*"...alternative frames evoke different mathematical intuitions, and one is much superior to the other." - Daniel Kahneman in Thinking, Fast and Slow*

This recent post covered why the long-term investor should actually prefer that the stocks they own for the long-term will underperform in the near-term and even intermediate term. In fact, maybe somewhat oddly, that investor shouldn't mind this even if (annoyingly) the stock drops meaningfully right after it has been bought.

Now, when a high price is paid, and the long-term outcome is dependent on speculative assumptions, this won't work. Assumptions that, while possibly even not unreasonable, cannot be known with enough certainty to narrow the range of outcomes.

Yet the real problem might be more about mathematical intuition and framing effects.

Think of it this way. Consider a stock with a price-to-earnings (P/E) of 100. Naturally, a stock like that must have significant growth prospects if it's going to work out well for owners. There's just not enough current earnings relative to price to provide a meaningful tailwind or sufficient return for the capital at risk. If earnings, for example, were to unexpectedly flatline, it'll be 100 years before the cumulative earnings will equal the price paid. Let's say, as a result of this disappointment, the stock were to fall by 50%. Well, it would still require, without growth resuming, 50 years of earnings to equal price. So, even after a quite large decline, without some real future growth, the price paid will still lead to a very unattractive outcome. The continuing shareholders who decide to hang on and wait for growth to resume, unfortunately, can't rely on buybacks to help the situation very much either. Here the investor is dependent on things not controllable: whether growth will return and will be sustained for a rather long time into the future.

Figuring this out may not be impossible but, to me, sure seems like a recipe for making some big mistakes.

Here's where the framing effects and their critical impact on decision-making becomes more apparent:

A 50% drop from 100 times earnings only increases the earnings yield from 1% to 2%.

In contrast, pay 10 times earnings for something with modest or even no growth prospects and every ten years or so it produces in earnings what was paid. If the stock price were to drop 50% for some reason, each incremental purchase makes a big difference whether via buybacks or through incremental purchases by the owner.

A 50% drop from 10 times earning increases the earnings yield increases from 10% to 20%.

In both cases, it was a 50% drop in price but the improvement in earnings yield is vastly different.

Framing in terms of earnings yield instead of price-to-earnings makes this more intuitive.

This is a big part of the reason why paying speculative premiums on stocks can be so dangerous. It's why I prefer to think in terms of earnings yield instead of price to earnings. Some will choose to discount the importance of framing effects, but I think some familiarity with what's known as "The MPG Illusion" just might change that.

Below is a quick explanation of "The MPG Illusion" but it's well worth reading up further on the subject:

Let's say you and a friend each have a car.

The one you own is a gas guzzler that gets 6 MPG. Your friend's current car gets 20 MPG.

Both of you are about to purchase new ones.

Both of you happen to drive the same number of miles each year.

The car you end up buying gets a still rather paltry 8 MPG.

Your friends new car gets 40 MPG.

Which

*decision*results in more fuel savings?

Seems straightforward enough.

Your car only improves MPG by 2 or 33%.

The other car improves MPG by 20 or 100%.

This seems like a no-brainer: trading in your car improves gas mileage by only 2 mpg (33%), while your friends car improves gas mileage by 20 mpg (100%).

So the intuition points us to what seems an obvious answer. Well, it's not so obvious.

Here's the math. If each car drives 12,000 miles a year...

Then you used to use 2000 gallons per year (12000 miles/6 MPG).

Doing the same math, the new car will use up 1500 gallons per year.

So the saving is 500 gallons per year.

Your friend, on the other hand, used to use 600 gallons per year (12000 miles/20 MPG) but, doing the same math, now uses 300 gallons.

So the saving that comes out of this decision is only 300 gallons.

It turns out that gallons per mile (GPM) is more intuitive. The inverse framing make this dynamic more plain and less likely to lead to misjudgments.

The 40 MPG car obviously still burns less gas overall, but the

*decision*to go from 20 MPG to 40 MPG versus from 6 to 8, counterintuitively, does not save as much fuel.

So how something is framed matters a lot.

Price to earnings functions much like MPG.

Earnings yield functions much like GPM.

So the high P/E stock is like the fuel efficient car. It's the better story to tell but much more is needed than intuition would suggest.

The low P/E stock is like the gas guzzler. It's still a lousy story but not much is needed for good things to happen.

Incremental earnings yield (as price drops) is a big advantage for the low P/E stock.

Incremental reduction in GPM (as efficiency increases) is a big advantage for the gas guzzler.

The more intuitive way to guide fuel economy decision-making is GPM.

The more intuitive way to guide investment decision-making is earnings yield.

This doesn't mean no high P/E stock deserves to sell at such a premium.

This does mean investors might decide to take more risk than they need to, in part, because of the way the information is framed.

So MPG is not the best way to frame fuel efficiency, and P/E is not the best way to frame business valuation.

For investors to consider the risk and reward appropriately, they need to be careful that how something is framed isn't getting in the way of sound judgments.

I suspect that one of the reasons market participants tend to overpay for growth is at least partially caused but this. I also think sometimes those who learn the higher and more complex maths forget the power of good old-fashioned arithmetic.

There's certainly nothing at all wrong with attempting to get attractive investment results through something that has exciting growth prospects.

The problems begin when a premium to current value is paid -- even one that seems warranted because of the excellent prospects -- in an always uncertain world. When the range of future outcomes is very wide (i.e. when judging what the future cash flows will be is difficult at best) it's tough to determine what's an appropriate margin of safety to reduce the likelihood of permanent capital loss.

Those that can avoid the big losses meaningfully improve their chances of doing well. This requires, at the very least, that a reasonable price is paid in the first place. This depends on owning long-term only what's truly well understood.

When the multiple of earnings paid is low, all that has to be judged is whether those earnings are mostly sustainable* to get a good or better investment outcome. That's not necessarily easy but, compared to judging which high flyer will live up their long-term potential, it sure seems more reliably doable.

With lower multiple stocks -- those, for example, with maybe modest or no growth but at least some sustainable advantages -- the end result can be an attractive one as long as capital allocation is done reasonably well.

Of course, that's hardly a given.

Some might argue that P/E is very different than MPG because the E can change significantly.

While that's clearly not wrong, it is a distraction from how the illusion contributes to misjudgments.

Related posts:

Multiple Expansion, Buybacks, & The P/E Illusion (Follow-up)

The Benefits of a Declining Stock

Buffett's Purchase of IBM Revisited

Buffett on Buybacks, Book Value, and Intrinsic Value

Buffett on Teledyne's Henry Singleton

Why Buffett Wants IBM's Shares "To Languish"

Buffett: When it's Advisable for a Company to Repurchase Shares

The Best Use of Corporate Cash

Buffett on Stock Buybacks - Part II

Buffett on Stock Buybacks

Buy a Stock...Hope the Price Drops?

* At extremely low earnings multiples, a decline in earnings may not even be a problem if the capital is well allocated and the business is otherwise sustainable. Of course, it's important that the business not be collapsing and will be around for a long time with, at least, similar core economics. Growth is either irrelevant or a bonus.

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