These 20 graphs form a pictorial essay of a company’s financial statements. This large company survived the Recession of 2007-8!
Copyright © 2017 Douglas R. Knight
The stock market lists several thousand stocks which have a variety of prices in relation to company profits. Company managers decide how they will use the profits to either pay dividends to shareholders or retain the earnings to build shareholders’ equity (ref. 1). The retained earnings may be used in ways that ultimately raise or lower the market price of the stock. Consequently, bankers and brokers pay attention to quarterly reports of the company profits measured as earnings per share (EPS).
Investors want to know whether the stock is priced too high (“overvalued”) or too low (“undervalued”) compared to the EPS. Professional analysts assist investors by preparing the PE, PEG, and PEGY valuation ratios.
PE is the ratio of stock price (P) to company earnings (E). Formula 1 is used to calculate the PE (ref. 1,2):
PE = P / E, formula 1
P is the price per share and E is the EPS accumulated over a 12-month period. For more information, please see notes at the end of this article.
example: if one share of stock is priced at $50 and the company’s annual EPS is $5, then 50/5 equals 10/1. The PE is 10.
The timing of company earnings determines whether the PE is labeled as “trailing” or “forward”.
Trailing PE is the current price per share divided by the EPS accumulated from the past 12 months or past 4 quarters. Trailing PE is based on known quantities. Forward PE is the current price divided by the accumulated EPS expected for the next 12 months or next 4 quarters. Forward PE is an uncertain forecast of future market value based on the management’s or analyst’s expectation the EPS for the next 12 months.
PE represents the market value of all shareholders’ claims to $1 of annual EPS, past or future. The market value is judged to be high (“overvalued”) or low (“undervalued”) compared to an arbitrary estimation of fair value. There are several ways of determining a fair value.
PEG is the ratio of PE to G (ref. 1,7,8; formula 2):
PEG = PE / G, formula 2
G is the compound annual growth rate of EPS over a time period of 3-5 years, perhaps even longer in special cases. For more information, please see endnotes.
example: if one share of stock is priced at $50 with an annual EPS of $5 and a 10% compound annual growth rate of EPS, then 50/5/10 equals 1.00. The PEG is 1.00.
PEG measures the market value of a stock relative to the company’s rate of earnings growth (ref. 7,8). The theoretical equilibrium between market value and the rate of EPS growth occurs at PEG = 1.0. PEGs below 1.0 suggest undervaluation and those above 1.0 suggest overvaluation (ref. 9).
Trailing- and Forward PEGs represent the stock’s market value relative to past and future eras (ref. 7,8). Trailing PEG is a factual measurement of market value provided that the EPS was measured during the past year and the EPS growth rate occurred during the past several years. Forward PEG is an uncertain prediction of market value based on the company’s expected earnings for next year and an analyst’s forecast of earnings growth for the next several years.
examples: when the forward PEG is above 1.0, the market expectation of growth exceeds consensus estimates and the stock is overvalued (ref. 8). If PEG is below 1.0, the stock is undervalued (ref. 2,7).
Limitations of PEG (ref. 3,8):
Some investors prefer high-yield ‘value’ stocks rather than low-yield ‘growth’ stocks. High yield stocks typically pay higher dividends at lower EPS growth rates (e.g., the stocks of utility companies). PEGY includes dividends in its valuation ratio for high-yield stocks (ref. 8; formula 3).
PEGY = PE / (G+Y), formula 3
Y is the stock’s dividend yield. Dividend yield is the ratio of the annual dividend per share to the price per share.
example: if one share of stock is priced at $50, the annual EPS is $5, the compound annual growth rate of EPS is 8%, and the dividend yield is 5%, then what are PEG and PEGY?
PEG = 50/5/8 = 1.25. PE is overvalued if the high dividend is excluded.
PEGY = 50/5/(8+5) = 0.77. PE is undervalued if the high dividend is included.
Besides measuring market value, the PE and PEG also predict the stock’s payback period. A payback period is the amount of time needed for the accumulation of company earnings to match the original amount of investment. If all accumulated earnings were paid to investors, which is unlikely, the payout would provide a 100% return. Longer payback periods represent riskier investments, especially when the company is still establishing its market position or competing with innovative companies (ref. 9,10,11).
The PE ratio also represents a payback period measured in years.
example: if a stock is priced at $50 per share and the EPS is $5 per share every year, then $50/share divided by $5/share/year equals the payback period of 10 years. The same units of $/share cancel each other in the numerator and denominator.
The PE payback period is the time needed for an accumulated EPS to equal the original share price, assuming the EPS remains constant during the accumulation period. Most companies don’t repeat the same EPS every year.
