Stock Market Prices

April 1, 2020

SUMMARY:

The Stock Market is a place where professional traders arrange cash-for-stock transactions between buyers and sellers.  Other securities are sold in the Market, but stocks occupy the vast majority of listed securities—(securities are investment contracts worth money, of which stocks represent shares of ownership in companies).

Every transaction is called a Trade.  Regular trades involve the buyer’s payment of cash for securities offered by the seller.  Buyers and sellers propose trades to their brokers who then send the proposals (orders) to professional traders.  Market rules require traders to fill orders at the next available price, either the highest Bid of a buyer or lowest Ask of a seller, depending on the type of trade.  The general trend of prices among many trades is calculated as the Market Index.  Investors should prepare trading orders carefully with awareness of the potential consequences.

Competitive prices

The Stock Market is designed to set prices for securities at an agreeable price among competitive Bids and Asks –(the buyer’s price is called a Bid and the seller’s price is an Ask).  The agreed price varies according to the prevailing action of trading orders in which Buy orders are filled at the lowest available Ask and Sell orders are filled at the highest available Bid.  In a ‘seller’s market’, the buyers’ surplus demand for securities raises prices for the sellers.  Examples include the rising prices in rallies and bull markets.  In the ‘buyer’s market’, the sellers’ surplus supply of securities lowers prices for the buyers.  Examples include the falling prices in corrections and bear markets.  

Market Index

The Market Index is a singular value which represents the prices of many securities traded in stock exchanges [see index methodology in the appendix].  Graphs of the market index display daily fluctuations (volatility), trends, and market cycles.  The trend of a market index is useful in several ways:

  • Analysis of supply-and-demand: An increased demand for shares drives prices upward and conversely, an increased supply of shares drives prices downward.  The index follows the price trends.
  • Benchmark: Investors like to know if the prices of their holdings are performing better or worse than the market index.
  • Passive management: Index funds (e.g. ETFs)  are investment portfolios designed to match the performance of an index.
market indices, 5y

Chart 1.  The ‘Dow’ represents stock prices of 30 large companies traded in the New York Stock Exchange and Nasdaq market.  The ‘S&P 500’ represents market capitalizations of 500 large companies traded in U.S. exchanges (market capitalization is the sum of prices for all shares of a given stock).  The ‘Nasdaq’ is calculated from market capitalizations of all companies listed in the Nasdaq market.

Chart 1 displays the parallel behavior of 3 popular indices; they are broad market indices by virtue of describing the price volatility and trends of many stocks listed in the Market.  Small fluctuations represent daily values reported at the close of the trading day.  Large fluctuations display short and long cycles of market activity.  A long market cycle consists of one “bull” and “bear” market in succession.  Long bull markets create a general upward trend of market prices that endures several market cycles.

Trading Orders

In contrast to the market index, which represents many stocks, the quote represents one stock.  Quotes are widely published in the media and brokerage firms.  A typical broker’s quote shows the last traded price, traded volume, and opposing prices (bid & ask).  

Investors place a trading order by consulting their broker or employing the broker’s online trading platform.  In a trading platform, the investor completes an order form with the following information:

  1. Ticker.  The trading symbol of the desired security
  2. Action.  Buy or Sell
  3. Volume.  Quantity of units (shares) to be traded
  4. Type.  Method for filling the order (Market versus conditional)
  5. Price.  conditional or Market.

The basic types of orders are Market and conditional.  Market orders are filled immediately at the next available price, but the investor is unable to specify the price.  Conditional orders enable the investor to specify the price of a future trade within a period called the “time-in-force” (typically 60 days).  Conditional trades are activated at the specified price and filled at the next available price. 

Limit and Stop are two types of conditional orders available to most stock investors.  A Limit is the preferred price for a Buy or Sell order.  The Limit order is activated when a future market price matches the Limit price.  The activated trade is then filled at the same price or a more favorable price; but, if the next available price becomes unfavorable due to price fluctuation, the Limit order is cancelled unfilled.  A Stop is the specified price of a Sell order.  The Stop order is activated at the specified price and then filled by a Market order.  The seller has no control of the price after a Stop order is activated.

