# Why Losses Hurt More than Gains Feel Good: Part 1. When 1 Doesn’t Equal 1

Written by Bruce Yates, Financial Advisor and Founding Shareholder

Many investors assume that as long as they are right more times than they’re wrong, they will end up with good results. That is a logical assumption. If you buy three stocks in succession, for instance, and two of them produce big gains, and only one of them suffers a loss of equal size, you should still come out pretty well…shouldn’t you?

Well, like many things, it’s not that simple. Understanding *why*, and the extent to which, that often is *not* the case is one of the most important investment concepts that you
can learn. It will certainly give you a better
foundation and perspective from which to view investment risk.

Let’s say we have $1,000, and we use it to buy one stock whose value can only do one of two things each year: it either goes up 50% or down 50%. The first year it goes up 50%, and the second year it loses 50%. We’re right back where we started, right? Then the third year it gains 50% gain. So we’ve had two years when this stock was a big winner and only one year when it was a loser. We should end up with a pretty good overall 3-year return, don’t you think? After all, when you add up those three returns (+50 -50 +50 = 50) and divide by 3, the average return seems like about 17% per year.

**Gain/Loss
Twilight Zone**

But let’s do the calculations, because the return is actually less than 17%…a *lot *less. As you can see in Table 1, the first year’s 50% gain turns our $1,000 into $1,500. When we then lose 50%, we are *not* back at $1,000, but rather we are down to $750 (50% of $1,500). Clearly, a 50% loss and 50% gain are not equal, and the loss hurts a lot worse. Even our third year’s 50% gain only takes us from $750 up to $1,125. (By the way, the end result is the same, regardless of what order those returns occur.)

**Table 1. Impact of Gain and Loss **

After what initially seemed like a great three-year run, our cumulative return on a $1,000 investment is only $125, which equates to about 4% per year, nowhere near the 17% we got by adding +50, -50 and +50 and dividing by 3. You really can be right, with big gains two out of three times, but end up just barely ahead of where you started.

This counter-intuitive phenomenon makes you stop and think,
doesn’t it? It certainly caused a
“paradigm shift” in the way I viewed risk years ago. Now let’s examine *why* this odd relationship between gains and losses works the way it
does, and how it pertains to you.

**Disproportional
Impact**

In the field of Behavioral Economics, research suggests that humans have a natural “loss aversion” (Kahneman & Tversky, 1979) that makes us perceive/feel potential investment losses as being worse (roughly twice as bad) as the positive emotions we feel about potential gains. It’s as if we somehow intuitively know that there is something worse about losses…and there is.

To better understand this, suppose that, in the first two years of our above example, we had added 500 *dollars* and then subtracted 500 dollars (both being 50% of our starting $1,000)? In that case, we *would* have ended up back at our original $1,000. The dollar gain and loss *would *be equal.

The difference is that our original example used successive *percentage* returns, not *dollar* gains and losses. Percent returns are, after all, what both you and the investment industry typically use when discussing investment results. So we need to be careful when comparing percent returns to one another, because, as we saw above, losing 50 *percent* does considerably more dollar damage than a 50 percent gain helps us, so they are *not *equal.

**What Percentages ****Are**** Equivalent?**

If a 50% gain doesn’t equal/offset a 50% loss, what *would* offset that 50% loss? Well, if we started with $1,000, a 50% loss would reduce our principal to $500. To get back to $1,000, we now need $500 more, or *double* the $500 we still have. Thus, it will take a gain of *100%* to recoup that loss!

You might think, “Well, how often do 50% losses (on a person’s
entire portfolio) really happen?” Not
very often, thankfully, but perhaps more often than you think. The last two
major bear markets (when the dot-com bubble burst in 2000, and when the Credit
Crisis struck in 2007) saw the S&P 500 index drop 49.1% and 56.4%,
respectively. Investors who had all of
their money in the stock market at those times likely *did* have 50% (or greater) declines in their total portfolios. To get the S&P 500 back to its pre-bear-market
levels required that it gain 96% and 129%, respectively, because those are the
“equivalent” gains needed to recoup 49.1% and 56.4% losses.

Table 2 takes this principal another step. It shows a number of possible losses, along with their corresponding gains. It includes the 50% loss—and 100% offsetting gain—that we were discussing above.

**Table 2. GAIN/LOSS EQUIVALENCIES **

Do you notice a trend in the relationship between the two columns? Are the gains needed to offset losses always *twice* as much, as is the case with 50%? On the contrary, losses less than 50% require gains *less* than twice as large, and losses greater than 50% require gains *more* than twice as large. In other words:

You can really see this in Table 3 below, which is the same
as Table 2, but with a third column added to show just how *much* larger each offsetting gain must be. I’ve used three colors to arbitrarily group them
according to increasingly disproportional gains needed to offset losses.

**Table 3. GAIN/LOSS EQUIVALENCIES, AND GAINS RELATIVE TO LOSSES**

Look at the top (green) section of the table. It really doesn’t take a big gain to recover from a small loss, does it? In fact, if we could limit losses to 5% or 10%, the gains needed to recover from them are barely larger than the losses, and those gains are certainly achievable. Even with 15% and 20% losses, the gains needed to recoup them aren’t too much larger than loss. But what about a 40% loss? A 60% or 70% loss?

Large losses really require *huge* gains to offset/recoup them. Indeed, as you look at the red section, and
the gains needed to recoup losses of 60%-90%, your first thought might (and
probably *should*) be something like,
“Yikes!” A loss like that to your total
investment portfolio is what I call a “Big Bad Surprise” (BBS), and avoiding that
should be a goal for every investor.

If nothing else, I hope this article has wiped from your
mind the idea that if you “win a few and lose a few,” it all evens out. In the world of investing, that just is *not* always true.

**What’s
Next **

In the other two articles in this series, we will look at what the disproportional impact of gains and losses means for investors, and ways to avoid having a BBS in your future.

**Part 2** explores the implications of these concepts for different investors, specifically **Retirees,** who generally require gains *even larger* than those in the above tables to recoup losses, and **Speculators**, who tend to operate in the red section of Table 3.

**Part 3** explains some of the tools/practices that can help reduce your investment portfolio’s exposure to huge (BBS) losses. They include a number of practices that we employ at Viridian in managing client portfolios. The objective of utilizing them is to move your portfolio up a few rows in Table 3 (i.e., suffer smaller losses, and therefore be able to recoup them more easily).

Author’s Note: This 3-part
series is excerpted from my upcoming book, *The
Reluctant Investor.*

*Viridian is an SEC Registered Investment Advisor (RIA) with clients across the United States. Viridian offers financial planning, investment management, and tax services (through its sister company, Viridian Tax and Accounting). Bruce Yates has been a fiduciary financial advisor for almost 35 years, and he is one of Viridian’s four Founding Shareholders.*

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