Daniel Brockman: AI & Asset Allocation, Appendix 2

"... when you can measure what you are speaking about, and express it in numbers, you know something about it;"

-- Lord Kelvin, 1883

< Part 1 | Part 2 | Part 3 | Appendix 1 | Appendix 2 >

Guide to Terms and Calculations

Lord Kelvin 1824-1907
Image: Messrs. Dickinson
London, New Bond Street

Here we have an extremely brief look at some arcane but useful terms and simplified useful techniques, and a little guidance toward more information for readers interested in further investigation. Generally, the research pages of your broker’s website are the easiest place to find this information (except what you must calculate yourself). You can readily find most or all of these terms and calculations using your favorite search engine or reading about them in Wikipedia.org.

Find explanations of some additional terms in Part 2.
For additional readings, see the sources list in Part 1.

Assets: All the company’s money, amounts loaned to or invested in others, property, supplies and materials on hand, funds set aside to pay future employee benefits, tax refunds expected but not yet received, and amounts billed to customers but not yet paid.

Bond: A debt owed by a company or government and divided into many uniform shares called “bonds”, having a maturity value (a.k.a. face value) to be paid at a future “maturity” date. Most bonds pay interest, a stated percent of maturity value, though some pay no interest. Some bonds are traded on securities exchanges.

Book value (a.k.a. Equity or Stockholder’s Equity): Assets minus liabilities. For a stock, see the company’s balance sheet, published annually. For stock ETFs for the long term beach investor (see Part 1), book value is the sum of the book values of the stocks held in the ETF, and the ETF has no significant liabilities (ETFs that have significant liabilities are called “leveraged” ETFs, and if you are wary of risk, then know that leveraged funds are playing with fire.).

Book Value Divided by Price: Your broker’s website will probably show the price per share divided by book value per share, or maybe they will show a blank or “N/A”. If the broker shows you price divided by book value, then calculate book value (b) divided by price (p) as

b/p = 1 / (price divided by book value).

If the broker shows you a blank or “n/a” or the like, then they feel challenged by b less than or equal to zero, in which case you should calculate book value manually from the most recently reported quarterly balance sheet (provided by the broker). Then, using market capitalization for the entire company, calculate

b/p = book value divided by market cap

If your broker reports multiple versions of book value, I recommend using "tangible book value (MRQ)", or something like that. "Tangible" means goodwill and intangible assets are excluded, two features of financial accounting that one may easily confuse with hot air. "MRQ" means "Most Recent Quarter" reported by the company.

Positively Correlated.
Image: Wikimedia, "Ordinary Least Squares", Public Domain

Correlated: If the price change usually goes up when the metric goes up, then we say the price change and the metric are “positively correlated”. If the price change goes down when the metric goes up, then we say they are “negatively correlated”. Correlation doesn’t tell us whether one causes the other, or how certain we are, or how intense is the effect. Correlation is a number between -1 and 1. Nearly all spreadsheet apps include the correl() function which calculates correlation, or the equivalent pearson() function. Example: For sector ETFs, we say beta (the metric) and the price change are negatively correlated, the correlation is a negative number, meaning that as beta decreases, we expect the future price change will increase, and as beta increases, the future price change declines.

Credibility: A weighted average of a useful, though not fully believable, measurement and a standard value, though general and non-specific and less relevant, such as the average for all stocks. The credibility calculation allows us to compare a stock like TWTR, which began trading about 5 years ago, with a stock like MA which has been around for decades. If you think an 5-yr price growth metric (g) is a more believable predictor than a 2-yr price growth, but you would need a 10-yr growth of price metric to believe it “completely” and compare it with other stocks, then we can base the weighting on the number of years available (y), divided by 10. Then we calculate the credibility (c) as

c = square root of the number of years available divided by 10

c = sqrt( y / 10 )

("sqrt()" is the spreadsheet software function for square root)

Example: TWTR has price history since 2014, so y=5, and then c=0.707.

