All-In’ Investment Expenses”) looks at the full gamut of expenses that detract from investors’ returns.

The most significant expense is a fund’s expense ratio. The expense ratio refers to the percentage of the fund used to cover administrative and management costs. Sharpe’s study cites an average expense ratio of 1.1 percent for a U.S. stock fund. International funds tend to have a higher expense ratio; bond funds tend to have a lower ratio.

The additional and largely hidden costs include transaction costs and cash drag. Bogle adds another .50 percent of transaction costs for the average actively managed fund. Although he points to other studies finding higher transaction costs (one study reported 1.4 percent on average), he adopts .50 percent as a conservative estimate.

Cash drag is another cost. Actively managed funds often hold 5 percent or more in cash while looking for investment opportunities. He estimates another .15 percent cost to investors caused by managers holding cash. This is, in effect, the cost of lost opportunity.

All-in, he estimates that the average fund investor pays costs of over 1.7 percent of their account value. Even that figure is before accounting for sales loads or advisory fees for which he adds another .5 percent, or taxes for which he adds another .45 percent.

The impact of these expenses over a period of years is startling. Sharpe’s study, which compared only the expense ratio of the average mutual fund and a low cost total stock market index fund, found the wealth accumulation in the lower cost fund was 11 percent greater over 10 years and more than 20 percent greater over 30 years.

Sharpe’s example assumed an investor making annual retirement contributions over the period of accumulation. John Bogle ran a similar analysis but, in addition to the expense ratio, he factored in the impact of the other investment expenses noted above. Bogle finds that the wealth accumulation in the lower cost fund was 13 percent greater over 10 years and 44 percent greater over 30 years.

Fund expense ratios are “the most dependable predictor of performance,” says Russell Kinnel, the director of fund research at Morningstar, a leading provider of fund data and analysis. If true, then controlling the “all-in” expenses of investing is even more important.

Heed Bogle’s warning: “Do not allow the tyranny of compounding costs to overwhelm the magic of compounding returns.”

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David Peartree, JD, CFP® is the principal of Worth Considering, Inc., a registered investment advisor offering fee-only investment and financial advice to individuals and families.  Offices are located at 160 Linden Oaks, Rochester, NY 14625; email david@worthconsidering.com.