Yes, You Lose Value When Your Investments Fall in Price
It's common to hear buy-and-hold investors make statements such as 'You don't lose money until you sell' and 'it's only a paper loss'. The underlying purpose behind this sentiment is to help investors avoid panic selling an investment that has dropped in value.
To be sure, anything that helps a buy-and-hold investor who has seen their long-term holdings drop in value avoid making an emotionally-driven bad decision is potentially good.
But there's a big problem with the idea of 'only a paper loss': it's both false and dangerous. Let me explain why.
This statement conflates the meaning of 'money' and 'value'. It's certainly true that money (i.e., cash) and monetary value (i.e., how much cash could be obtained by selling an asset) are not strictly equal to each other, but in this context, that's a distinction without a meaningful difference.
For instance, according to Miriam-Webster, a millionaire is "a person whose wealth is estimated at a million or more (as of dollars or pounds)." This is completely logical. Virtually no one believes that someone who owns a collection of stocks, bonds, real estate, etc. worth $1 million but no cash is not a millionaire because of the absence of cash. Wealth is far more than cash. After all, cash has virtually no value at all beyond what it can be traded for. Perhaps nothing in the modern era illustrates this better than 'Reserve Bank of Zimbabwe' notes, which are now only worth a few U.S. dollars as collectibles.

Money only has value in the sense that it can be traded for something desirable to the person giving it up in an exchange. As we all know, U.S. dollars have lost significant value over the last couple of years due to inflation (i.e., it takes more dollars to buy most goods and services than it did before). So, let's not confuse money with wealth when the latter is what investors are justly concerned about.
Ford stock has dropped in 2022 from $21.77 on January 3rd to $11.36 at the close of December 24th, meaning that the monetary value of a share of Ford stock has dropped 48% over this period. If an investor bought the stock at $21.77 and sold it at $11.36, everyone agrees that this person would have lost money on the deal. But those claiming that 'you only lose money when you sell' argue that if the investor continued to hold the stock, s/he would not have lost money. It's true that the investor would not yet have realized the loss for tax purposes, but the monetary value of the investor's stock most certainly dropped.
I've also heard those who favor this argument say that investors who sell a stock that has declined in value are giving up the opportunity for the stock to recover. While true, there is no guarantee that this will happen, especially for an individual stock, and investors who sell such a stock are also foregoing the possibility of the losses continuing to mount. As such, this logic doesn't hold water.
If the current market price of something like a stock is not the current monetary value of that investment, then what would the monetary value be? If one claims that anything other than the current market price is the current monetary value, one is saying that one knows the value more accurately than the market does, that the value of the stock goes beyond dollars and cents, or both.
That said, when applied to a buy-and-hold investor who is holding this flawed idea to keep from panic selling a fund with hundreds or thousands of stocks, it's probably not harmful. It's a 'Jedi mind trick' that some use to try to keep from abandoning their strategy at a poor time.
However, when it's applied to individual stocks, this idea can certainly be harmful. While there is no guarantee that a given fund or even the entire stock market will recover within an investor's needed time frame, it's far more likely that such a recovery will occur than the recovery of an individual stock that has fallen in value. Individual stocks fall in value and never recover literally all the time.
This idea can also be problematic in that it may encourage an irrational focus on dividends. If an investor views his wealth in terms of shares and not the market value (i.e., shares multiplied by the current market price), he is prone to not want to sell any of the shares, even if they have appreciated in value tremendously, for fear of 'selling my capital'. If the shares are never sold, then the only source of monetary value (beyond loans using the shares as collateral) the stocks can provide is through dividends. Dividends are not 'evil', but they aren't a free lunch either, and specifically seeking after dividends is liable to increase certain forms of risk the investor is exposed to. Karsten Jeske from the Early Retirement Now blog has an excellent post on this precise issue.
This idea also increases the risk of the investor who holds it falling victim to several cognitive errors, such as anchoring bias, the sunk cost fallacy, and the endowment effect. Anchoring bias refers to humans placing too much importance (i.e., anchoring) on the first piece of information they are exposed to. Those who believe that they won't lose money unless they sell an investment are more likely to hold a poor investment in the hopes that it will eventually go back up in value. But obviously, the market does not care what price a given investor paid for an investment.
The sunk cost fallacy refers to people relying on past behaviors and/or information and subsequently failing to change their behavior to maximize their value going forward. The quote below from Investopedia describes an example of this very well.
"Jennifer buys $1,000 worth of Company X’s stock in January. In December, its value has dropped to $100 even though the overall market and similar stocks have risen in value over the year. Instead of selling the stock and putting that $100 into a different stock that is likely to rise in value, she holds on to Company X’s stock, which in the coming months becomes worthless."
If that doesn't sound like a prime example of one of the pitfalls of the 'you only lose money if you sell' idea, I don't know what is.
Placing more value on an investment than the market does, as is liable to happen to an investor with the 'you only lose money if you sell' mindset, opens the door to the endowment effect taking hold. This effect refers the rather strong tendency of humans to place more value on an object they own simply because they own it. If an investor exhibits the endowment effect, she is apt to irrationally believe that an asset she owns is worth more than its current market price.
Despite the fact that it some investors claim that belief in the idea that 'you only lose money if you sell' helps to keep them from panic selling, investors should not need to believe in such a clearly flawed idea in order to keep their emotions from taking control of their behaviors.
This highlights a real problem in investing that's very seldom discussed: human emotions (and deep risks) make all investment strategies difficult in different ways and usually at different times. I intend to elaborate on this in a future post.