Penny Singleton, left, and Arthur Lake, from 1947's Blondie's Holiday."

CHAPEL HILL, N.C. (MarketWatch)Not all methods for calculating investment performance are created equal. Thats important to point out because many of us otherwise think that performance is a simple, straightforward fact.

In fact, however, there are numerous ways of calculating performance that reach dramatically different conclusions. While each method can be factually correct, they can also be highly misleading. And if financial advisers arent careful when comparing managers for their clients, they can inadvertently end up comparing apples to oranges if those managers calculate their returns in different ways.

To illustrate this, consider the contrasting returns of the Value Line Arithmetic and Value Line Geometric indexes, both calculated by the well-known research institution Value Line Inc. Both indexes include the same 1,700 widely-followed U.S. stocks, and both give equal weight to each stock each day. Neither includes dividends.

Yet their returns over the last 20 years could hardly be more divergent. As illustrated in the accompanying chart, the Value Line Arithmetic index has gained 563% since August 1997 while the Value Line Geometric index has gained just 17%. (On an annualized basis, this is the difference between 9.9% and 0.8%.)

Why such a big difference? Their names provide the clue: The Arithmetic index is based on the return of the average stock (the arithmetic average) while the Geometric index uses the return of the median stock (the geometric average).

Value Line details this on its website, further explaining that the daily percentage price change of the Value Line Arithmetic Index will[in virtually all circumstances] be higher than the Value Line Geometric IndexThe greater the market volatility, the larger the spread between the geometric and arithmetic averages becomes.

This isnt a criticism of Value Line. The firm is well aware of the differences between the indexes, and would be the first to say that both indexes have their plusses and minuses.

My point here is that unscrupulous or unsuspecting advisers can draw hugely different conclusions depending on which index they use as their performance benchmark. Big as it is, the contrast between the two Value Line indexes is just the tip of the iceberg when it comes to the divergent stories you can tell using different performance methodologies.

Below are some common ways in which unsuspecting or unscrupulous advisers can tell highly misleading stories even when their actual performance calculations are factually correct:

Overlooking the asymmetry between gains and losses. To overcome a percentage loss of any size, it takes an even bigger percentage gain. A 50% loss, for example, requires a subsequent 100% gain to break-even.

Its therefore possible for a losing strategy to accurately report that the average gain of its recommended stocks nevertheless has been positive. You therefore should be skeptical of any performance claim of the form the average gain of our recommendations is X%.

Ignoring the impact of unequal portfolio allocations. Hardly any responsible adviser would allocate as much to a stock option as to a broadly-diversified stock index fund. But when performance is reported as a simple average of all recommendations, the implicit assumption is that there was an equal amount allocated to both.

Once again, you should be skeptical of performance claims reported as simple averages.

Misuse of annualization. Any gains turned in over periods of less than a year can be made to look huge by annualizing them. Consider an option that doubles over a months timea gain that, in and of itself, is hardly unusual. On an annualized basis, however, its return becomes an eye-popping 409,500%.

An adviser who takes that gain into account when calculating his average can make it appear as though he made money even when all other of his recommendations lost money.

Path dependency. It makes a big difference to how much money you make whether your gains occur before your losses, or after. This is also known as sequence risk, and since I devoted a column to it earlier this year I wont belabor the point here.

Suffice it to say that unsuspecting or unscrupulous advisers can paint false pictures by glossing over this dependency or risk.

The best way to report performance, in my opinion: How much money is made by an actual portfolio over the long term expressed as a percentage change.

While it might seem Draconian, I advise investors to ignore advisers with track records shorter than 15 year. The unfortunate reality is that over shorter periods there is a too-high probability that market-beating performance was due to luck rather than skill.

Such an approach neatly sidesteps the issues involved with each of the pitfalls identified above. And, when reported this way, the performance is closest to what your individual performance would have been if youd following that adviser in the real world.

Perhaps not surprisingly, many advisers choose not to report their performance this way. Though they may have legitimate reasons for doing so, that doesnt mean you have to take their performance claims at face value.

At a minimum, you should carefully analyze how a managers performance numbers are calculated to insure that youre comparing apples to oranges.

While it is no doubt frustrating that we cant simply rely on performance numbers to tell a complete and accurate story, we cant. We unfortunately have no other choice but to adopt a trust but verify attitude toward any and all performance claims.

For more information, including descriptions of the Hulbert Sentiment Indices, go to The Hulbert Financial Digest or email mark@hulbertratings.com.

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Why measuring investment performance is trickier than you think - MarketWatch