The PEG payback period accounts for the desired phenomenon of EPS growth. The PEG payback period is the number of years that the growth of earnings accumulates enough value to match the original investment (ref. 9,10).
example: if a stock is priced at $50 per share, the EPS is $5 per share, and the EPS growth rate is 10%, it would take 7 years for the EPS to accumulate a value of the original stock price of $50. The PEG payback (7 years) is earlier than the PE payback (10 years) due to the 10% rate of earnings growth.
Company earnings are a strong determinant of stock value. PE, PEG, and PEGY ratios represent the stock market’s valuation of company earnings. Don’t rely solely on company earnings to judge the investment value of stocks. Also assess the business performance and company value (ref. 2,6).
Formula 1: PE = P / E
Formula 2: PEG = PE / G
1. How to Find P/E and PEG Ratios, by Thomas Smith, Investopedia LLC. http://www.investopedia.com/articles/fundamental-analysis/09/price-to-earnings-and-growth-ratios.asp?lgl=v-table
2. How to use the PE Ratio and PEG to tell a stock’s future, by the Investopedia Staff, updated March 17, 2016. http://www.investopedia.com/articles/00/092200.asp
3. What is the PEG Ratio? https://www.fool.com/knowledge-center/peg-ratio.aspx
4. Aswath Damodaran, Intrinsic Valuation in a Relative Value World. http://people.stern.nyu.edu/adamodar/pdfiles/country/relvalFMA.pdf .
5. PEG Ratio; From Wikipedia, the free encyclopedia. pages 6-7. https://en.wikipedia.org/wiki/PEG_ratio
6. How useful is the PEG Ratio? Joseph Khattab, April 6, 2006. The Motley Fool. https://www.fool.com/investing/value/2006/04/06/how-useful-is-the-peg-ratio.aspx
7. Price/Earnings to Growth- PEG Ratio. Investopedia LLC. http://www.investopedia.com/terms/p/pegratio.asp
8. PEG Ratios Nail Down Value Stocks, by Ryan Barnes, 11/24/2015. Investopedia LLC. http://www.investopedia.com/articles/analyst/043002.asp?lgl=v-table
9. Double your dollars. Selena Maranjian, September 7, 2010. The Motley Fool. https://www.fool.com/investing/value/2010/09/07/double-your-dollars.aspx
10. Payback period = double your money. Course 304: PEG and Payback Periods. Morningstar, 2015. http://news.morningstar.com/classroom2/course.asp?docId=3066&page=2&CN=C
11. The longer the payback period, the greater the risk. Course 304: PEG and Payback Periods. Morningstar, 2015. http://news.morningstar.com/classroom2/course.asp?docId=3066&page=3&CN=C
Copyright © 2017 Douglas R. Knight
Physics needs math, so does Finance. Then no wonder some curious physicists began to create math models of financial markets in the 19th Century, only to find the task more difficult than imagined. Advances during the 20th Century ulitmately generated great wealth among a group of saavy traders known as the “Quants”. Their sophisticated trading models worked for a while until widespread use by firms in ‘Wall Street’ caused the global financial system to collapse in 2008. New models continue to evolve today. This book pays tribute to scientists who tackled the problem of modeling financial markets.
Today’s market models are still imperfect!
1526: Cardono wrote an unpublished book on the theory of probability based on the odds of dice games. For example, what is the chance of rolling 2 dice for a sum of 10?
1654: Pascal and Fermot established the modern theory of probability based on various gambling games. They realized that probability is a chance, not a certainty. In the 20th century, it was realized that the a probability becomes a certainty when taking an infinite number of chances [Law of Large Numbers].
Bacheleier invented mathematical finance in the late 19th century. His graduate thesis applied probability theory to market speculation. In his ‘efficient market’ theory, Bechelier assumed that future prices take a ‘random walk’ within limits that describe the graph of a bell-shaped curve. In other words, stock prices have a normal distribution with a stable average. Bechelier’s ‘random walk’ model spawned 2 books in the 20th century.
1959: An astronomer named Maury Osborne wrote “Brownian motion in the stock market”. Osborne dismissed the idea that stock prices have a normal distribution. Instead, the rate of return was normally distributed. His plot of stock prices was not bell-shaped, but lump-shaped with a long tail to one side. Osborne was first to show the importance of the log-normal distribution of prices to markets.
1960s: Benoit Mandelbrot discovered fractal geometry and adapted the consequences to understanding markets. Mandelbrot’s method described extreme market events.
1965: The issue was whether to analyze stock prices with Osborne’s or Mandelbrot’s method of analysis. Today’s consensus is that rates of return are fat-tailed with an unstable average.
1973: Burton Malkiel adopted Osborne’s work in a book called “A Random Walk Down Wall Street”.