A Trading Story

Two fictional investors named ‘Green’ and ‘Red’ decided to place opposite trading orders for the same security on March 5th when the quoted price was $49.  ‘Green’ thought the price would eventually drop and wanted to buy 100 shares for a bargain at the Limit of $45.  The intended bargain was a $400 reduction of investment cost.  ‘Red’, who owned 100 shares, thought the future price would drop for a loss.  “Red’ wanted to prevent a deep loss by selling 100 share at the $45 Stop.  ‘Red’ would be happy if the Stop order were never activated, but just in case prices declined, the loss of $400 could be tolerated.  The outcomes are illustrated in Chart 2.

trading orders

Chart 2: The Fate of 2 Conditional Orders.  Red and Green symbols represent respective Stop and Limit orders made on March 5th.  The dashed line indicates that both orders remained-in-force until activated and filled on March 9th.  An overnight crash of prices halted trading at the start of the March 9th trading day.

On March 9th, a market crash activated both orders at the moment trading was halted by a circuit breaker.  When trading resumed, ‘Green’ bought 100 shares at the very favorable price of $41, even $4 cheaper than the intended $45 Limit.  ‘Green’s’ bargain was $800 instead of $400.   ‘Red’ sold 100 shares at the very unfavorable price of $41, $4 below the intended $45 Stop.  ‘Red’s’ original market value of $4,900 dropped by $800 instead of $400 after the activated Market order filled at the next available price of $41.

–Lesson: Limit orders protect a preferred range of transaction prices.  Market and Stop orders don’t protect the transaction price.

References

  1. Trading orders, Invsetopedia.com
  2. Supply and demand, Investopedia.com
  3. Stock quote, Investopedia.com
  4. DJIA index methodology, Investopedia.com. 
  5. S&P 500 index methodology, Investopedia.com.
  6. Do ‘Circuit Breakers’ Calm Markets or Panic Them?: QuickTake. Nick Baker & Sam Mamudi.  The Washington Post 3/19/20, WashingtonPost.com 

Appendix: Index methodology

The stock Index is a special sum of weighted prices for many stocks, (w * Price) of many, listed in the stock market. The sum is divided by a special divisor, D.

Index(w * Price) of many ÷ D

The stocks, their weighting factor (w), and the divisor (D) are proprietary definitions of the Index provider.  Repeated calculations of the Index create a string of values that reveal the general volatility and trend of stock prices.

Copyright © 2020 Douglas R. Knight


Language of the Stock Market

February 29, 2020

Summary: New investors might find it helpful to understand the basic language of the Stock Market.  In this article I discuss the basic vocabulary as it relates to practical ideas for personal investing.  Links are provided for further reading about a particular topic.

Investment returns

An investment is the payment of capital to earn a return.  The return is a gain (or loss) of value in the investment.  Taxes on returns are regulated by the Internal Revenue Service (I.R.S.) and local governments.   

  • Principal: the amount of money invested.
  • Capital: the cash or goods used to generate income.
  • Capital gain (or loss): the increase (or decrease) in cash value of an asset.
  • Dividend: a company’s cash payment to its stockowners.   
  • Interest: the borrower’s cash payment to the lender that is added to the principal of the  loan.

Investment portfolio

Financial assets are potential sources of income for investors.  Asset classes are groupings of assets that earn income in uniquely different ways.  The most popular asset classes are Equities and Fixed Income Securities.  Equities earn income by the sale of a security (e.g., shares of a Stock).  Fixed Income Securities earn guaranteed interest (e.g., bonds) or guaranteed dividends (e.g., preferred stocks).  Securities and investors are regulated by the Securities & Exchange Commission (S.E.C.). 

  • Securities: contracts that require an investment of money to generate profits from the efforts of other people. 
  • Stock: a security that represents part ownership of a company.  
  • Common stock: a security that entitles its owner to vote on important issues, collect dividends, and earn capital gains from the stock market.   
  • Preferred stock: a security that entitles its owner to receive dividends before dividends are paid to owners of the company’s common stock.  Preferred stockowners have no voting rights.    
  • Bond: the debt that requires a company to return an investor’s principal, plus interest, by the date of maturity.    

A Portfolio is the investor’s collection of financial assets called holdings.  By comparison, an Investment Fund is a portfolio of financial securities which are professionally managed on behalf of the fund’s investors.  Famous examples are mutual funds and exchange-traded funds (ETFs).  An actively managed portfolio generally seeks to earn higher returns than one which is passively managed.  The passively managed portfolio seeks to duplicate the returns of a market index.  

Glossary:

  • Market index: a hypothetical portfolio designed to measure the value of a market or market segment. 
  • ETF: an Investment Fund that sells shares of the fund in the stock market.  Index ETFs are passively managed. 

