jankythoughts2

Foreword

This post discusses leverage, a tool to magnify the profits (or losses!) from your portfolio. Think of leverage as a tool — you can use it to ramp up the risk you are taking in your portfolio, or tamp down the risk (by reducing leverage). In that sense, leverage provides a lot of power to the investor or speculator to fine tune their exposure to the market.

But remember — with great power, comes great responsibility.

As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.

If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.

Definition

First off, let’s clarify what I mean by “leverage”.  Typically, leverage means you borrow money, or via some other means, put a multiplicative effect on your capital, such that potential gains or losses are magnified as well.  For example, borrowing $100 on top of your existing $100, to buy $200 worth of stocks, or buying options, trading futures, etc.

I generally quantity leverage as a continuum between 0 to infinity, where a leverage of 0x means you’re in 100% cash, and a leverage of Nx means for every 1% move of the asset (some people use “market”, defined as S&P 500 index), your portfolio value moves by N%. For example, if you have a portfolio of $100, of which $50 is in SPY, then your leverage ratio is $50 / $100 = 0.5x.

Next, I’d like to discuss a term I invented — “holding power”.  Essentially, think of this as a mix of psychological and financial wherewithal to hold on to a position.  If you have $100 to your name, and you need that $100 to buy food for tonight, then you have very low holding power — you desperately need that money to survive, so you are not financially capable of losing that money.  If you have $1m to your name, but you really cannot stand the thought of losing money, you too have very low holding power — even though you can afford the loss financially, you are not psychologically prepared for it.

Why is leverage important?

The term “Sharpe Ratio” gets thrown around a lot.  Implicitly, a higher “Sharpe Ratio” is generally taken to be a good thing — it means your strategy is more likely to make money.  But does it really?

The Sharpe Ratio is just the ratio of the expected returns over the standard deviation of returns (1).  The layman way of thinking about it is:
Your portfolio doesn’t return the same amount everyday.
You can think of it as, your portfolio returns R, with some “noise”, N, for a daily return of R + N(day),
where R is a constant (the expected return) and N(day) can be expressed via the standard deviation of daily returns.

Sharpe Ratio = R/N then, gives you an idea of how your expected return compares, against “random noise” in daily returns.
Higher = more signal = less noise = better.

One of the first uses of Sharpe Ratio, is for portfolio planning.  The intuition is simple — If you have a strategy that is high Sharpe, then you can put more money (i.e: more leverage) into that strategy.  Because a strategy with Sharpe >1 has a low (2) chance of losses on a daily basis (or whatever period you use to calculate your Sharpe Ratio), you can worry less about a margin call (more on this later).

In other words: higher Sharpe Ratio = more “holding power”.

In CAPM and MPT, one of the core assumptions/results is that you leverage more (i.e: put more money into) assets with higher Sharpe Ratio’s. So, if you are discussing CAPM, MPT or Sharpe Ratio, but you are steadfastly against leverage, then it’s… kinda weird?

Margin loan

A margin loan is a direct loan you take out from your broker to buy stocks.  For example, if you deposit $100 into your brokerage account, and you buy $150 worth of stocks, you have $100 in equity and $50 on margin, and your leverage ratio is ($100 + $50) / $100 = 1.5x.

Typically, brokers use Reg-T (this is the name of the SEC rule) to determine how much margin you can have.  The math is complicated and has a lot of corner cases, but essentially, you are required to have ~50% equity (i.e: 2x leverage) when you open new positions.  IIRC, maintenance margin is 25%, which means at any time, you must have at least 25% equity (i.e: 4x leverage).

If you fail either of these 2 tests, your broker will issue a margin call to demand that you put in additional equity (usually via wiring more money).  Some brokers give you 1-2days to send in the money, others give you (literally) 5-10minutes… or less.  If you fail to meet your margin call, your broker has every right to force close your positions (i.e: close your positions) until you meet the requirements.  In some cases, the broker can force close more than is absolutely necessary to meet the 2 tests, e.g: get your maintenance margin to 50% or even higher. Some brokers may even force close your positions without issuing a margin call.

In other words:

• Margin loans lowers your financial holding power.
• More leverage lowers your psychological holding power.

Some brokers offer what is known as “portfolio margin”.  This is a case by case basis, and each broker implements it slightly differently, but essentially allows you more leverage than the 50%/25% of Reg-T. They do this by analyzing your portfolio, and if they deem it low risk, they can extend you more leverage.

Now, consider a margin loan — you put in $100, you buy $100 worth of StockA and $100 of StockB.  Is your loan to buy StockA or StockB?
The answer is, neither, and both.

Instead of thinking about “getting a $100 loan to buy Stock?”, you should think of it this way:

• You have assets of $200.
• You have debt of $100 (the margin loan).
• You thus have equity of $200 – $100 = $100.

Effectively, you are giving the broker $100 (cash) to maintain a position of $200 of assets. Whether the broker used your actual $100 to buy the stocks, or put your $100 in a little box and then used their own $200 to buy the stocks, doesn’t really matter. The $100 you put in, is the collateral for the broker.

Any losses to the $200 of assets, first comes out of that collateral.  If the collateral is depleted, then the broker may start losing money — because the asset is now worth less than the loan, unless the broker can force you to cough up the difference, they’ll have to eat the loss.

Therefore, the broker will generally force you to put in more collateral (margin call), or force reduce your position (so they cannot drop in value even further), way before your equity reaches $0.

If you think of it this way (using collateral), then it’ll be easier to reason about why you need to put money in when you are shorting stocks (and thus getting cash from selling the stocks) — you aren’t putting money in to sell stocks, you are putting collateral in to support your position of “short stocks”.

Futures

You can also get leverage by trading futures.  A future contract is essentially a standardized forward contract — Forward contracts cannot be traded on exchanges, they are just bespoke contracts any 2 entities write to each other to transact at a future time.  A future contract has standardized terms, so the contract itself can be traded.

I won’t go into details of a future contract, but the gist is:

• To open a position (long or short) in a future contract, you need to put in collateral.
• If you buy 1 contract of MES, you are agreeing to buy 5x<S&P500 value> at the expiry.
• To make sure you can cover 5x<S&P500 value>, the exchange may require collateral of (I can’t remember exact value, this is completely made up) $100.
  • i.e: $100 of collateral, lets you control ~15k worth of future trade value.  Hence leverage.
• Like margin loans, futures subject you to margin calls.
• Unlike margin loans, futures usually allow you to get much higher leverage ratios.

Most types of leveraged ETPs (3) are actually implemented on the side of the fund provider as futures. In other words, for every share of a leveraged ETP, the fund provider just buys some futures on behalf of the ETP owner.