Bachelor, Osborne, and Mandelbrot neither traded nor earned profits; they were academics.
1961: Edward O. Thorp beat the game of Roulette with a successful strategy. He later showed that math models could earn profits from financial markets by operating a hedge fund. Thorp believed that the stock market is the world’s biggest casino. Buying stock is betting that the price will rise and Selling stock is betting that the price will fall. The true price of a stock is where the odds of winning and losing are equal. He devised the ‘delta hedging’ strategy of picking the right mix of warrants and stocks to consistently earn a 20% annual return. The idea was to simultaneously short-sell warrants and buy underlying stocks. The stocks would soften the impact of a bad bet and augment the impact of a good bet.
1967: Thorp co-authored the book, Beat the Market. Jay Regan, a stock broker, partnered with Thorp to create the Princeton-Newport Partners hedge fund.
1969: Fischer Black derived a relationship destined to become the Black-Scholes-Merten model for the pricing of options. Black made quantitative finance an essential part of investment banking.
1991: Physicists James Dayne Farmer and Norman Packard studied nonlinear forecasting. Given a chaotic process such as the financial market, their goal was to predict the next movement of prices.
1991: Farmer, Packard, and McGill formed The Prediction Company with the goal of profiting from Wall Street. They developed black box models of algorithmic trading which often worked for unknown reasons but also suffered unpredictable failures. It is still a mystery how market patterns are corrected.
1997: Didier Sornette, a geophysicist, studied the patterns of complex systems to predict critical events in the physical and social sciences. He filed a patent notice in 9/17/1997 that predicted a market crash the following month. Then he bought far-out-of-the-money Put Options to earn a 400% profit from his prediction.
2008: The economic collapse of 2008 presented an opportunity to change how economists think about the world.
2009: Smolin, Weinstein, and others convened a conference of intellectuals to develop new models of economics. They failed to agree on the problems and solutions.
All of the physicists’ models had successes and failures, but their works represent steps in the evolution of understanding markets. Financial modeling is an evolutionary process in which excellent assumptions can be destroyed by a change in market conditions. The realistic goal is to develop a model that provides a good answer at the moment. Why? One reason is that markets are evolving in response to economic growth, regulations, and innovation. Models ultimately fail!
The life cycle of a successful company progresses through periods of rapid growth, slow growth, no growth, decline, and demise. An adaptable company may endure with successive cycles of renewal, rebirth, and resurgence. This book describes a pathway to success. Finance is a sub-theme; other themes are accounting and management.
A general ledger of all transactions is used to prepare all financial reports and assess the company’s performance. Companies that issue publically traded stock are required to publish 3 financial statements every quarter of the fiscal year. They are:
The Balance sheet is a snapshot of the company’s financial condition at the end of the fiscal period. Items are reported under headings that conform to this equation: Assets = Liabilities + Equity. Assets and Liabilities are subdivided into Current and Long-term transactions. Current transactions are expected to be completed in the next 12 months and indicate the company’s liquidity. Long-term transactions indicate the company’s leverage, plus more. Equity is the company’s net worth. Within this framework, the author explains and discusses items of special relevance to business management.
The Income statment describes business operations during the time period between 2 balance sheet dates. According to rules for accrual accounting, every transaction has an order date and delivery date. Subtotal transactions are grouped under revenues, production, operations, other transactions, and net income. Net income (i.e., company profit) is the bottom line of accrual accounting in the Income statement. Readers of this chapter learn how to evaluate the business and its managers.
More businesses fail due to the lack of cash than the lack of profit. Consequently, it’s important that the Cash Flow statement reports a net cash balance from the net cash flows of operations (CFO), investing (CFI), and finance (CFF). The CFO is derived from Net Income (in the Income statement) by excluding non-cash transactions listed in the Income statement such as depreciation, receivables, pre-paid expenses, inventory, and payables.
The remaining chapters are devoted to these topics:
The market value of your stock equals your principal (i.e., the amount you invested) plus any profit or loss from price fluctuation. The market price that moves below what you paid to purchase the stock will produce a loss of principal if you sell the investment. Here are several risk factors that may drive stock prices downward:
The risk of an extreme loss can be prevented by setting a stop-loss price (“stop”) to sell part or all of your shares.
The systematic way is quite simple. If the market value is below your invested principal, then select an absolute loss or a fraction of the principal. Examples:
The technical way is based on the stock’s historical prices. If you want to minimize the chance of a sale, set the stop at the lowest price from the past 5-10 years. Beware that setting the stop at a historical low may incur a steep loss. Other ways involve the more complicated analyses of trendlines, moving-average lines, or price statistics.
