The Truth about Stock Prices: 13 Myths

No-fee trading has invited a huge influx of people new to trading. In this article, I discuss the basics of “price formation,” the mechanism by which stock prices are determined.

Like many of us, for much of my life I assumed that a stock had a well-defined “price” at any given point in time. You could buy or sell at that price, and the price would move based on this activity. If it went up you made money, if it went down you lost money. Trading was easy: you just picked the stocks which would go up.

Unfortunately, a youthful indiscretion landed me doing five years at the Massachusetts Institute of Technology. When the doors finally slammed shut behind me, I emerged with little more than a bus ticket and some physics-department issued clothes. Women crossed themselves, and men looked away. Nobody reputable would hire a man with such a checkered past, and the PhD tats didn’t help. So I ended up with the only sort of people interested in such hard cases: Wall Street.

After a couple of years, I caught the eye of a particularly unsavory boss, and he recruited me into a crew doing stat arb at a place called Morgan Stanley. It took me five years to find a way out, and even then the way was fraught with peril. I tried to get out, but they kept pulling me back in. I was in and out of corporations for the next few years, and even did some contract work for a couple of big hedge funds. Only in the turf wars of 2008 did I manage to cut ties for good. The big boys were so busy bankrupting one another, who’d notice one missing guy? The scars are still there, and I always keep an eye on the street. Who knows when a van full of Harvard MBAs will come for me.

On the plus side, I did learn a bit about market microstructure. As it happens, my erstwhile view of prices were naive in many ways.

Rather than a detailed exposition on market microstructure (which varies from exchange to exchange, but has certain basic principles), I will go through a number of possible misconceptions. Hopefully, this will be of some small help to new traders who wish to better understand the dynamics of the stock market. At the very least, it will make you sound smart at cocktail parties.

Because we live in America, and everybody sues everyone about everything, I’ll state the obvious. Before you do anything, make sure you know what you are doing. If you read it here, that doesn’t mean it’s right or current. Yes, I worked in high frequency statistical arbitrage for many years. However, my specific knowledge may be dated. You should confirm anything before relying heavily on it. In particular, I am no tax expert. Be sure to consult an accountant, a lawyer, a doctor, a rabbi, and a plumber before attempting anything significant. And if you do, please send me their info. It’s really hard to find a good accountant, lawyer, doctor, rabbi, or plumber.

Seriously, don’t take anything I say (or anyone else says) as gospel. I’ve tried to be as accurate as possible, but that doesn’t mean there aren’t technical errors. As always, the onus is on you to take care of your own money. As someone pointed out when I started, back when the traders still seemed like superstars: they weren’t paid the big bucks not to make mistakes, but to catch those mistakes before they became problems. My advice, and the best I can give, is that you inform yourself, do research, check, recheck, and recheck again before committing to a trade. In my personal trading I’ve never missed out by being slow and cautious, but I have gotten hammered by being hasty.

Now to the possible misconceptions. I’ll call them “myths” because that’s what popular websites do, so obviously it’s the right thing to do, and I prefer to do the right thing because the wrong thing is wrong.

In what follows “STCG” refers to “Short Term Capital Gain” and “LTCG” refers to “Long Term Capital Gain”. “STCL” and “LTCL” refer to the corresponding losses (i.e. negative gains).

Myth 1: There is a “price” for a stock at any given point in time. When a stock is traded during market hours, there is no single price. There is a bid (the highest priced buy-order) and an ask (the lowest priced sell-order). Often, what people call “the price” is the last trade price. However, sometimes it is the midpoint (bid+ask)/2 or (bid*bidsize+ask*asksize)/(bidsize+asksize), and sometimes more complicated limit-book centroids are used.

Myth 2: I can put a limit order for any price I want. Stocks (and options) trade at defined ticks. A tick is the spacing between allowed prices, and may itself vary with price. For example, the tick-size in stock ZZZ could be 0.01 for prices below 1.00 and 0.05 above that. Often, ticks are things like 1/8 or 1/16 rather than multiples of 0.01. The tick-size rules are per-exchange (or per-security-type on a given exchange) rather than per-stock. In our example, any stock’s price would have allowable values of …, 0.98,0.99, 1.00,1.05, 1.10, …

Myth 3: Limit Orders are better than market orders. Limit orders offer greater control over execution price, but they may not be filled or may result in adverse selection. Suppose ZZZ is trading with a bid of 100 and an ask of 101, with a tick size of 0.50. Alice places a limit order at 100.5 for 100 shares. It is quite possible that it will be filled right away, giving her at least 0.50 of execution improvement (per share) over a market order. But what if it is not filled? If the stock goes up, Alice has incurred what is called “opportunity cost.” Rather than 0.50 in savings she now must pay a higher price or forego the purchase. Why not just leave the limit order out there? Surely it will get filled as the stock bounces around. In fact, why not put a limit order at 98? If it gets executed, it’s free money. The problem is adverse selection. The limit order most likely would get filled when the market was dropping. Sure it could catch a temporary dip, but it also could be caught during a major decline. Statistically, the order will be filled at 98 when Alice does not want it to. She would have been able to buy at 97 or 96 or will be stuck with a falling stock. In the presence of an alpha (a statistical signal informing a predicted return) a noncompetitive bid may at times be appropriate, but In general there is no “free money.”