Stock market

A new stock is issued in its primary market.  The primary market is a private assembly of the company’s founders, venture capitalists, and third parties such as banks and advisors.  The stock may later be sold by public auction in the secondary market.  The secondary market is the familiar stock market where millions of investors, —like us!—,  trade cash for stocks and other exchange-traded securities (e.g., ETFs). 

Trading orders

The stock market participants include Investors who make offers, Brokers who generate orders, and Traders who finalize orders.  The broker’s trading platform is a computer program that assists investors with placing trading orders.  The platform provides a market “quote” comprised of the current purchasing price (the “bid”), sales price (the “ask”), last-traded price, and latest number of traded shares (the “volume”).   On any day there may be millions of orders to buy and sell in the stock market.  Orders are filled at the market price determined by an auction of shares conducted by the broker’s trader.  Brokers and traders often charge a fee for their services.  Custodians are hired by brokers to store traded securities in electronic accounts on behalf of investors.   

The simplest trading order, a MARKET ORDER, specifies the number of shares to be traded.  Market orders are filled immediately provided the shares are available; otherwise, the order remains open until shares are available.  Conditional limit- and stop orders are stored in computers until activated or expired at the end of a period called the time-in-force.  The LIMIT ORDER requires an investor to specify a preferred price for the trade.  Limit orders are activated when the market price reaches the preferred price and then filled at the preferred price or a better price. Please be aware that a sudden market event could displace the market price outside the limit range of an activated order, in which case the limit order is cancelled unfilled. The STOP ORDER is activated at a specified price after which it is converted to a market order to be filled immediately regardless of the next available price. 

Stock market index

Analysts like to follow the price trend of stocks by graphing a representative number called the stock market index.  The index rises and falls at any moment according to fluctuations in share prices during stock market transactions.  An influential sales surge moves prices downward and a buying surge generally sends prices upward.

Daily index values are strung together to form an observable trend called the market cycle.  The long market cycle is comprised of a “bull” market followed by a “bear” market.  The short market cycle is either a rally or a correction. Spikes and crashes are brief events caused by a sudden, large change of the index (chart 1).  

  • Bull market: a 20% rise of the market index over 2 months or more.
  • Bear market: a 20% fall of the market index over 2 months or more.  
  • Rally: a rise of the market index due to a burst of buying that subsides after the money is spent.
  • Correction: a 10% decline of the market index over 2-10 days.
  • Spike: a sudden large upward or downward price movement.
  • Crash: a sudden correction that lasts 1-2 days.
  • Circuit breakers: programmed halts of trading designed to offset a downward plunge of stock prices.  

Chart 1. Long and short cycles of the Dow Jones Industrial Average (“DOW”).

market cycles, DJIA

In chart 1, the vertical scale shows values of the DOW Index during a 20 year time period shown by the horizontal scale.  The jagged line represents daily fluctuations of market prices. Green, red, and black symbols illustrate the timing of various market cycles and events.  The horizontal line of green and red segments portrays 4 long cycles of the DOW Index.  After the partial 1st cycle (Jan 2000-Jul. 2001), the complete 2nd (Oct. 2001-Aug. 2002) and 3rd cycles (Sep. 2002-Mar. 2009) show orderly sequences of bull and bear markets.  The nearly complete 4th cycle began with a very long bull market of eleven years (Mar. 2009- Jan. 2020) that recently reverted to a bear market at the time of this writing.  Chart 1 also shows short cycles of rallies (green triangles) and corrections (red triangles).  A few market crashes (black triangles) in Nov. 2008 and Mar. 2020 represent 1-2 day periods of a 10% drop in the Index.  Rapid declines of the Index by 7% in one day triggered temporary halts of trading (black circles) known as “circuit breakers”.

Diversification

Stocks are high risk investments with respect to potential capital gains (upside risk) and losses (downside risk).  Capital loss occurs when the company declares bankruptcy or its share prices decline.  Stock diversification, dollar cost averaging, and dividend reinvestment plans (DRIPs) are effective strategies for managing the common risks of stocks.  Monthly purchases of a Stock-index Fund accomplish these strategies.  Chart 2 illustrates the potential capital gains from investing in a Stock-index Fund that duplicates a broad market index such as the S&P 500.

Chart 2.  Historical prices of the S&P 500 Index.

dividend reinvestment

Assuming that the Fund matches the performance of the S&P 500 Indexthe difference between holding the original investment in the Fund without further action (red graph) and augmenting the holding with reinvested shares (blue graph) illustrates the potential benefit of a dividend reinvestment plan.  In this example, the benefit became ‘significant’ after 6 years.       