In effect, leveraged ETPs can be thought of as futures, but packaged in such a way that prevents you from getting margin calls. This is not always a good thing! In exchange for not getting margin called, the leveraged ETPs stand a chance of losing a large portion, including 100%, of their value very quickly. In some sense, margin calls tend to protect against a 100% loss (because the broker will usually force close your positions before you even get close).

Options

Options are the last form of leverage commonly available to retail traders.  An option contract is basically a standardized warrant contract, i.e: forward to future, is the same as warrant to option.

Buying an option contract gives you the right, but not the obligation, to buy (call) or sell (put) 1 lot (usually 100 shares) of the underlying stock at expiry, at a certain price (strike price). The seller of the option is at the mercy of the buyer — the buyer decides whether and when to exercise the option and force the trade in the underlying.

Depending on expiry date and strike price, the cost of the option contract changes.  It is possible, though rarely profitable, to get 100x or even more leverage with options.

Brokers are not allowed to let anyone buy options on margin. Therefore, if you buy an option contract, the maximum amount of money you can lose, is the amount of money you spent buying the contract.

Therefore, being long option contracts doesn’t lower your financial holding power.  However, they may still lower your holding power overall, because options are still leverage, and that can lower your psychological holding power.

Cost of leverage

Now, how much should a broker charge for a margin loan?  How much should the exchange demand in collateral for a futures contract?  How much should an option contract cost?

The answer to all these is basically dependent on 2 things:

1. Volatility
2. Prime rate (or risk free rate, since they are related)

Margin loans

How much margin you are allowed (the 50%/25% bits) is actually modified by the volatility of the asset you are buying.  Some assets are rated at 100% (e.g: $1 in ICSH is worth $1 of equity).  But some assets are rated at less (e.g: $1 in GME is worth less than $1 of equity in Jan 2021), because those assets are too volatile.

So, volatility affects your maximum leverage. More importantly, remember that volatility of an asset can change at any time, so your maximum leverage can change at any time.

At the same time, the actual cost of the margin loan is typically fixed at some offset from prime rate, e.g: your broker may charge you 8% over prime, which means prime rate + 8% on an annualized basis, for every dollar of margin loan.

Margin loans tend to be very expensive, regardless of volatility.

Futures

Futures pricing is complicated, but essentially takes into account prime rate — otherwise you can arbitrage by buying a future, shorting the stock, and investing the net cash in safe assets like Treasuries.

In general, futures cost more as prime rate goes up. However, because prime rate is generally low (0-1%) pretty much since 2009, the cost of leverage using futures is “cheap”.

At the same time, if the asset is volatile, the bid/ask spread of the future contracts may be larger.  So while the midpoint of the future contract may remain static, it can still cost you more to trade futures if volatility is high (via crossing the spread).

Options

Like futures, options are priced off prime rate.

However, because options are not symmetric (unlike futures, where both sides must trade, options give one side the right to decide whether to trade), the price of options tend to go up when volatility goes up.

Essentially — the more likely the stock price moves (higher volatility), the more you should expect to make money off the option contract, and thus the more the contract should cost.

In general, futures are the cheapest form of leverage, followed by options, followed by margin loans.

Why is holding power important?

The market doesn’t go up or down in a straight line.  Even if the market will definitely be higher tomorrow, from now till tomorrow, it can still go down.

Having more holding power allows you to wait through the ups and downs of your portfolio, and, assuming your thesis is correct, avoid you being forced to close your position before you can realize your profits.

In particular, remember that margin loans and futures give someone else the right to force close your position, if you are in breach of your contract (futures contract or margin loan contract).  This means that you need to build more buffer in, effectively reducing your leverage.

Why is any of this important?

Because you can potentially save money, and/or increase your holding power (and thus more likely to profit) if you structure your portfolio’s leverage properly.

For example, if you have $100, and you want to buy 100 shares of a stock worth $2 each, $200 total, it may be cheaper to do:

1. Sell 1 put at strike $2
2. Buy 1 call at strike $2

At expiry, if the stock is below $2, the buyer of the put will force you to buy 1 lot (100 shares) of the stock at $2 each.  If the stock is above $2, you can exercise the long call to buy the 100 shares at $2 each.

To support the short put, you need to have enough equity to support holding100 shares.  However, because you aren’t actually buying the shares, you don’t pay for the margin loan — you just need enough cash in your account to support that hypothetical position. If you have margin enabled on your account, this amount of cash can be substantially less than $2 * 100 = $200 — it’s likely around $100, reflecting 2x Reg-T margin requirements.

Also, when you sell the put, you get some money, which you can then use to offset (perhaps completely!) the cost of the call.

In the end, you need roughly the same amount of equity to support this synthetic long position.  At the same time, the pricing of both call and put will be reflective of the current spot price of the stock, adjusted for volatility and prime rate.

So you “pay” for volatility when you buy the call, but you also “sell” volatility when you sell the put, so your net price is relatively immune from volatility changes.  You do, however, pay for the leverage via prime rate (it’s complicated), i.e: your cost of leverage is roughly prime rate, which is a lot cheaper than the typical retail brokerage margin loan rates of prime + 6-10%!

Note: The short put means that you are obliged to buy the stock if it falls under $2.  This effectively means that if your equity falls too low, your broker can margin call you.  Unlike being long options, when you are short options you are subject to margin calls.

There are a lot of different ways you can structure your leverage to reduce cost of loan, and/or to increase your leverage without dramatically decreasing financial holding power (e.g: by doing it in a way that doesn’t allow your broker or the exchange to margin call you).

In practice, I very rarely use margin loans — instead, I typically use futures or options instead when I want leverage.

Footnotes

1. Not exactly — it’s actually the expected excess returns over standard deviation of excess returns.   For simplicity, however, many people just ignore the risk free rate.  This becomes even easier to ignore after 2009, where RFR is almost 0% most of the time.
2. I believe 5%?  I don’t know, I’m really bad at statistics.
3. ETP stands for exchange traded products, which is a generic name for both ETF (exchange traded fund) and ETN (exchange traded note), combined.

Foreword

This post discusses some common techniques on evaluating the fundamental value of a company by looking at its income statement, for those who are investing, as defined in Investing vs Speculating.

There are, of course, other ways of evaluating the value of a company, which we will cover in other posts. Other posts in this series:

• How to value a company – balance sheet
• How to value a company – cash flow statement

As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.

If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.

How do companies work?

Before we tackle the topic du jour, let’s get down to brass tacks and consider what is even a company? What does a company do? How does it work?