Myth 4: I can buy or sell any quantity at the relevant price. The bid and ask have sizes associated with them. In fact, the dynamics are more complicated. Each stock has a limit book (or order book), which consists of a sets of buy and sell orders at different prices. Suppose ZZZ has a bid of 100 for 200 shares and an ask of 101 for 50 shares, and a ticksize of 0.50. The spread is two ticks (101−100)/0.50. The quote (bid, ask, bidsize, and asksize) actually is a summary of the inner level of the limit book. The latter consists of a set of levels (maybe 101, 101.5, 102, and 104 on the ask side), each with a queue of orders. The “quote” simply consists of the innermost levels (the highest bid and lowest ask, along with their total sizes). Suppose Bob puts in a market order for 100 shares of the stock. This is matched against the orders at the lowest ask level (101 in this case) in their order of priority (usually the time-order in which they were received). Suppose there only are 50 shares at 101. After fulfilling those orders, we now go to the second level and match the remaining shares at 102, and so on. Each fill is a match against a specific sell-order, and a given trade can result in many fills. For highly liquid stocks, no order you or I are likely to place will match past the inner quote. However, that quote can move quickly and the price at which a market order is executed may not be what you see on the screen. Next, suppose that Bob places a limit order to buy 50 shares at 100.5, right in the middle of the current spread. There now is a new highest bid level: 100.5, and Bob is the sole order in it. Any subsequent market sell order will match against him first. This may happen so fast that the quote never noticeably changes, but if not the new quote bid and bidsize will be 100.5 and 50 shares. If instead, he placed his buy order at 100, he would join the other bids at 100 as the last in the queue at that level. What if he places it at 101? If there were 25 shares available at that ask level, he would match those 25 shares. He now would have a bid for the remaining 25 shares at 101. This would be the new best bid. If he placed the limit order at 110 instead, it effectively would be a market order and would match against the 101 and 102 levels as before. Note that he would not pay 110. The limit book constantly is changing, and to make things worse there often is hidden size. On many exchanges, it’s quite possible for the limit book to show 25 shares available at 101 and yet have Bob filled for 50 at that level. There could be hidden shares which automatically replenish the sell-order but are not visible in the feed. This is intentional, and not a matter of update speed. While it often is possible to subscribe to limit book feeds, most of us only have access to simple data: the current quote (innermost limit-book levels) and the last trade price.

Myth 5: The price at the close of Day 1 is the price at the open of Day 2. This clearly is not true, and often the overnight move is huge and generated by different dynamics than intra-day moves. There are two effects involved. Some exchanges have provision for after-market and pre-open trading (not just order placement), but the main effect is the opening auction. Whenever there is a gap in trading, the new trading session begins with an opening auction. Orders accumulate prior to this, populating the limit book. For example, orders still can be placed outside trading hours However, no crossing (i.e. fills or trades) can occur. This means that the limit book can cross itself, and some bids can be higher than some asks. This never happens during regular trading because of the crossing procedure described earlier. The opening auction is an unambiguous algorithm for matching orders until the book is uncrossed. The closing price on a given day is the last trade price of that day. It often takes a while for data to trickle in, so this gets adjusted a little after the actual close but is fairly stable. The prices one sees at the start of the day involve a flurry of fills from the uncrossing. This creates its own minor chaos, but the majority of the overnight price move is reflected in the orders themselves. If sentiment is negative, there will be significant sell pressure (lots of sell orders and few buy orders), and vice versa if it is positive. There also are certain institutional effects near the open and close because large funds must meet certain portfolio constraints. Note that the opening auction is not restricted to the actual open. Some exchanges (notably the Tokyo Stock Exchange) have a lunch break, and extreme price moves can trigger temporary trading halts. In each case, trading begins with an opening auction.

Myth 6: The price moves because when someone buys people get optimistic and when someone sells people get pessimistic. That certainly can happen. However, there is a more basic reason the price moves. When you buy at the ask, some or all of the sell-orders at that ask-level are filled. There may be hidden size which immediately appears or someone may jump in (or adjust a higher sell-order down), but generally the quote changes. Your trade also is registered as the last trade.