Another way is to adjust the price gap (gap = market price – stop) to the growth of capital gains. As the market price increases over time, choose a narrow gap to protect the capital gain or a wide gap to reduce the chance of a trade. Generally speaking, widening the price gap will reduce the chance of a trade at the risk of incurring a bigger loss.
A brokerage firm will enforce your stop order for 30-90 days depending on the firm’s trading platform. The firm’s computer activates the order when the latest market price reaches the stop. The order is then filled at the next available price. In a chaotic market, the price could plunge below your stop to an exceptionally low value at the next available trade, resulting in a bigger loss than you planned. You might be able to prevent this result by setting a limit slightly below the stop. The trading order would be filled somewhere within the stop-limit price zone unless the transaction is cancelled, unfilled, when the next available price dips below the limit. The limit helps protect the extent of your loss.
Nobody’s immune, but long-time investors have the least concern. Investment strategies such as dollar-cost-averaging and automatic-dividend-reinvestment plans will help protect against damages from periodic bear markets. Short- and intermediate-time investors are at greater risk for incurring an extreme loss from market down-cycles. For example, families who are saving to pay college fees or to buy a home risk big losses from a bear market.
Stop orders are used to set the price for buying or selling exchange-traded products such as stocks, ETFs, and REITs. This article discussed the use of a stop-limit order to sell a stock in a declining market. Brokerage firms may restrict the duration of stop-limit orders to 30-90 days after which the order is cancelled without a transaction until you renew the order. Periodic renewals allow you to reconsider your strategy in light of the prevailing price trend. In a downtrend, simply renew the order. In an uptrend, you may wish to protect a growing profit by resetting the stop-limit order to higher prices. Click on this link to skimming a profit for another perspective on protecting a growing profit.
Copyright © 2017 Douglas R. Knight
Selling all or part of a profitable investment is a tough choice to make. On one hand, holding the investment allows time to accumulate a high return, but at the risk of losing profit in the market’s next big decline. On the other hand, selling portions of the investment to ensure a profit today will diminish the future return.
Both choices are easy to illustrate by imagining a stock investment that pays no dividends. Assume there is a consistent growth of stock price and that no additional shares are purchased after the original purchase. The profit is skimmed by selling part of the investment when its market value grows to twice the original purchase. Repeat the process every time the market value doubles until the investment is closed. Chart 1 illustrates the skimming of a $1,000 investment.
After 5 years, the investor could claim a profit of $1,000 on the original $1,000 investment. Then the choices would be to close the investment at $2,000, withdraw only the $1,000 profit and wait for more (green circles), or withdraw nothing and wait for a bigger profit (black squares). The largest profit is made by waiting 20 years.
Chart 2 illustrates the accumulated cash balances of the HOLD and SELL strategies.
After closing the investment in 20 years, the accumulated cash balance would be $16,367 from the HOLD strategy and $5,045 from the SELL strategy.
The accumulated cash balance will vary according to the annual rate of return (appended chart 3), the amount skimmed (appended chart 4), and the payment of dividends (appended chart 5). In every condition, the total profit of the HOLD strategy exceeds the total profit of the SELL strategy.
On the question of whether or not to skim profits, skim if you need cash in the next 5-10 years. Otherwise, don’t sell without reassessing the investment or using a risk management scheme. The question of selling for a loss was excluded from this discussion; that’s a different topic.
Charts 3-5 are tables of cash balances that represent profits from an imaginary investment of $1,000. The choices for taking a profit were to HOLD the investment for 20 years before liquidating the account or to SELL profitable portions of the investment. Assume there were no trading fees.
Chart 3 shows that a 15% annual rate of return earned a bigger profit than a 7% annual rate of return. Furthermore, the HOLD strategy earned a larger profit than the SELL strategy at both rates of return.
Chart 4 illustrates the effect of skimming 50%, 100%, or 150% increments of market value.
The HOLD strategy outperformed the SELL strategy. With the SELL strategy, waiting longer to skim bigger profits accumulated a larger cash balance after 20 years. Why? The bigger profits were less frequent, which had the effect of preserving the investment’s principal for longer time periods.
Chart 5 reveals a surprising effect for skimming profits from reinvested dividends.
There were no surprises in the HOLD strategy. Reinvested dividends accumulated the largest cash balance over 20 years. However, reinvested dividends accumulated the lowest cash balances in the SELL strategy. Why? Slightly more shares were sold every 5 years from ‘reinvested dividends’ compared to ‘no dividends’. Yet the same number of shares were sold from ‘cash dividends’ compared to ‘no dividends’. The cash dividends directly augmented the cash balances.
Copyright © 2017 Douglas R. Knight
They need protection from the ‘streets’, a decent eduction, and financial skills.