When is a loss not a loss?

So you invested with fund manager Kevin earlier this year. Unfortunately, he’s already down 20%. Not to worry, says Kevin. It’s merely a paper loss, “stored alpha”[1] that you’ll earn back soon. Kevin promises to be like Warren Buffett and “never risk permanent loss of investment capital” although “quotational shrinkage for extended periods can’t be avoided.”[2] You see, you haven’t actually lost 20%, it’s merely quotational shrinkage, like a silly typo that the market will get around to correcting eventually. In fact, Kevin is glad he’s down 20% because now he can buy more securities for you at bargain prices. Each loss he incurred is actually a coiled profit ready to spring.

Kevin grows animated. The important thing is not to panic and pull out; you’ve got to ignore meaningless volatility because as Howard Marks says, “Permanent loss is very different from volatility or fluctuation.”[3] The drawdown is an unpleasant but necessary step on the road to Kevin’s total vindication: it’s the broccoli before the ice cream; the darkness before the dawn; the Death Star before Luke Skywalker’s inevitable victory. Loss is just another word for profit that hasn’t happened yet. Your money isn’t really “lost”; it’s just on vacation.

Is Kevin spouting nonsense? Yes, mostly. Is it possible for Kevin, or anyone else, to identify securities that will never have “permanent loss of investment capital?” No, that’s delusional, unless we’re talking about riskless Treasuries. No individual can magically know which risky assets are guaranteed to go up over the long-term; that’s what “risky” means.

Given that Kevin is spouting nonsense, should you fire him? Not necessarily. You’re hiring him for his ability to pick securities on a forward-looking basis, not for his wisdom about return predictability (you can get wisdom from me for free).

Is there any truth at all to Kevin’s claims? Yes, some truth. Here's the big picture:

• Almost all losses are permanent. Usually, when you lose money in financial markets, it’s not coming back. It’s gone forever. A loss is not a boomerang; a loss is a loss.
• Some losses are partly temporary. In some situations, you’d expect to earn back part of your losses either over the coming days or weeks (short-term reversals a.k.a. liquidity provision) or over the coming years or decades (long-term reversals a.k.a. time-varying expected returns a.k.a. anchored strategies).
• Denial is not a river in Egypt. When anyone, even Warren Buffett, uses a six-syllable euphemism (“quotational shrinkage”) for a one-syllable concept (“loss”), that’s a red flag.
• Tomorrow is another day. You should make decisions based on forward-looking probability assessments, not on backward-looking denial of losses (of course, your forward-looking assessments must reflect the tax and trading consequences of past decisions).

Let me sketch out two extreme scenarios: one where losses never come back, and one where sometimes losses are reversed in the future.

Scenario 1: Returns are completely random

The most relevant scenario is when there is zero return predictability. You’ve heard of the famous random walk theory of efficient markets. Here, I start with an even simpler scenario where prices are constant but we still have the possibility of losses and gains due to random fundamental shocks.

Suppose you have two possible ways to invest your money. First, you can put your money in your mattress, earning a sure return of 0%. Second, you can buy a farm and hold it for many years. Each year, the farm will either generate $500K in profit or $300K in loss, with equal probability. Suppose we live in a world where there is zero price risk; the farm will last forever, every year generating profits with unchanged probability, and the market price of the farm will always be $1M.

Here, we never learn any new information about the fundamental value of the farm. The value is always $1M, and the expected cash flow is always $100K per year. So the farm is like a stock where the return is either +40% or -30% every year. The expected return is 10%, and the farm has a Sharpe ratio similar to the U.S. stock market (the return standard deviation is 40% and the Sharpe Ratio is 0.25).

Let’s say you have a 10-year investment horizon. You buy the farm for $1M and put the rest of your money in your mattress. Every year, if the farm makes a profit, you put cash in the mattress, and if the farm makes a loss, you remove cash from the mattress. How should we think about losses and wealth in this scenario? Let’s evaluate some claims.

• “Losses are stored alpha that you’ll get back.” No. If the farm loses $300K in a given year, you never get that money back. A loss is a loss.
• “Buy the dip.” No. A loss today predicts nothing about future profitability.
• “The worst thing to do is panic and sell after a drawdown.” It’s true that you shouldn’t panic, but in some settings it’s rational to sell after a series of losses.
• “There’s virtually no risk of loss if you hold for 10 years.” No. In this scenario, risk doesn’t magically disappear over long horizons.

Let’s do the math. If you expect to make profits of $100K a year, at the end of 10 years you expect a total profit of $1M. Sounds pretty good, right? Much better than the mattress.