Legally, a company is simply a legal structure where one or more people get together to perform some tasks, generally a business. The company provides a shell to ringfence the business, so that there is a clear separation of concerns between its individual owners, and the business itself. A company, then, can be thought of as a container of a business — though that business may itself be the acquisition of other companies and/or businesses. For example, Berkshire Hathaway, is a holding company, whose main business is to buy other businesses, such as See’s Candies, GEICO, etc. Another interesting example of a “container” company is the SPDR S&P 500 Trust ETF. It is an investment company structured as an exchange traded fund (ETF), with the ticker symbol SPY, and its main business is to buy and hold stocks to track the S&P500 index.

Regardless of the business(es) a company is in, there are a few common aspects shared by all of them:

• Companies typically seek commercial profit (we are excluding charities and non-profits in this discussion).
• Companies generally have one or more products. Products may be be tangible, like a watch, a machine, etc., or they may be intangible, like a website, an online service, movie rights, etc.
• Companies start by taking money from investors (also called shareholders) to invest in producing the product(s).
  • Note that this refers only to the initial investors, generally before the company starts trading on the markets.
  • If you buy shares of a company with a broker, the company does not generally see a single cent of that money — instead, that money goes to pay off earlier investors, who sold you their shares.
• They may also sell bonds or otherwise acquire debt to raise cash to invest in producing the product(s).
• Finally, they sell the product(s), ideally at a price higher than the cost of manufacturing the product(s). If they manage to do so, they make a profit.
• Profits can then be retained by the company to invest in producing future product(s), or they can be used to pay down debt, or returned to investors via dividends, or to reduce the number of investors/outstanding shares by buying back shares.

Common accounting terms

Even in our simple model of a company above, a lot of interesting terms pop up. Understanding how to read a company’s income statement will require some basic understanding of these terms.

Revenue Gross sales	The total amount of money the company generates from the sales of its product(s). This is almost always the first line of a company’s income statement, so literally the “top line”. Example: A company that sells 1,000 wooden figurine for $20 each, will have revenue of $20,000.
Operating expenses	The expenses that the company incurs through its day to day business operations. These can include costs of customer acquisitions, payroll for its workers (not directly producing the product(s)), research and development, etc. In economics terms, it is essentially the equivalent of “fixed costs”. Example: Our wooden figuring company may have to rent some factory space for its woodcarvers, at, say $6,000, which is its operating expenses. Note that regardless of how many wooden figurines are made or sold, the rent remains at $6,000. For now, we assume the factory is large enough to accommodate any amount of production.
Cost of goods sold	The expenses that the company incurs directly in the production of its product(s). For example, the costs of the materials used to produce the product(s), the payroll for factory workers, etc. In economics terms, it is essentially the equivalent of “marginal costs”. Example: Let’s say that to produce a single figurine, the company has to buy a block of wood for $5, and pay a woodcarver $4 to carve the wood into a figurine. So the cost to produce each figurine is $9. With our sales of 1,000 figurines, our cost of goods sold is $9,000. Note that cost of goods sold is directly proportional to the amount of wooden figurines sold. The more figurines sold, the more our cost of goods will rise.
Gross income Gross margin Gross profit	This is the the difference between “revenue” and “cost of goods sold”. Gross income tells you how much money the company generates simply from producing and selling its product(s). Example: In our example, our company will have gross income = revenue ($20,000) – cost of goods sold ($9,000) = $11,000. Notice that gross income relates directly to our marginal profitability — if gross income is negative, no amount of additional sales will save our company from eventual bankruptcy! In fact, if gross income is negative, then the company must be selling each unit of product at a loss. So the more units the company sells, the more money the company loses! Imagine a business that sells $1 notes for 50cents. That company has negative gross income and will go bankrupt eventually — the more “products” it sells, the faster it goes bankrupt!
Operating income Operating profit	This is the difference between “gross income” and “operating expenses”. Operating income tells you how much money the company generates from its operations. Example: Continuing with our wooden figurine company, its operating income = gross income ($11,000) – operating expenses ($6,000) = $5,000. Since operating expenses are (mostly) independent of how many product(s) we sell, operating income is basically just what’s left over, after our gross income is used to pay for “overheads” like rent, utilities, legal fees, administrative fees, etc. Note how a company that has negative operating income, but very high gross income, may actually be in good shape! It may simply be a new company, that needs to ramp up sales. With more sales, gross income will quickly overtake operating expenses and thus lead to high, positive operating income.
Non-operating income	Any income that the company receives that is not due to its primary business. Example: Our company has a interest-bearing savings account which paid the company interest, for a total non-operating income of $1,000. Note that for some investment companies, some types of interests and dividends from its assets may be considered revenue!
Non-operating expenses	Any expense that the company incurs that is not due to its primary business. Example: Our company once sold a defective wooden figurine to a customer, who sued and won a judgement of $2,000, which would fall under non-operating expenses.
Income before tax	This is the total amount of profit the company makes before paying its taxes. This is simply “operating income” + “non-operating income” – “non-operating expenses”. Example: Our company has an income before tax = operating income ($5,000) + non-operating income ($1,000) – non-operating expenses ($2,000) = $4,000.
Net income	This is the income of the company, after paying (or setting aside money for) any taxes it may owe. Example: Our company has a tax rate of 20%, which works out to total taxes = income ($4,000) * 20% = $800. Therefore, its net income = income ($4,000) – taxes ($800) = $3,200.
Normalized income before tax	Normalized income tries to remove the “noise” of regular income by removing one off expenses or gains. The goal here is to smooth out fluctuations of our income statements, so that long term performance of the business(es) can be easier to discern. Example: Our company has some non-operating expenses and income: Interest from its savings account of $1,000 Payment for a lawsuit it lost for $2,000 Since our company will likely continue maintaining its savings account, but will (hopefully) not be sued (and lose!) on a regular basis, the $1,000 can be considered recurring income, while the $2,000 payout can be considered a one off expense. Therefore, our normalized income before tax = income before tax ($4,000) + one off expenses ($2,000) – one off income ($0) = $6,000. Warning: Be careful about how companies classify “one off” expenses and income. It is easy to make the income statement look better than it is, if we classify every expense as “one off” and every source of income as “recurring”! The astute investor should recognize if the level of “one off” expenses remains stubbornly high over long periods of time. Such persistently high “one off” expenses, may really just be a real cost of business that management is misclassifying. Similarly, if certain sources of income fluctuate greatly over time, then maybe those incomes are really one off!
Normalized income after tax	This is just normalized income before tax, with the taxes due removed. For example: In our example, normalized income after tax = normalized income before tax ($6,000) – taxes ($800) = $5,200. Notice how the tax rate is based on actual income before tax, and not normalized income before tax! This is another reason why one should be really careful about how some incomes and expenses should or should be classified as “one off”.
Weighted average shares outstanding	Over the course of a reporting period, a company may issue shares to its employees, executives or board members as a form of compensation for their services. At the same time, a company may choose to buy back some of its outstanding shares on the open market with excess cash it may generate. Because of these, the number of shares outstanding of a company is rarely static — it typically changes slightly over time. The weighted average shares is just the sum of number of shares outstanding over the reporting period, weighted by the fraction of the period those shares are actually outstanding. Example: At the start of a reporting period, our company has 1,000 shares outstanding. One-quarter of the way through the reporting period, our company buys back 200 shares. Half way through the same reporting period, our company issues 400 shares to its employees. So, for the first quarter of the period, there are 1,000 shares outstanding. For the next quarter, there are 800 shares outstanding. And for the remaining half, 1,200 shares outstanding. Weighted average shares outstanding = 1,000 * 0.25 + 800 * 0.25 + 1,200 * 0.5 = 1,050 shares.
Diluted weighted average shares outstanding	In addition to issuing new shares, a company may also issue warrants (or options) on its shares. These directly issued warrants/options give the bearer the right, but not the obligation, to buy more shares directly from the company at a certain price — the strike price. If and when the bearer exercises these warrants/options, the company is obligated to create new shares out of thin air, and sell them to the bearer at that strike price. Once these warrants/options are issued, the company has no control on when the bearer may decide to exercise them. However, until the bearer actually exercises them, these warrants/options are not actual shares — they have no voting rights and they do not partake in any financial gains of the company. In order to show the potential effects of these warrants/options on the number of shares outstanding, we can look at diluted weighted average shares outstanding. This is simply the weighted average shares outstanding, increased by the number of shares that the company would be obligated to issue if all outstanding warrants/options directly issued by the company are exercised. Example: In addition to the outstanding shares, our company has issued 2 warrants, each for the purchase of 100 shares (200 shares total), to the CEO. Diluted weighted average shares outstanding = 1,050 + 2 * 100 = 1,250 shares.
Basic earnings per share Primary earnings per share	“Basic” and “Primary” means non-diluted in this case, so basic earnings per share simply refers to the ratio of net income, over the weighted average shares outstanding. Example: For our company, we have net income of $3,200, and weighted average shares outstanding of 1,050. Therefore, the basic earnings per share = $3,200 / 1,050 = ~$3.05 / share.
Diluted earnings per share	We can also look at earnings per share on a fully diluted basis, in which case, we’ll use the diluted weighted average shares outstanding as the denominator of the ratio. Example: For our company, we have net income of $3,200, and diluted weighted average shares outstanding of 1,250. Therefore, the basic earnings per share = $3,200 / 1,250 = $2.56 / share. Notice how the dilutive effects of the 2 warrants issued to the CEO dramatically reduced our earnings per share! While directly issued warrants/options don’t represent actual shares until they are exercised, they still represent potential claims on the future profits of the company and should not be overlooked.
Basic normalized earnings per share	We can also consider earnings per share on normalized earnings to smooth out one off expenses and income. Example: For our company, we have normalized income after tax of $5,200, and weighted average shares outstanding of 1,050. Therefore, the basic earnings per share = $5,200 / 1,050 = ~$4.95 / share.
Diluted normalized earnings per share	Finally, we can consider earnings per share with normalized earnings, on a fully diluted basis. Example: For our company, we have normalized income after tax of $5,200, and diluted weighted average shares outstanding of 1,250. Therefore, the basic earnings per share = $5,200 / 1,250 = $4.16 / share.