Postscript

Stock investing is a time-consuming process that might not interest many people who wish to put their money in the market.  They can save time (and money) by investing in a Stock-index Fund that provides an instant portfolio of diversified stocks for long term investment.

Stocks are one of several investable asset classes.  People with short term goals should consider diversifying their portfolio with different asset classes.

Copyright © 2020 Douglas R. Knight 


What is a stock and how much is it worth?

August 21, 2018

A stock is an offering of part ownership in a company.  Each part, — called a share—, is worth the price that buyers are willing to pay.  

A new stock is sold for the first time in the primary market.  The primary market is a private one comprised of the company’s founders, venture capitalists, and third parties such as banks and advisors.  Venture capitalists take a big risk that the company might fail.  In return, they have considerable influence on how the company is governed and operated.  They hope to earn a generous profit from selling their shares.

The stock may be sold again in the secondary market by public auction.  The secondary market is the familiar stock market where thousands of investors, —like us—,  trade cash for stocks and other exchange-traded securities.  We also hope to earn a generous profit from selling shares. Some companies may occasionally choose to pay us a cash bonus called a dividend.

Wise buyers seek the best price for a good company.  The best price is determined by ‘valuation’ and the quality of the company is assessed by ‘fundamental analysis’.

Copyright © 2018 Douglas R. Knight


The joy of stock returns

August 5, 2018

A good reason for investing in stocks is to earn more money than the interest paid by a bank account or savings bonds.  Some investors ignore their stocks until it’s time to cash in.  Most prefer to watch the growth of returns, in which case they need to know the total return and holding period.   

Total Return

Stock profits depend on the capital gains and dividends.  A capital gain is the amount earned when the current stock price exceeds its purchase price.  A capital loss is the amount lost when a current price is below the purchase price.  The capital gain (or loss) is “unrealized” if the investor doesn’t sell the stock or “realized” if the investor sold the stock.  Some companies make occasional cash payments, called dividends, to their stock holders.  

Total Return is the total profit from your stock investment.  It represents the stock’s change in market value combined with all dividends you received from the company.  In equation 1, the change in market value is equal to “market value – total cost”.  

total return = market value – total cost + dividends

  • Market value is the combined value of all shares owned at the current market price (market value = current price * volume; volume is the number of shares).  
  • Total cost is the value of all shares purchased (cost = purchase price * volume) during the holding period 
  • Holding period is the period of stock ownership.  

Trading fees are ignored in order to simplify this discussion. In actual transactions, trading fees reduce the market value and increase the cost by small amounts so as to reduce the total return by a small amount.  The impact of trading fees on profits is lower in larger transactions.  For example, a $5.00 trading fee is 5% of a $100 purchase compared to 0.5% of a $1,000 purchase. 

Return on Investment (ROI)

ROI is the basic measurement of profitability (ref 1).  It is the ratio of total return to total cost (equation 2).

ROI = total return/total cost

Significance: the ROI shows how much profit you earned from every invested dollar.  If the ROI were 0.2/1, which is 20%, then you earned 20 cents per invested dollar.

“Price performance” (equation 3) may not measure the ROI.  Price performance = (price2 – price1)/price1, where price1 is the earlier number and price2 is the later number.  Price 1 may neither be the purchase price nor the only purchase price.  ROI includes all purchase prices.

Rate of Return

The rate of return measures profitability with respect to time.  Think of if it as the ROI for the holding period (equation 4). 

Rate of Return = ROI/holding period

Don’t forget that the ROI compares profit to cost when the time period is anchored to the date of the initial purchase.

ISSUE: The rate of return is most precise when there is just one purchase.  Serial purchases require a more complicated calculation of the “annual return”.  

Annual return

The annual return is a number that represents the average rate of growth per year of the holding period.  The annual return has several important properties:

  1. It doesn’t change during the holding period.
  2. It’s a geometric average, not an arithmetic average.  The graph of geometric growth is a curved line (“exponential”) rather than a straight line (“linear”).
  3. The geometric average represents the phenomenon of compounded growth known as “compounded interest”.

Stock investors are interested in 2 types of compounded growth:

  1. The compound annual growth rate (“CAGR”) of a single purchase.
  2. The internal rate of return (“IRR”) for a series of purchases.  

There are free calculators which are posted online to determine the CAGR (ref 2) and the IRR (ref 3).  

ISSUE: The annual return is usually inaccurate during the first year of compounded growth and becomes more accurate over longer time periods.  