Unfortunately, there’s always a downside. There’s a chance that you’ll get 10 straight losses in a row, in which case you end up losing $3M. Granted, there’s only a 0.1% chance of this extreme outcome, but there’s a 17% chance of losing at least $600K. So in this situation, “permanent financial loss” is a real possibility.

There’s a widespread misconception that stocks are riskless in the very long run, because if you hold the asset long enough, the risk cancels out or is dominated by the expected return. Untrue. While long-term risk is a complicated subject (see Campbell and Viceira (2002)), it’s generally true that as your horizon lengthens, your expected wealth rises but the worst-case scenario gets worse. If you hold the farm for 1 year, you expect to make $100K but the worst case scenario is -$300K. If you hold for 10 years, you expect to make $1M but the worst case is -$3M.

In this situation, would it ever make sense to sell the farm after a drawdown, or would that be irrational panic? If you have some minimum level of terminal wealth you’re trying to maintain, then you might want to sell the farm after a large drawdown, as argued by Grossman and Zhou (1993). While I’m skeptical that this stop-loss logic is useful for most investors, it’s certainly relevant for highly levered actors.

Let’s now consider a more complicated world where prices are not constant but instead move in response to new information. Suppose we learn that the farm’s best possible profit going forward will be $400K instead of $500K, so the expected annual cash flow will fall 50% from $100K to $50K. In response, the farm’s price will also fall 50%. If you own the farm, you suffer an immediate loss of $500K.

Here again, you aren’t getting that $500K back. It’s gone forever, like tears in rain.

The market price is a forward-looking estimate that embodies new information. It doesn’t matter if you sell the farm after 10 years or hold it forever. In this world, a loss is a loss, whether you choose to sell or not. That’s the standard, efficient market, random walk intuition, and it should be your baseline approach when considering moves in market prices. The market’s pretty efficient and future returns are close to being unpredictable.

Scenario 2: Returns are completely predictable

Suppose the price today of a 10-year zero-coupon Treasury bond is $80 and you believe the U.S. Treasury will never default. You buy this bond and plan to hold to maturity, receiving $100 for sure in 10 years.

Now suppose the price falls 20%. Is this loss a loss? In some sense, no. If you believe with metaphysical certitude that the bond will repay $100 in 10 years, and if the price falls 20% today, then you are going to get that 20% back at some point.

Here’s Cochrane (2011) describing this case:

Suppose now that bond prices plunge, and volatility surges … Should you sell in a panic to avoid the risk of further losses? No. You should tear up the statement. “Short-term volatility” is irrelevant. Every decline in price comes with a corresponding rise in expected return.

Why is scenario 2 different from scenario 1? For the farm, expected return is constant at 10%, and realized returns only depend on fundamental cash flow news. For the bond, expected returns (Treasury yields) rise from 2.3% to 5.6% when the price falls from $80 to $64, but there’s zero fundamental cash flow news.

So in scenario 1, realized returns are 100% driven by fundamentals and you cannot predict future returns. In scenario 2, realized returns are 100% driven by expected return movements, and a negative return today will be offset by a positive return in the future. Thus the bond has negatively autocorrelated returns or equivalently it has a mean-reverting valuation.

Let’s talk about time horizons. We know that a price fall from $80 to $64 will eventually reverse. It’s possible that this reversal takes place at the daily or intra-day horizon. Suppose the bond is very illiquid, with a bid price of $64 and an ask price of $80. Every day, we observe the price bouncing between bid and ask. Here, we see short-term negative autocorrelation of returns, reflecting liquidity provision by whoever is posting the bid and ask prices.

In this situation, when we observe the price fall from $80 to $64, can we say that this fall is merely “quotational shrinkage” that does not reflect long-term reality?

Well, sort of. It depends on your investment horizon and possible liquidity needs over the next 10 years. If you hold the bond to maturity and you buy at $80, you can just ignore the bid price of $64. On the other hand, if you have urgent need for cash sometime over the next 10 years, you might have to sell at the bid and experience “permanent” damage.

Let’s run through the same questions as before:

• “Losses are stored alpha that you’ll get back.” No, not in general. It depends on price vs. fundamentals. If the price falls from $80 to $64, then you do get your losses back. But if the price falls from $120 to $100, you don’t get that back.
• “Buy the dip.” No, not in general. It is true that the yield goes up when the price goes down, but it’s not obvious that you should wait for a dip before buying. Maybe the price is 80 today and will never be lower; don’t wait for a dip that may never come.
• “The worst thing to do is panic and sell after a drawdown.” Mostly yes, but if you have some maximum drawdown you’re allowed to incur, you still might rationally reduce your position after a series of losses.
• “There’s virtually no risk of loss if you hold for 10 years.” Yes, assuming a purchase price below 100 and you actually can hold for 10 years, and you are not fired after five years of losses.