Valuation models

When considering the income statement, there are a few natural ratios, or valuation models, that we can use. Here we discuss the more common ones, using our example company above. For reference, we’ll assume that each share of our example company is selling for $100 right now.

Price / Earnings (P/E) ratio	The most popular ratio, the P/E ratio is available on almost every major financial research platform and provides a quick and easy reference number that is reasonably comparable across multiple industries. The P/E ratio can be computed as: Price per share / Earnings per share. In general, “P/E ratio” refers to “basic P/E ratio”, that is, price per share divided by basic earnings per share. Be very careful though! Just as there are 4 common variations of “earnings per share”, there are also 4 common variations of P/E ratios. Even though most sources quote “basic P/E ratio”, that is not true of every source! More egregiously, some sources quote different flavors of P/E ratios across different companies they report on, taking the confusion to a whole new level. To make things even more confusing, some sources make a distinction between “forward P/E ratio” and “trailing P/E ratio”. The former is computed using earnings projection for the future, while the latter is computed using realized, historical earnings. Looking at the P/E ratio is simply answering the question “how much do I pay, for $1 of net income?” — A P/E ratio of 30, means you pay $30 for every $1 of net income the company generates. Example: For our company, the P/E ratio is simply 100 / 3.05 = ~32.8. The diluted P/E ratio is 100 / 2.56 =~ 39.1. The normalized P/E ratio is 100 / 4.95 = ~20.2. The diluted normalized P/E ratio is 100 / 4.16 = ~24.0. Notice how dilution and normalization of earnings dramatically changes our computed “P/E ratio”. When to use P/E ratio: P/E ratio is generally comparable across companies in the same sector/industry. For example, comparing the P/E ratios of 2 companies manufacturing the same (or similar) Widget can give you an idea of which one may be a better value to invest in. Be careful when comparing P/E ratios of an established company and a startup! As discussed above, net income is affected more by sales and less by fixed costs when a company is more mature, while net income is affected more by fixed costs and less by sales when a company is young. At the same time, gross income tends to improve as companies ramp up their sales, due to economies of scale, which further exacerbates this issue. When comparing across sectors/industries, caution also needs to be exercised. Due to the rules of accounting, and the nature of different businesses, P/E ratios don’t tend to be comparable across sectors/industries. For example, a high growth industry may naturally support higher P/E ratios, because investors are looking towards the future, where higher income will naturally deflate the P/E ratio. However, a low growth industry will likely have lower P/E ratios, because the future is likely very similar to the recent past. The most egregious examples where P/E ratios don’t even work are generally due to accounting rules — Consider a real estate investment trust (REIT) that owns commercial buildings and rents them out. A cost of business would be the cost of the buildings themselves — buildings age with time and eventually need to be rebuilt/replaced. However, the lifespan of a building depends on the weather, the type of building, seismic activities in the region, whether maintenance is properly done on the building, and a myriad of other issues. Clearly there is no easy way to quantify all of these to arrive at a reasonable “expense” line item. Yet REITs need a way to be able to deduct this very real cost from their income — no company wants to pay taxes on “profits” that it did not really earn, because that “profit” is really just a deferred “cost of goods sold”. The accounting rules that are used to allow REITs to recognize the very real cost of building depreciation tends to be overly generous when buildings are properly taken care of — in general, buildings last longer than the rules assume, so actual amortized cost is usually lower than what the accounting rules assume. This results in income statements that look worse than they really are, because the “operating expense” of “depreciation” distorts the picture significantly. In situations like this, another measure other than the P/E ratio can be used to evaluate the company’s worth — REITs tend to be valued using their cash flow statements instead of their income statements, a topic we’ll discuss in a future post. For now, it is important to note that almost all major companies have some amount of factory equipment, buildings and/or other assets that depreciate over time. The accounting rules clearly is not able to quantify the actual depreciation rates in all cases. Therefore, the take away is this — the higher the “depreciation and amortization” line items on a company’s income statement are, the more likely they are distorting the income (and thus P/E ratio) of the company.
Price / Sales (P/S) ratio	Another common ratio used to evaluate companies, the P/S ratio is generally seen as “cleaner”, because it avoids completely the distorting effects of how accounting rules affect different sectors/industries. The P/S ratio can be computed as: Market capitalization / Revenue. Where “market capitalization” is just price per share multiplied by weighted average shares outstanding. Notice how this metric completely bypasses “normalization” of income, because we are not considering expenses. Also, this metric is almost always used in the basic form — P/S ratio is almost never computed with diluted weighted average shares outstanding. Looking at the P/S ratio allows us to answer the question, “how much am I paying, for each dollar of sales?” — A P/S ratio of 3, means that for every dollar of sales, the investor is paying $3. Example: For our company, the P/S ratio is simply (100 * 1,050) / 20,000 = 5.25. When to use P/S ratio: Remember our example above, about comparing a mature company’s P/E ratio against that of a startup? We said that this comparison doesn’t work, because the startup’s income is unfairly dominated by its fixed costs, which will become less of an issue once the company ramps up it sales. The P/S ratio does not have this issue! If we are confident that, at steady state, the startup will have a similar marginal gross income (that is, gross income per unit of product sold), and that the startup will have a similar operating expense as the mature company, then one easy way to compare the operating metrics of these 2 companies right now, would be to consider their P/S ratios. Next, let’s consider those sectors/industries that are highly cyclical, such as heavy industrial manufacturing. Companies in these sectors/industries tend to require high levels of investment in factories and equipment every few years. If you look at the net income of these companies, you’ll notice that they are highly cyclical — there will be long periods of low (or even negative) net income, which coincides with periods when the companies are building out new factories and equipment. These will then be followed by long periods of much higher net income, when the build out is at a lull. Due to this need for cyclical investment in their businesses, the P/E ratios of these companies tend to also fluctuate significantly over time, and thus are not reliable indicators of the companies’ health. Instead, the P/S ratio may be more suitable, because it