Myth 7: The price behavior of a stock reflects general market sentiment. Though often the case, it need not be. The price we see in most charts and feeds is the last trade price, so we’ll go with that. Consider an unrealistic but illustrative example: ZZZ has a market cap of a billion dollars. Bob and Alice are sitting in their respective homes, trading. [Spoiler: No, they don’t end up together after a series of outlandish rom-com mishaps.] The rest of the market, including most of the major institutions which own stock in ZZZ, are sitting back waiting for some news or simply have no desire to trade ZZZ. They don’t participate in trading and have no orders out. So it’s just Alice and Bob. ZZZ has a last trade price of 100. Bob has a limit order to buy 1 share at 100 and Alice has a limit order to sell 1 share at 101. This is the quote, and the entirety of the limit book. Bob gets enthusiastic, and crosses the spread. The price now is 101. Since he sees the price going up, Bob decides to buy more. Alice still has shares she wants to unload, and puts in a sell limit order for 1 share at 102. Bob bites. The price is now 102. The pattern repeats with Alice always offering 1 share at p+1, with p the last price, and Bob always buying after a minute. They do this 50 times, and the closing price is 150. Two people traded a total of 50 shares, so has the price of a billion dollar company really risen 50%? Admittedly, this is a ridiculous example. In reality, the quote would be heavily populated even if there was little active trading, and everybody else wouldn’t sit idly by while these two knuckleheads (well, one knucklehead, since Alice does pretty well) go at it. However, similar phenomena do arise. Lots of small traders can push the price of a stock way up, while larger traders don’t participate. In penny stocks, this sort of thing actually can happen (though not in such an extreme way). When a stock is run up, it is important to look at the trading volume and (if possible) who is trading. Institutional traders aren’t necessarily skilled or wise, and can get caught up in a frenzy or react to it — so these sorts of effects can have real market impact if they persist. However, they often are temporary and do not reflect true market sentiment.

Myth 8: Shorting is just like buying negative shares, and the only difference is the sign. In many cases, it effectively behaves like this for the trader. However, the actual process is more complicated. “Naked shorts” generally are not allowed, though they can arise in anomalous circumstances. When you sell short, you are not simply assigned a negative number of shares and your PnL computed accordingly. You borrow specific shares of stock from a specific person. The matching process is called a “locate”, and is conducted at the broker-level if possible or at the exchange-level if the broker has no available candidates. There is an exception for market-makers and for brokers when a stock is deemed “easy to borrow”, meaning it is highly liquid and there will be no problem covering the short if necessary. Brokers maintain dynamic “easy to borrow” and “hard to borrow” stock lists for this purpose. There are situations in which a short may not behave as expected. Suppose Bob sells short 100 shares of ZZZ stock, and the broker locates it with Alice. Alice owns 100 shares, and the locate assigns these to Bob. If Alice decides to sell them at some point, Bob needs to be assigned new shares [note that this has no effect on the person Bob sold short to, just Bob]. If these cannot be located, he must exit his position. The short sale is contingent on the continuing existence of located shares. Moreover, if the market goes up a lot Bob may have to put up additional capital for the cost of covering at the higher price. In principle, a short can result in an unlimited loss. In practice, Bob would be closed out by margin call before then.

Myth 9: Shares are fungible. When you sell them, it doesn’t matter which ones you sell. They are fungible from the standpoint of stock trading (aside from the short-selling locates just discussed), but not from a tax standpoint. Most brokers allow you to choose which specific shares you are selling. Suppose Bob bought 100 shares of ZZZ at 50 three years ago and bought another 100 shares of ZZZ at 75 six months ago. ZZZ now is 100 and he decides to sell 100 shares. Selling the first 100 shares generates a LTCG of 5,000, whereas selling the second 100 shares generates a STCG of 2,500. The tax implications can be significant, and are discussed further below. The specifics of Bob’s situation will determine which sale is more advantageous (or less disadvantageous). Brokers generally default to FIFO accounting, meaning that the first shares bought are the first shares sold. Most brokers allow alternatives to be specified at the time of the trade, however. These may include LIFO (last shares bought are first shares sold) or direct specification of the shares themselves. Note that such accounting only applies within a given brokerage account, whereas the tax consequences are determined across all brokerage accounts.

