Unintended Errors from Flaws of Comparisons in the Investment World

Illustration: The Aesop Tale of the Hare and the Tortoise                                                                                

The flaws of comparing two different things using just one metric …

Should you try to compare different investments with each other simply by balances alone?

Markets have been going up [at the time I write this] and people feel good when they look at their statements. The hare is ahead in the race. New market highs makes it irresistible not to check balances.

When the markets are doing well, it’s “fun” to check your balances because that produces dopamine and you feel good (and markets have done well year over year since 2020).

This can then lead to bad decisions when you see balances go down (which they’re likely to do every year, not just this year because markets have gone down sometime every year in the past … so don’t be surprised when they do). This checking-balances-too-often is a mistake … so you should check less often and avoid mental and behavioral mistakes! [Another reason will be discussed below relating to the proper way to calculate returns].

When all you do to measure investment success is to compare today’s balance to a past balance, your brain is getting fooled.

Your brain gets extra fooled when you compare two different accounts with different allocations and different holdings making up those allocations as well as different cash flows… and that’s the main point for this piece. You can’t compare apples and oranges.

So why does this subtle distinction matter to you?

Taking mental shortcuts, called heuristics, leads to bad decision making.

Framing comparisons solely by comparing balances is a framing heuristic… and a bad one at that. Bad because it short circuits the fundamental question – Why?

Why might one be doing better than the other?

Below is a discussion of some things to consider when answering the question – Why?

First, comparisons may only work when you do nothing with that/those account(s)! You don’t add any contributions, AND you don’t make any withdrawals. That sounds like it might work for some if they think this is what they’re doing – not making withdrawals. But you ARE still adding contributions indirectly via dividends, interest and capital gains.

Also, different holdings have different cash flows from differences in dividends, differences in interest, and differences in capital gains. So when you decide (take a mental shortcut) that one investment is doing better than another, you’ve taken a mental shortcut ignoring those differences between what you’re comparing … when all you do it compare balances over time.

Finally, in addition to the above …

When you have different risk exposures (i.e., allocations are different) between what you are comparing, you get different results! That should come as no surprise, but most people forget this fundamental fact.

So by framing choice by only one thing (balances), it’s an apples to oranges comparison from the get-go. You can NOT compare different things by balance comparison alone!

What should you do instead … how should you think about differences?

Are you working and contribution? Or are you retired and withdrawing?

The above introduction having been said, temporarily while you are working and making contributions, you may seek slightly greater returns through greater risk. Why? Because that greater risk means greater volatility. That downward volatility is where you buy more shares! More of something going up is where you’re additional gains, relative to fewer shares, comes from.

Always remember that risk and return are on opposite sides of the ladder and go hand in hand together … higher return as you go higher up goes hand in hand with higher risk and volatility too.

When actively making contributions of your own earned dollars while working, you are actually not really seeking greater return after all, you’re seeking to maximize the number of shares you own. This can backfire though if the diversification of your holdings are not also optimized as well. Diversification and allocation are NOT the same.

To be more specific … In brief … the principles of Modern Portfolio Theory, where diversification and optimization are diligently applied to your portfolios to put your money on the efficient frontier. Why? Because these are the best-known principles today that help you reach your goals by balancing risk with return across many academically identified and defined asset classes

Two identical allocations in two accounts on the surface, for example, both being 60% global stocks and 40% global bonds will have different results if the first one is optimized and the second one is not (paragraph above introduced optimization).

Even though they are both 60/40 allocations, the optimized allocation will produce better results (read more dollars) over the long run (the rest of your life) because it is more efficient by design … meaning those dollars are working harder than the non-optimized allocation. This is an important point most people miss! Identical allocations often do not produce identical results!

So, it’s okay to take a little more risk when you’re making contributions so that you get a little more volatility … which may provide buying more shares than you could with lesser risk. Your wealth (balances) go UP over time simply by having more shares to go up! Now, it is not necessary to take a little more risk though, because you’re still buying more shares through those additional contributions anyway.

The riskier, contributions while working (read your employer retirement account like a 401k, 403b, 457, etc) also grow faster simply because you’re adding more money on a regular basis! Of course that balance will grow over time … because contributions are buying more shares!

But … the farther something goes down, the longer it takes to get back to where it was (relative to a less risky portfolio that doesn’t go down as much … less risky portfolio gets back sooner).

Also, TIME is the key too.

The closer you get to retirement, the closer your portfolio allocation should be to the optimum allocation you should have when you retire. Remember, once retired, AND regardless of retirement age, you still have years ahead of you IN retirement!

However, the biggest apples and oranges comparison is between a riskier account where you’re making contributions with a less risky account where you are NOT contributing (and even bigger when withdrawing money).

Once retired, the riskiness of the allocation should also slowly go down with TIME (age). The older you are, the less time you have for an allocation to recover from market misbehavior. This COMBINED with the fact that withdrawals means you’re selling more shares (when you run out of shares is when you run out of money.

I ALWAYS SUGGEST LOOKING AT NUMBER OF SHARES INSTEAD OF BALANCES, WHILE WORKING AND WHILE RETIRED).

Thus, age and time go hand in hand regardless of whether you’re working (contributing) or retired (withdrawing). The proper optimum allocation is based TIME (AGE).

Moral of the story:

The cautionary tale of the hare and the tortoise is why it matters. “The race is not always to the swift.”

Greater returns means greater risk … the question is … is that really the risk you want? And, is that an optimal risk compared to those returns (and are those returns optimal as well)?

The hare may lead the race towards the beginning (when you’re working), but the tortoise may lead the race to cross the finish line (when you’re retired) because it takes longer to recover when markets misbehave, and they always do (think 2001, 2008 and 2020 as most recent examples).

In other words, seeking a greater return often leads to greater loss. TIME (AGE) plays a huge part in what kind of risk you should take since the further allocations drop, the longer to recovery (the farther behind you get).

Those larger declines of a riskier allocation are akin to the hare taking a nap, while the less risky allocation catches up sooner and passes the riskier one.

When you have lots of time ahead of you, it doesn’t really matter, especially while making contributions (up to your own personal limits of comfort with risk) … you BUY MORE shares.

The race outcome does matter, when time continues to shrink and shrink it does as you approach retirement, as well as in retirement, combined with the fact that you SELL MORE shares when markets misbehave as they always do, and will continue to do so, in the future.

Remember, when you run out of shares, that’s when you run out of money!

PS. A related comparison between different holdings is trying to calculate rate of return on your own. That is a flawed approach and you should not do that. Investment returns calculated by investment companies doing this properly through geometric returns should be used. The difference between geometric returns (investments) and arithmetic average returns is beyond the scope of this piece (but is discussed here for those wishing to dive deeper (and you may ignore the advertisement at the end as well as others on the page)).

Back of the napkin returns calculations just don’t cut it when you’re trying to compare one thing to another. Those comparative returns need to meet standards in order to compare apples to apples and oranges to oranges.

Here’s a great deep dive into the issue of calculating returns properly for comparison between different investments, for those who wish to even dive deeper for a better understanding, where the Modified Dietz Method may even be used.

Ultimate moral of the story:

So, you see … trying to calculate returns or compare balances on your own is fraught with plenty of errors! How do you avoid some of these errors? Check your balances sparingly. And when you do, look at the number of shares rather than balances (which go all over the map).

The prudent measure is how fast or slow you’re accumulating, or spending down, NUMBER OF SHARES.

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