takes away the distorting effects of the cyclical costs of investing in the business. There are some caveats to the P/S ratio, of course. Unlike the P/E ratio, P/S ratio does not take into account costs of business, which while liberating in some cases, can be highly misleading in others. For example, a software company may be able to earn a high operating margin (the ratio of its revenue that eventually translates into profits), but a retail store may not! In general, the same dollar of sales in different sectors/industries may not translate into the same profit, which dramatically curtails the use of P/S ratio comparisons across sectors/industries. Similarly, a company that is mostly funded by debt will have much higher debt servicing costs than another company that is mostly funded by equity. In the former case, after paying the interest on the debt, the company will likely have much less profits left for shareholders compared to the latter case. Finally, like the P/E ratio, the P/S ratio does not take into account growth of the company. A company that is rapidly growing, may command a higher P/S (and P/E) ratio, because investors are looking towards the future, where highly sales will naturally bring both ratios down.
Price / Earnings-to-Growth (PEG) ratio	To account for potential future growth, the P/E ratio is sometimes augmented by normalizing it against projected (or historical) earnings growth. This gives rise to the PEG ratio. The PEG ratio can be computed as: (Price per share / Earnings per share) / Earnings per share growth = P/E ratio / Earnings per share growth Where “earnings per share growth” can be either forward (i.e: projected) or trailing (i.e: from historical data), giving rise to “foward PEG ratio” and “trailing PEG ratio”. Note that in both cases, the basic (i.e: non-diluted) version of P/E and earnings per share are used. The PEG ratio does not conform to any reasonably English question that we can ask. Instead, it is a unitless value that just gives an indication of how expensive a stock is, with regards to both earnings and growth. Example: Recall that the basic P/E ratio of our company is ~32.8, and it has earnings per share of $3.05. Let’s assume that the previous year, the earnings per share of our company was $2.50, and that in the next year, the earnings per share of our company is projected to be $3.50. Trailing earnings per share growth = (3.05 / 2.50) – 1 = 22% Future earnings per share growth = (3.5 / 3.05) – 1 = ~15% Trailing PEG ratio = 32.8 / 22 = ~1.49 Future PEG ratio = 32.8 / 15 = ~2.19 Clearly, our company was a better value PEG ratio-wise, last year, than this year! When to use PEG ratio: The PEG ratio gives an idea of how expensive a stock is, compared to its rate of growth. This may be useful as a complement to any other valuation methods which did not take into account growth of the company, such as the P/E ratio, or the P/S ratio. The smaller the PEG ratio of a stock, the more attractive it is with regards to earnings growth. Therefore, when comparing two companies in the same sector/industry, but with dramatically different growth profiles, the PEG ratio may be a useful measure to take into consideration.
Enterprise value / Earnings before interest, taxes, depreciation and amortization (EV/EBITDA) ratio AKA Enterprise multiple	Now, let’s take a step back, and consider a company from another view point — that of a potential acquirer, say, a competitor. What would the competitor use to quickly evaluate whether our company is worth buying? First, let’s consider what the competitor would care about. The competitor likely wouldn’t care very much about the interest expense that the company pays — assuming the competitor has the deep pockets to buy out our company, it may very well also have the ability to pay off the company’s debts, which will nullify the interest fees. After all, how a company finances its operations (through debt or equity) is fungible as money is fungible. The competitor likely cares about taxes paid, but the consideration is more complex than just what our company pays in taxes. Remember that taxes is on profits, which is affected by expenses such as interest, which we’ve already discarded. Separately, combining two companies may reduce operating expense (remember that operating expenses are those expenses that tend not to scale with units of product sold — so some of these expenses can be removed when the companies merge), which then increases profits and taxes. In general, the final effect of taxes on the combined company is not as simple as just adding up their individual tax bills. So we can probably exclude taxes too, for now. The competitor also probably doesn’t care about our company’s accounting of depreciation and amortization effects either. Accounting rules tend to reset depreciation and amortization line items every time an asset changes ownership, which then changes the buyer’s accounting of depreciation and amortization. And finally, any cash that our company owns, is irrelevant — using cash to buy cash is just silly, so we should ignore them. If our company has $1,000 in cash, the competitor will have to pony up an additional $1,000 to buy our company, but this $1,000 on both sides of the ledger will cancel out. So, what is the actual cost to our competitor for acquiring our company? They’ll need to pay off all existing shareholders at the current share price (share price * outstanding shares = market capitalization), they’ll need to pay off all debts, and they can ignore the cash balance on our company, because cash is just fungible. This gives us a definition of enterprise value: Enterprise value (EV) = market capitalization + debt – cash and cash equivalents At the same time, by paying “enterprise value”, our competitor is getting a stream of earnings that ignores interest payments, taxes, depreciation and amortization, or “earnings before interest, taxes, depreciation and amortization” (EBITDA). So the ratio they care about is EV/EBITDA. Example: For our company, market capitalization = 100 * 1,050 = $105,000. We have no debt, and $1,000 in cash, so enterprise value = $105,000 + $0 – $1,000 = $104,000. $104,000 is how much it would cost, for a competitor to acquire our company outright. And by paying this $104,000, our competitor would get value in the form of EBITDA, equal to = net income ($3,200) + taxes ($800) + interest payment ($0) + depreciation/amortization ($0)= $4,000. And the enterprise multiple = 104,000 / 4,000 = 26. When to use enterprise multiple: Enterprise multiple is mostly only useful for considering the unlevered (i.e: no debt, fully equity funded) operations of a company, and without considering such costs as taxes, depreciation and amortization, which tend to change dramatically after a company is merged with a larger entity. After the merger, the combined company can then decide to re-lever (i.e: get into debt) its operations, but that is a future consideration. For the personal investor, enterprise multiple isn’t particularly interesting, except where the company may be a candidate for acquisition. For example, sectors/industries tend to consolidate as they mature, where larger companies buy out their smaller competitors. In these cases, it may be useful to consider how the larger companies may value their competitors. After all, if you can buy a company that is primed for acquisition at a good enterprise multiple, there is a good chance that one of its larger competitor will then buy the company from you in future at a higher enterprise multiple, ensuring a good profit! (1)