What we take as the standard (s) could be the average for all stocks for which we have 10 years of information, or the median, or the S&P500, or whatever we are prepared to believe if we don’t know the 10-yr metric for the specific stock, knowing we aren’t exactly right, but knowing the standard is a better estimate than “n/a”. Then we weight the partial growth information (g) we do have by the credibility (c), and for the information we don’t have, we use the standard (s) weighted by (1 - c).

Credibility weighted 10-yr price growth = c * g + ( 1 - c ) * s

Example: if TWTR, y=5, g=1.1, s=3.1, then c=0.707

and

credibility-weighted 10-yr growth = 1.7.

Liabilities: Money owed to others, salaries and benefits owed to employees, advance payments from customers, amounts billed to those few customers that probably won’t pay (doubtful accounts), bills for purchases not yet paid, taxes not yet paid, and payments promised to lenders, stockholders and investors.

Market Capitalization (a.k.a. Market Cap or Capitalization): Generally, price multiplied by the number of shares outstanding. If a company has more than one kind of stock, then the market cap of the company (your probable topic of interest) is the sum of the market caps of the various kinds kind of stock.

Price: Unless otherwise indicated, these articles refer to the price of the last trade when the exchange closes for the day, the “closing price” or “last price” on a given day.

Rate of dividend increase (or decline) per share: I take the most recent five years of dividends reported by the company, summarize them by 12-month periods, and apply exponential least squares regression to get the average annual rate of increase. NO, you don’t need to do that. All you need is some way to come up with an unambiguous, repeatable, generally applicable estimate of what rate of increase to expect in the future, so that you can compare one stock with another. If you don’t know exponential least squares regression, and you don’t feel like reading how to do it on Wikipedia https://en.wikipedia.org/wiki/Ordinary_least_squares, or asking a friend, there are satisfactory alternatives.

Here is one. Use the slope() function included with nearly all spreadsheet software. A stock with larger (steeper) slope number has dividends increasing faster.

s = slope of least squares line

= slope(y1:y5,x1:x5)

For more information, type “slope function” into your favorite search engine.

Here is a second. Divide the year 5 (most recent) dividend (d5) by the year 1 (earliest) dividend (d1), take the square root of that, then take the square root of that. That is, you can get an estimate of the future rate by either of the following two equivalent calculations.

Estimated rate = sqrt( sqrt( d5 / d1 ) ) = ( d5 / d1 ) ^ ( 1/4 )

Reinvestment of dividends: Using dividends you receive to buy additional shares of the investment that produced them. Many or most brokers will automatically reinvest dividends for you, at no charge, on your request.

Return: The amounts of money you get from an investment, usually compared with what you pay to get it in the first place. That is, how much money do you have when you get out of this investment, compared with how much you put into this investment in the beginning. Includes the dividends you receive while you hold it, and the price you get when you sell it, less the costs of holding and keeping and selling it, including taxes and broker’s fees and your time. For many purposes, the price you sell for, compared with the price you buy for, gives you a good approximation of the return.

sqrt(), square root. The square root of x is sqrt(x). Nearly every spreadsheet app provides sqrt(), and you probably have a square root function on the calculator app on your phone, and you can type “square root of 0.93” into your favorite search engine to get the calculation, and you can calculate it by hand (ask your favorite search engine).

Ticker (a.k.a. Ticker Symbol): A standardized few letters or numbers representing a stock or bond or ETF or mutual fund or something else traded on an exchange. Examples: AMZN is the ticker for Amazon.com, IYR is the iShares U.S. Real Estate ETF, LUV is Southwest Airlines, VOO is the Vanguard S&P500 ETF, STZ/B is the Constellation Brands Inc. class B shares.

10-yr growth of price: the most recent price divided by the price on this date ten years ago.

< Part 1 | Part 2 | Part 3 | Appendix 1 | Appendix 2 >

Images and Sources

See Part 1.