Some things change. Others don’t.

Costs matter. This is one of the eternal verities of investing. We know this from John Bogle, founder of Vanguard and patron saint of index investing. If we act on this simple fact, we can improve our investment results.

This isn’t what Wall Street tells us. The investment community tells us that only its constant attention, its cadres of M.B.A.s and Ph.D.s, and its special knowledge of the world can lead us to good returns. They intimate that the more we pay them, the more likely we will get superior performance. They spend millions of dollars on advertising to convince us.

Alas, it isn’t so.

A simple exercise with the cost factor, however, can improve our results. Let me demonstrate.

At the end of May, there were 194 mutual funds that Morningstar categorized as “moderate allocation,” or balanced, funds with at least five-year histories. These funds are typically a 60/40 mix of equities and fixed income. Their annualized return over the last five miserable years was 0.94 percent. Their average net expense ratio was 1.17 percent.

The top 25 percent of funds by expense cost at least 1.35 percent to manage, averaged 1.8 percent in expenses and produced an average return of 0.21 percent. If you selected from this group at random, hoping that high expenses would buy better management, you had only a 32 percent chance of doing better than average.

If you went in the other direction and chose from the 25 percent of funds that were least expensive, costing 0.88 percent or less a year to manage, the average return was 1.4 percent a year. You had a 55 percent chance of beating the average for the category. In other words, you’ve got a better shot — not a guaranteed shot, just a better shot — at superior results if you insist on lower expenses.

We can improve our odds a bit by selecting from the 25 largest funds. Doing that gives us an average return of 1.33 percent and a 60 percent chance of beating the average fund. One reason is that the largest funds also tend to have lower expense ratios — the group averages 0.75 percent. We can, in other words, virtually double our chance of above-average performance simply by favoring the large funds that tend to have lower expense ratios. We’ll have a 60 percent chance of above-average return rather than only a 32 percent chance.

Not thrilled by those odds? I don’t blame you. This is your retirement money we’re talking about.

Thankfully, there is a better way. Marketwatch columnist Paul Farrell calls it the “lazy portfolio” way. Years ago he started reporting on the performance of do-it-yourself portfolios that could be built with low-cost index funds. These portfolios range from some of my Couch Potato portfolios to Bill Schultheis’ “Coffeehouse” portfolios, William Bernstein’s “Coward’s Portfolio” and David Swensen’s “Yale Model” portfolio. (Today there are quite a few of these funds — trailing performance figures for 30 of them are reported monthly on my website, www.?

Eighteen months ago I showed that 11 of 14 balanced “lazy portfolios” beat the average for all balanced mutual funds over the preceding three years. So taking the lazy way out gives you a 79 percent chance of beating the category average.

The superior performance of these lazy portfolios continues today. If there were ever a period when perceptive selling and wise buying should have made a difference and put managed funds on top of the heap, it has to be the last five years. But superior decision making, once again, did not prevail. Measured over the five years ending May 31, the average managed balanced fund provided an annualized return of 0.94 percent. Over the same period, the 25 largest funds returned 1.33 percent. But the 14 lazy portfolios averaged 1.45 percent, and a random choice would have provided an 85 percent chance of beating the average.

What does this mean for you and me? It means don’t be afraid. If you have fear and anxiety about making your own investment decisions — fear that you don’t know enough, fear that professionals will make much better decisions — it’s time to take a reality bath. The reality is if you choose just about any “lazy portfolio,” odds are you will do better than if you choose the more expensive alternatives. There is no certainty. All we can do is search for the best odds.

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