How much is too much?

So, now that we have a “brief” overview of the different metrics that can be used to evaluate a company, based on its income statement, the next obvious question is, what yardstick do we use?

Is a P/E ratio of 10 good? How about 30? 100? Or may be a P/S ratio of 2? 3? 5?

The short answer, is that there is no real yardstick that works across all companies. As discussed above, P/E ratios tend to mellow (come down) as companies mature. They are also affected by various other issues like accounting and the cyclical nature of some sectors/industries. P/S ratio, PEG ratio and the enterprise multiple all have their own issues as well.

For simplicity, going forward, I’ll only consider the P/E ratio, with the assumption that somehow, all the distorting non-operations related issues are ironed out and accounted for. This argument then generalizes better across the different valuation metrics, and we are considering only the raw, operational characteristics of the company. (2)

How much do we want to pay?

So, given our new “perfect P/E ratio”, what yardstick should we use? This is where price discovery comes in.

Remember that the P/E ratio is simply how much we want to pay, for each dollar of earning. Clearly, that is a decision that is dependent on the individual.

For someone who has the option of investing either in a public company on the open market or investing in a private company at a fixed valuation, then the price they would be willing to pay for the public company would be dependent on the valuation of the private company — if the private company is selling for a P/E of 20, then it makes very little sense(3) to invest in the public company at a valuation much higher than a P/E of around 20.

However, for someone else who has only the option of investing in the same public company, or putting their money in a savings account earning 1% interest (i.e: paying $100 to earn $1, or “P/E ratio” of 100), then they may be willing to pay substantially more.

The final clearing price of the company’s stock, will then be a reflection of all opportunities available to all investors, such that all capital is properly deployed across all assets (in this case, the public company, the private company, and the savings account). The final result may very well be that the first investor deploys their capital entirely into the private company, while the second investor deploys their capital into the public company at a P/E ratio of 100.

Yes, this means that the private investor, at least nominally, stands a higher chance of coming out ahead in the long run, but that is not a consideration for price discovery, but a reflection of the intrinsic inefficiencies of the markets (both public and private).

So, to put it simply, for the rational, purely financial(4) investor, and assuming a “perfect P/E ratio” can be defined, then the highest P/E ratio they should pay, should be the P/E ratio of the next best investment available to them.

How certain are you?

In a perfect world, where you can be certain of your projections of a company’s growth, where you can define a “perfect P/E ratio”, etc., choosing the “next best” P/E ratio to pay is the rational thing to do. However, the world is hardly perfect, and uncertainty abounds.

For example, how confident are you in the projections that management makes for the company’s forward progress? Is management likely to overestimate? What are their incentives? Also, even if management is perfect at estimating their own company’s operations, how good are they are estimating the operations of competitors? What about future competitors that don’t even exist right now?

In reality, companies rarely perform according to their projections, and events in the future may dramatically diverge from our projections. Because of this, we need to build some amount of “margin of safety” into our assumptions.

For example, in the case of our public investor, choosing between investing in a public company and a savings account, they need to recognize 2 important facts:

1. The savings account is guaranteed by the FDIC, so unless they have more than the FDIC insurance limits in the account, or the FDIC itself goes bankrupt, they are very unlikely to lose money. Therefore, the “capital” “invested” in a savings account is generally considered safe.
2. Any capital invested in the public company has no such protections. An unforeseen event, say a once-in-a-hundred-years pandemic, may occur, causing irreparable harm to the company’s business and forcing it to shutdown, leaving shareholders with nothing.

So when choosing between investments, we also need to consider the potential risks in the investments, not just of the risk of returns (i.e: the probability that returns in future will match returns in the past), but also the risk of loss (i.e: the probability that we won’t even be able to recoup our initial investments).

It is with this in mind that we define a “margin of safety” — when considering between a “safe” “investment” like a 1% yielding savings account (implicit “P/E ratio” of 100), and a public company, we may very well decide that the public company should only command, at most, a P/E ratio of 17, because of all the inherent future unknowns that we need to account for. This gives our company a nominal yield of around 6% (1 / 17 = ~0.059 = 5.9%), for a “margin of safety” of 4.9% (5.9 – 1 = 4.9%).

This “margin of safety”, is sometimes also called the “equity risk premium”. It is, roughly speaking, the additional yield that investors demand from equity investments, over risk-free investments due to the inherent riskiness of equity investments.

Obviously, different investors have different appetites for risk — some investors may demand a 5% equity risk premium (i.e: stocks should yield at least 5% more than risk free investments), while others may demand much lower or higher premiums.

The combined preferences of all investors across the whole market, for all possible investment assets will interact to settle on a clearing price for all our investments.