Real world applications

In the real world, all assets are somewhere on the spectrum between scenario 1 and scenario 2. Individual stock returns are mostly unpredictable. Aggregate stock returns are pretty predictable at multi-year horizons. Let’s run through some cases.

Aggregate U.S. stock market

Some argue that because the stock market is too volatile, you should ignore its short-term volatility. That interpretation is a mistake. It’s completely true, as argued by Shiller (2014), that the aggregate stock market is excessively volatile relative to a world of constant returns (scenario 1) and we see long-run mean-reversion (scenario 2). But that fact does not imply that losses always get reversed.

Here’s my interpretation of Campbell and Shiller (1998). The aggregate stock market has long swings above and below its fundamental value. When the stock market is too expensive, as in 2000, it will eventually revert down to fundamentals, with low returns over the next 10 years. When the stock market is too cheap, as in 1976, it will eventually revert up to fundamentals, with high returns over the next 10 years.

What are the implications? Consider early August 2024. The market fell about 8% from its previous high. Let’s assume there was no new fundamental information that explains the fall. Does the Campbell and Shiller (1998) approach say “buy the dip, because the 8% will be reversed?” Absolutely not. Valuations, measured for example by the cyclically-adjusted price-earnings ratio (CAPE) were high in July. Therefore, the fall of prices in August was a movement of prices towards fundamentals that will never be reversed. In contrast, if the market had inexplicably gone up 8% in August, then we’d expect that to reverse.

Here’s the right way to think about long-term aggregate stock market reversals in a Campbell and Shiller (1998) world:

• If you see the stock market fall X% today
• And fundamental value did not fall X% today
• And the market was not previously more than X% overvalued
• Then you’d expect to recoup some of the X% every year over the next 10 years.

When these criteria are not satisfied, a loss is a loss. Even if they are satisfied, it does not follow that volatility is meaningless noise or that losses can be safely ignored because they are temporary. If it takes 10 years for a loss to get reversed, that doesn’t sound meaningless to me.

Systematic equity strategies

Long-term reversals are what we find in scenarios with an “anchor:” a value or valuation ratio to which price eventually reverts. In the bond example, the terminal value of 100 is the anchor. In the aggregate stock market example, the CAPE ratio is the anchor, and the empirical claim is that when prices get too far from earnings, it is prices that adjust. That is, when P/E is too high, it is P that subsequently falls as opposed to E subsequently rising.

For value strategies, one possible anchor is the value spread, defined as the cheapness of value relative to growth. If value stocks fall, and the value spread widens, then we’d expect some of the value losses to be reversed over the next 10 years as the value spread subsequently narrows. As with the aggregate stock market, fundamentals matter; if value stocks fall due to bad fundamental news, then the value spread will not widen, and we wouldn’t expect losses to reverse.

In contrast to value, many other systematic strategies such as momentum have no anchor and hold stocks for short periods. When momentum strategies do poorly, there’s no special reason to expect them to do well subsequently.

“The pretence of knowledge”

So, back to Kevin. He’s just lost 20% of your money. Are you getting it back?

• Under the baseline scenario of unpredictable returns, no. Kevin might be a good bet going forward, but 20% of your wealth is gone for good.
• Under the scenario of long-term reversals driven by slow-moving mispricing, it’s conceivable that you’ll get some of your 20% back if all the stars align, but you’ll need to wait 10 years.
• Under the scenario of short-term reversals driven by illiquidity, it’s conceivable that you’ll get some of your 20% back in the coming days.

How do we know which scenario describes Kevin? We don’t. These are conceptual possibilities, not actionable insights in most situations. Perhaps Kevin has amazing abilities that allow him to discern which scenario applies, but I doubt it. We should be humble in the face of market prices; as Hayek (1975) argued, it is the “pretence of knowledge” to pretend that we always know more than the market.

Let me quote my colleague Seth Weingram:[4]

… as a practical matter, in the moment, it is very difficult to distinguish between “normal volatility” and “incipient permanent loss” (or gain). Was market volatility prior to Lehman’s collapse “noise?” At what moment should an investor have been able to distinguish a “typical correction” from the advent of a potentially unrecoverable generational crisis? Once severe losses had occurred, when should an investor have been able to recognize that the U.S. market wouldn’t suffer a 25+ year slump like Japan following its late-1980s implosion?

When is a loss not a loss? That’s a riddle with an unsatisfying answer. If you’ve just lost 20% and you want to know if you’ll get it back, all I can tell you is “reply hazy; ask again in 10 years.”