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\( F(t) \) Income stream ($/time)
\( \text{NPV} \) Net present value
\( r \) Hypothetical rate of return

How to think about stocks, part 1

Let us begin with some basic definitions

investing: the act of attempting to use money to make money as distinct from consumption (using money to increase the comfort of life temporarily). involves the buying and selling of securities and is distinct from gambling in many important ways (to be discussed below)

security: anything which can be bought and resold at a negotiable price, usually refers to stocks, bonds, and options. All securities are either equities, debts, or a combination.

equity: the value of something for sale that is not debt. Cars, houses, and companies are the things most often associated with equity.

stock: the ownership of a small percentage of a company. Right now Exxon is trading at $76 which means the smallest piece of Exxon you can buy is $76 (1 share of stock) or 2.38x10e-8% of Exxon. If you had an extra $100 billion lying around, you could buy 33% of Exxon and then you would have a real say in what Exxon does next year. If you own 2.38x10e-8% of Exxon you do not have much say in anything, you just have the ability to profit or lose money as a result of what Exxon does.

debt: the promise of one entity to pay another entity a sum of money later in exchange for a sum of money today, usually includes interest.

bond: fancy word for loaning money to a company or government. In other words, bonds are the financial tool by which small individuals and large institutions alike may purchase or sell the debt of other large institutions and governments.

leverage: the ratio of debt vs the value of assets. If I owe $100,000 on my mortgage, but my house is worth $5,000,000, I am not very leveraged. If my house is only worth $110,000, I am very leveraged.

There a lot of ways to use money to make more money but the three most common reliable are real estate, bonds, and stocks. Real estate requires more effort on the part of the investor so we call it a less "passive" choice. Bonds make sense, you give money to some corporation or government, they promise to give it back later with interest. It is a loan where you are the bank. Stocks are surrounded by the most misunderstandings on that list.

What is the value of a company?

Why buy stocks? That is to say, why do people who work in finance recommend you buy ownership shares of publicly traded companies instead of rocks, or cars, or paintings, or houses? This question probes an interesting and under-considered problem, what defines a company's value? Why are Coca-Cola, Microsoft, and General Electric worth $192, $550 and $237 billion respectively (as of 2017)? Why not double or half of those numbers? Intuitively, we understand that companies are groups of people organizing their labor and resources to make a profit but that understanding gives neither a reason for the common sudden fluctuations in company values nor a rigorous method of estimating the value of a company.

There are two things at play here. The primary consideration is the company's real value which is a quantifiable single value (but unknowable because it would require absolute knowledge of the future). A company is worth all of the money it will ever make minus all of the bills it will ever pay multiplied by the appropriate time discount on all of those cash flows. However, that value is a function of uncertain events in the future so a company's value may fluctuate wildly in time with investors' perception of the likelyhood of future returns. The secondary consideration driving the price is the speculation over what other people think about the company's future prospects. The speculator is much less interested in the value as defined above, and more interested in trying to anticipate other investors' thoughts about that value. The speculator buys a stock hoping that other investors will rapidly change their opinion about that company's value (in response to an earnings report, scandal, news of industry trends, new company policies, etc). The speculator is interested in buying and selling on a much faster time scale, days to a year, instead of a value investor expecting to hold a stock for a minimum of 10 years. As markets have gone electronic, speculators have been able to buy and sell on far shorter time scales. This has born an entire industry of stock traders with no interest in the stock's underlying value, but rather an interest in predicting the stock's appraisal by other speculators working on slightly longer time scales. Some speculators hold stocks for under 1 second. Unless you have an army of statisticians working for you, you will lose money attempting to speculate on a daily basis (unless the market trend as a whole is pushing prices up enough to cover the commissions you will incur). Individual investors do occasionally make money speculating the way gamblers in Vegas occasionally make money but that does not make the Roulette table a prudent recommendation for retirement savings. History has shown that value investing, that is to say, investing on a decade-plus timescale, is the only reliable way to make a profit in the stock market.

This brings the question, what is an appropriate amount to pay for a company? Given we do not know with certainty what the future earnings of a company will be, all we have for certain are the records of what a company has earned thus far. If a company is earning $X per year, that revenue stream is either paid to the investors as dividends or reinvested in the company as new factories, employees, ads, or other value creating enterprises. In either case, so long as the the reinvested earnings are not spent on fruitless endeavors, the value to the investor has risen by $X per year. We already know what $X per year are worth from the net present values article. Established large companies trade at values that reflect the NPV of their earnings per share with rates of return between 4% and 10%. New companies often do not trade in this range, especially in the tech sector where people are often convinced the profits will come later so there is nothing to worry about today. It is true for some companies some of the time but in general that line of thinking leads to truly absurd valuations which do not come to fruition.

Plot of net present value analysis of earnings for a company

[Caption] The true present value of a company is a single value dependent on the company's income, expenses, and the time discount value of money, \(r\). (Panel a) Earnings per share per year of a real multibillion dollar. As is true for all companies, the earnings are volatile year to year. (Panel b) Net present value factor for various rates of return. (Panel c) The net present value of the company is the integral of all earnings multiplied by the appropriate time discount. Here we take the integral from 0 to 56 years because that is the price history we have. Depending on the time discount value of cash at the time (which depends on your other options), the stock was worth between $50 and $100 per share in 1960.

The average rate of return we can reasonably expect is between 4% and 10%, therefore a company is worth between 10 and 25 times its annual earnings (also known as the price to earnings ratio or P/E ratio). This is the sober analysis and the point at which we can see how pervasive stock market foolishness can be. When speculators chase one another’s tails, the price of a stock can vary widely as a function of imagined future earnings. If you are planning to pay more than 25X annual earnings per share for a stock, you need to have exceptionally good, articulatable reasons for believing that the company is likely to be significantly more profitable in the future.

Tech companies are notorious for ridiculous evaluations because in theory they can rapidly become profitable if they have built a large customer base. Often these theoretical hopes lead to delusional valuations. All these wild hopes and trendy evaluations lead to some hilarious sarcasm in the finance sections of major publications such as the example below.

Snapchat is popular among people under 30 who enjoy applying bunny faces and vomiting rainbows onto their pictures. But many on Wall Street are critical of its high valuation and slowing user growth. Snap has warned it may never become profitable. - Reuters 5 June 15, 2017

This kind of foolishness is common in the finance world.

© MC Byington