Footnotes

1. Note that this is delving into speculation territory, since we are depending on someone else valuing the company higher than we do, instead of just making a profit purely on the operations of the company.
2. Obviously, this is a departure from reality — such a measure that properly takes into account all the myriad of issues is simply not possible. The assumption here is that the reader will consider all the relevant metrics (PEG ratio for growth companies, P/S ratio for startups, etc.), and come up with a personal composite that they believe in.
3. This assumes our investor does not care for diversification, which is obviously not traditional and generally not advised.
4. “Purely financial” here meaning that the only consideration is financial — the investor does not care about other things like sentimentality (I just like the stock), environmental concerns (I like green stocks), etc.

Foreword

This post discusses what happens from the time when you send an order, to the time when your order is either rejected, cancelled or executed.

As usual, a reminder that I am not a financial professional by training — I am a software engineer by training, and by trade. The following is based on my personal understanding, which is gained through self-study and working in finance for a few years.

If you find anything that you feel is incorrect, please feel free to leave a comment, and discuss your thoughts.

Definitions

Instrument	Any tradable thing, generally interchangeable with “security”.
Lot	Usually means 100 shares of a particular stock. Some stocks, like BRK-A are so expensive that a “lot” of that stock is just 1.
Odd lot	Any number of shares of a stock less than a lot. For example, 50 shares of AAPL is an odd lot.
Order	A firm commitment to trade an instrument at a certain price, either buying or selling. An order can be cancelled, but until it is, the issuer of the order must stand ready to fulfill their promise to buy or sell.
Flow	A stream of orders, sometimes also used for a stream of IoIs.
Book	The totality of all orders that an entity knows about, for a particular instrument. For example, NASDAQ may have a book for GOOG that looks like: Bids: 100shares@$100, 200shares@$90 Asks: 100shares@$101, 300shares@$110
Top of Book (ToB)	The best bid and ask of a book. In the example above, the ToB would be: Best bid: 100shares@$100 Best ask: 100shares@$101
Trade	Also called an “execution”. A trade happens when 2 orders, one buying and one selling, agree upon a price and quantity for an instrument. This results in money going from the buyer to the seller, and the instrument going from the seller to the buyer.
Order matching	The act of finding 2 orders to produce a trade. In our example above, no 2 orders can match, because the best bid is below the best asking price. However, if a new order comes in to buy 50shares@101, then this order can be matched with our best ask, to produce a trade 50shares@$101 After this trade, our ToB would be: Best bid: 100shares@$100 Best ask: 50shares@$101
Market data	A (maybe real time, maybe delayed) stream of information about the trades and the state of the books of an exchange.
Venue AKA trading venue	A venue refers to either an exchange or alternative trading system, where traders can send their orders to get routed to another venue, or to be executed.
Exchange AKA lit exchange AKA lit venue	A trading venue that publishes market data publicly, e.g: NASDAQ, NYSE, Amex, etc.
Dark pool AKA Alternative Trading System (ATS)	A trading venue that does not publish market data publicly, e.g: Sigma X, CrossFinder, MS SORT, etc. They are not always an “exchange” — an “exchange” implies a book and order matching — dark pools may not have a book and may not match orders, they may trade against incoming orders using their own portfolio.
Protected quotes AKA National Best Bid and Offer (NBBO)	This is the ToB of all lit exchanges put together. For example, if NASDAQ has these quotes for MSFT: Bids: 100@$50, 200@$49 Asks: 300@$52, 400@$53 and NYSE has these quotes for MSFT: Bids: 500@$49, 600@$48 Asks: 700@$51, 800@$52 Then the NBBO is: Best bid: 100@$50 Best ask: 700@$51 Note that odd lots are generally ignored for the purpose of computing the NBBO. i.e: Odd lots are generally not protected, even if they are the best bid or ask.
NMS	National Market System, created by Investment Act of 1933. NMS is a rule which says that any order that is executed, must execute at a price within NBBO (inclusive).  There are some exceptions, but these typically don’t apply to retail orders.
Regular trading hours (RTH)	Between 9.30am and 4pm Eastern time on a trading day. This is the period of time when the market is said to be “open”, and starts with the opening auction at 9.30am, and ends shortly after the closing auction around 4pm.
After hours	Any time other than RTH.
Broker	An entity that takes an order and figures out where to send it so that it can get matched and executed.
Dealer	An entity that takes an order, and trades against it (i.e: the dealer is the counterparty of the order creator).
Broker/Dealer (BD)	Most brokers are also dealers, and vice versa. Because of this, brokers and dealers are collectively known as brokers/dealers or BDs for short.
Market maker (MM)	An entity that is mandated by SEC/FINRA rules to always keep a bid and ask up for the instrument that it is market making for, on a particular exchange. Note that a market maker for FB on NASDAQ may not be a market maker for FB on NYSE, etc.
Wholesale market maker (WMM)	Really a BD, a WMM is an entity that accepts orders from retail brokers, and either a) Figures out where to route that order so that it can be matched and executed, OR b) Trades against the order using their own portfolio, OR c) Holds the order in their own book for matching against future orders.
Informed	An adjective to describe either an entity, order or flow. An informed entity, order or flow is someone or something that has an edge. In general, this edge involves some non-trivial understanding of the system and/or the macro and/or micro environment(s). Usually, “informed” is applied with a very short time horizon. For example, an order is informed if within a few milliseconds to seconds of the order being sent, the price of the instrument moves upwards. Also called “toxic”. (1)
Uninformed (1)	An adjective to describe either an entity, order or flow. An entity, order or flow that is uninformed is, well, not informed. Typically synonymous to “retail orders/traders”, it is also generally applicable to more sophisticated entities, such as hedge funds, if they are not trying to optimize for very short term (milliseconds to seconds) time horizons.

Basics

There are 10+ lit exchanges in the US for equities, several more for options, futures, etc. In general, to be called an “exchange” requires being subject to stringent regulatory rules set by the SEC, a Federal government agency. Exchanges, in turn, are part of FINRA, which is a self-regulatory body consisting of exchanges and large brokerages. Together, SEC and FINRA set the rules that govern all equities trading in the USA.

A trade can happen as long as all the rules that SEC/FINRA impose are met. The rules which generally apply are:

• NMS is enforced during RTH and so all trades must occur within NBBO (inclusive).
  • There are exceptions to this rule, such as for large orders (block trades), corrective trades (busts, corrects), etc.
• During RTH, prices cannot move by too much within a 5-minute period. The bands are defined using an algorithm the SEC dictated.
  • Orders which are outside the band must be modified to comply or rejected by the broker.
  • Even if trades are within the bands, if volatility is too high as judged by various parties (SEC, FINRA, exchanges, etc.), trading in a particular stock can be halted.
• During RTH, circuit breakers are in effect — if the price of S&P500 declines by too much, the entire market is halted for defined periods of time, up to an including an early end of the trading day.