Myth 10: A “no-fee” trading account is better than one with fees. The transaction cost of a trade involves several components. The main three are broker fees, exchange fees, and execution. “No-fee” means they dispense with the broker fee. Unless many small trades are being executed with high frequency, the broker fee tends to be small. The exchange fees are passed along to the trader, even for “no-fee” accounts, but are smaller than typical broker fees. Often, the quality of execution comprises the bulk of the transaction cost. Serious trading shops use transaction cost models and order working strategies to optimize execution. As a small trader relying on a retail broker, we don’t have the speed or positioning to be able to do this. No or low-fee brokers often cross flow internally or sell flow to high-frequency firms which effectively front-run the trader. Market orders see slightly worse execution than they could, and limit orders get filled with slightly lower frequency than they could (or are deferred to face an indirect cost via adverse selection). These effects are not huge, but something to be aware of. Suppose Alice buys 100 shares of ZZZ at 100. Broker X is no−fee, and Broker Y charges a fee of 7.95 per trade but has 10 bp (0.1%) better execution than Broker X on average. That 10 bp is a price improvement of 0.10 per share, and amounts to 10 for the trade. Alice would do better with Broker Y than Broker X. This benefit may seem to apply only to large trades, but it also applies to stocks with large spreads. For illiquid stocks (including penny stocks) the price improvement can be much more significant. There are trading styles (ex. lots of small trades in highly liquid stocks) where no-fee trumps better execution, but often it does not.

Myth 11: Taxes just nuisances, and the price is what really matters. Taxes can eat a lot of your profit, and should be a primary consideration. Tax planning involves choosing accounts to trade in (401K or other tax-deferred vs regular), realizing losses to offset gains, and choosing assets with low turnover. Note that some mutual funds can generate weird capital gains through their internal trading. In extreme cases, someone could pay significant tax on a losing position in one. Why are taxes so important to trading? The main reason is that there can be a 25% (or more) difference in tax rate between a LTCG and a STCG. STCGs often are taxed punitively, and at best treated like ordinary income. Here in MA, the state tax alone is 12% for STCGs vs 5% for LTCGs. Federally, STCGs are treated as ordinary income while long term gains have their own rate. STCGs are defined (currently) as positions held for under one year, while LTCGs are held for over one year. Note that it is the individual positions that matter. If Bob owns 200 shares of ZZZ, bought in two batches then each batch has its own cost basis (price he paid for it) and purchase date. Also note that most options positions are expire in less than a year and would result in a STCG or STCL. A STCG can only be offset by a STCL, but a LTCG can be offset by a LTCL or STCL. Needless to say, STCLs are valuable (unpleasant since they’re losses, but valuable from a tax standpoint). They can be rolled to subsequent years under some circumstances, but may be automatically wasted against LTCGs if you are not careful. A good understanding of these details can save a lot of money. To illustrate the impact, suppose Alice has a (state+federal) 20% LTCG rate (marginal) and a 45% STCG rate (marginal). She makes 10,000 on a trade, not offset by any loss. If it is a LTCG, she pays 2,000 in taxes and keeps 8,000. If it is a STCG, she pays 4,500 and keeps 5,500. That′s an additional 2,500 out of her pocket. Since the markets pay us to take risk, she must take more risk or tie up more capital to make the same 8,000 of after-tax profit. How much more risk or capital? Not just the missing 25%, because the extra profit will be taxed at the 45% rate as well. We solve 0.55*x= 0.8*10,000, to get 14,545. Alice must take (loosely speaking) 45% more risk or tie up 45% more capital to take home the same amount. Note that the appearance of 45% both here and as the tax rate is coincidental.

Myth 12: Options act like leveraged stock. This is untrue for many reasons, but I’ll point out one specific issue. Options can be thought of as volatility bets. Yes, the Black Scholes formula depends on the stock price in a nonlinear manner, and yes the Black Scholes formula significantly underestimates tail risk. But for many purposes, it pays to think of options as predominantly volatility-based. Let’s return to our absurd but illustrative scenario involving Alice and Bob and their ridiculous behavior. As before, they trade ZZZ stock and are the only market participants. Alice sells to Bob until the price reaches 110, then decides she misses her 10 shares of stock. Bob too has an epiphany. He decides he hates ZZZ stock. They now switch roles and Bob sells her a share at 110, but he gets her strategy backward so the price goes down with each share rather than up. He sells her a share at 110, then 109, then 108, down to 101. Now he’s out of shares and they have both another revelation. They return to their original roles, and up the price goes. The day’s trading involves ZZZ stock price see-sawing between 101 and 110 in this fashion. Neither makes a net profit, and the price ends where it started (well, 101 vs 100 but that’s not important here). Consider somebody trading the options market (we said Alice and Bob were the only stock traders, but there could be a thriving options market). At the start of the day and the end of the day, the price is pretty much at the same level. However, the price of both call and put options has risen dramatically. Options prices are driven by several things: the stock price, the strike price, the time to expiry, and the volatility. If the stock price rises dramatically, put options will go down but not as much as the price change would seem to warrant. This is because volatility has increased. In our see-saw case, everything was constant (approximately) except the volatility. The stock price is unchanged, but the option prices have changed dramatically.

Myth 13: There are 13 myths. If you spend your time puzzling over this rather than trading, you will end up with the same amount of money (on average and minus transaction costs). Which leaves the market to me, so I can run the stock up to infinity, then sell to the one unwary buyer who gets greedy and dips his toe in at the wrong time. All your base are belong to me.