Order handling

Only licensed BDs are allowed to connect directly to exchanges. As part of maintaining that license, BDs agree to a shared responsibility to “maintain orderly markets”. What this means, is that all rules that the SEC/FINRA impose, must be adhered to by all BDs. If an order which is in breach of the rules is received by a BD, they are responsible for either modifying the order so that it is compliant, or rejecting the order. Any BD who forwards (routes) a non-compliant order to another BD or exchange, may find themselves being disciplined by the SEC/FINRA.

Because there are so many rules to pay attention to just to validate an order, most BDs don’t actually connect to the exchanges directly. Instead, they have contracts with other BDs, such that the original BD is allowed to send some types of non-compliant orders to the second BD, and the second BD assumes the responsibility of validating and possibly rejecting those orders. In effect, our original BD has its own BD. The original BD, the introducing BD, will forward any orders they receive to the second BD, the executing BD. The executing BD will then figure out what to do with the order, also known as “working the order”.

Retail orders

In general, retail BDs, such as Robinhood, E-Trade, Charles Schwab, etc., typically do not know how to work an order. They are, for the most part, glorified UI+app+accounting.  When you send in an order to a retail BD, they will route the order to a specialized BD, also called a WMM, not to be confused with a regular MM — though most WMM’s are also regular MMs, in some capacity (i.e: some instrument+exchange pairs). There are 3 major WMMs in the US – Citadel Securities, Two Sigma Securities and Virtu Financial. There are also a bunch of minor WMMs in the US, but they have very little flow compared to the big 3.

So, when JoeRetail sends an order to RetailBroker, RetailBroker will send the order to WholesaleMarketMaker, who then has 4 choices:

1. Trade against the order, using their own portfolio.
   • There are a bunch of rules they have to comply with, enforced by the SEC/FINRA, to ensure that the WMM gives JoeRetail a reasonable deal.
2. Forward the order to a dark pool or lit exchange or another BD.
3. Hold the order on its books.
4. Cross the order against another order already on its books.
   • Must comply with all the rules mentioned above relating to order execution.

From worst to best for JoeRetail:

• In general, the first option is usually a bad deal for JoeRetail — because the WMM is informed, while JoeRetail is almost definitely uninformed — there is an information asymmetry and generally speaking, the WMM will come out of the deal better off.
• Routing to a dark pool is generally bad for the order as well, for similar reasons.
• Being held on the WMM’s books is sort of bad — it implies the order is not immediately executable (it does not cross the far price, which is the best bid for a sell order, or the best ask for a buy order), so the WMM is putting it on ice until something changes and the WMM can decide again later.
• Routing to another BD just repeats the process.
• Immediately crossing against an order already on the WMM books is OK, but not the best thing.
• Routing to an exchange is probably the best thing that can happen to the order.

National best guess for bid and offer

Why is it not the best thing for the order to trade against other client orders on the WMM’s books?  Surely those orders must also be uninformed?
Yes, those orders are uninformed, but the problem is that NBBO is weird.

Remember that WMM has to execute within NBBO.  But NBBO is not the best bid/offer of all exchanges (it’s just called that).  It is just the best protected and lit bid/offer.

For example, if the absolute 2 best offers on all lit exchanges are:
Sell 99 GOOG @ $100
Sell 100 GOOG @ $101

The first order (@ $100) is not the NBBO — because it is an odd lot. So, even though the WMM knows about that order (lit exchange books are public), and you only want to buy 99 GOOG, the WMM does not have to execute your trade at $100, it can execute your buy order at $101. However, if your order to buy 99 GOOG was routed to the exchange, it’ll definitely be executed at $100.

More interestingly, and this is something that most people don’t appreciate — the WMM may not be allowed to fill your buy order @ $100, even if it wants to.  For example, if NASDAQ has both those sell orders, and NYSE has this buy order:
Buy 100 GOOG @ $100.10

Then the NBBO is $100.10 to $101.  Which means filling your order at $100 will be below the $100.10 best bid, which is against the NMS rule.  This situation is known as a crossed market.  It happens, but rarely and usually not for very long.

Another problem with NBBO is that it is not well defined.  Remember that all the exchanges are located at different geographic locations.  So, depending on where you are, market data (i.e: the book) of different exchanges will reach you at different times.

So even if you use the exact same algorithm to build the NBBO, someone in Kentucky and someone in Connecticut can genuinely see different NBBOs, simply because the exchanges’ market data reach them at different times.

Because of all these issues, BDs cannot just use any NBBO algorithm. The algorithm they use must be blessed by the SEC/FINRA.  OR, they can just use the SIP. The SIP is a company that publishes various market data for all participants.  Because it is sanctioned by the SEC/FINRA, if you use the NBBO published by the SIP, you’ll generally be fine — SEC/FINRA generally won’t give you grief about that.

But that introduces 3 other problems:

1. The SIP itself is located at some location, which means it’s seeing market data of a certain latency.
2. The SIP itself has very little incentives to get better (since it’s effectively a mandated monopoly), so it’s software is very slow compared to the rest of the market.  It’s common for the SIP to send out data that’s 1-100ms behind what the rest of the market actually see.
3. Depending on where you are in relation to the SIP source, you may get data that’s even slower because now the data source is 2 hops away.

Finally, the last bad thing about NBBO is that it doesn’t account for hidden orders.  We already know the NBBO ignores odd lots.  But it also is ignorant of hidden orders.  Venues (lit or otherwise) typically allow orders to be hidden from the public and not published in market data.  These are typically orders that are big, because if someone wants to sell 1,000,000 shares of GOOG in a single order, anyone seeing that order will freak out and dump GOOG (OMG! They know something we don’t!). To avoid market panic, these large orders are typically hidden — sometimes totally hidden, sometimes they may show up as only 100 shares on the books of the exchanges. That’s why even if you see NBBO as $100 – $101, and you send an order to an exchange to buy at $100.50, you may actually hit a hidden order, and get executed.

Of course, because these orders are hidden, they don’t show up in NBBO, which means WMMs don’t have to honor that $100.50, even if they can reasonably guess that the order is there (there are ways to forecast/predict this, I won’t go into that).

To conclude, by not going to an exchange, you potentially lose out on potential liquidity that can fill your order at a better price.  WMMs can, perfectly legally (and sometimes forced to by SEC rules), fill your order against their own portfolio, then go out and buy/sell at a better price on the lit exchange to make an instant profit.

Footnotes

1. Yes, yes, yes, the terms sound disparaging. They are not meant to be — these are official (and technical) terms. If you don’t like it, talk to the textbooks.