Rule of 72 

The payback period is something to celebrate!  It’s the point when the investment doubles your money.  Payback is measured by the ratio of total cost to the rate of return.  Or, it can be estimated by the Rule of 72 (equation 5).  

Rule of 72 = 72/assumed annual return

Significance: the Rule of 72 is used to forecast the holding period needed to double your money (ref. 4).  For example, assume that your total return will grow at a constant rate of 10% per year [approximately the same rate as the growth of the U.S. Stock Market].  The expected payback period is 7.2 years (7.2 = 72/10).  

Summary

The total profit of your stock investment is called the total return.  The simplest way to measure profitability is to calculate the ROI with equation 2.  The ROI is insensitive to time until you calculate the rate of return with equation 4, which allows you to compare the profitability of several stocks in your portfolio.  The annual return of compounded growth is a refined measurement of your calculated rate of return.  After a holding period beyond one year [to avoid the chance of considerable inaccuracy], the annual return may be determined with an online calculator for a single investment (CAGR) or serial investments (IRR).    

References

1. Return on Investment (ROI). https://www.investopedia.com/terms/r/returnoninvestment.asp 

2. Compound annual growth rate (CAGR) calculator.  http://www.moneychimp.com/calculator/discount_rate_calculator.htm  . 

3. XIRR calculator to calculate IRR of non-periodic cash flows. https://www.free-online-calculator-use.com/xirr-calculator.html   . 

4. Brian Beers. What is the Rule of 72? https://www.investopedia.com/ask/answers/what-is-the-rule-72/ , 1/2/2018.

Copyright © 2018 Douglas R. Knight


Ways to invest in stocks

July 19, 2018

There are thousands of  investors who want to own ‘good’ companies that avoid ‘trouble’.

  • they invest in stock shares [stock shares are equal units of part ownership]
  • a good company
    • operates a profitable, growing business
    • avoids financial distress and regulatory penalties

Investors purchase and sell shares in the stock market.  They hope to sell their stock at a desirable price and may also receive cash rewards from companies that pay dividends.  Investors earn a profit (called a capital gain) when the sales price is above their cost of investment or lose money (called a capital loss) when the sales price is below cost.  

Stock Analysis

Two ways of evaluating a stock are called technical analysis and fundamental analysis.  Technical analysis measures the performance of share prices and share volumes in the stock market.

  • Shares are units of part ownership which are traded in the stock market.
  • Price: the price of a share in the stock market.
  • Volume: the total number of shares traded in the stock market 

Fundamental analysis evaluates the business performance of a company by way of searching through its quarterly and annual filings.  The business description, financial statements, and CEO’s annual letter to shareholders are important sections of the filings.

  • CEO: Chief Executive Officer; top manager of the company.
  • Filings: periodic reports to shareholders that are required by the U.S. Securities and Exchange Commission (SEC).

Business performance is also assessed by the company’s market share and competitive advantage within its industry.  This information is available online.

Investment Strategies

The most common investment strategies for stocks are swing trading, value investing, and growth investing.  

Swing trading (cyclic trading) uses brief upward or downward trends in share prices to determine when to buy or sell stocks.  The typical holding period is from one day to several weeks.  The investor hopes to earn a capital gain (–if seeking a profit–) or capital loss (–if seeking to reduce the short term capital gains tax–).  The investor uses either a technical analysis or guesswork to judge the price trend.  The main risks of incurring a loss are due to price volatility and taxation of returns.

  • Hold: to own.
  • Short term: one year or less.
  • Short term capital gains tax: the taxation of a capital gain at the regular income tax rate.
  • Price volatility: the random fluctuation of prices based on the market forces of supply and demand.
  • Return: the profit or loss from an investment.

Value investing seeks a capital gain by purchasing the stock at an unusually low price (e.g., 60% of intrinsic value) and then selling it at approximately double the purchase price.  The holding period depends on the length of time for the stock price to become profitable. During the holding period, an investor will receive any dividends paid by the company.  The informed investor uses a fundamental analysis to assess the quality of the company and the intrinsic value of its stock.  The causes of an unusually low price include a market downtrend (e.g., economic recession) and poor company performance.  The main risks of incurring a loss are due to an eventual delisting of the company and taxation of returns.  

  • Intrinsic value: the share price calculated by a professional analyst’s secret formula.  However, you can estimate the intrinsic value as the net worth of the company (book value) per share, based on the idea that a wealthy investor could acquire the company at its intrinsic price by puchasing all shares of stock at the book value per share.   
  • Dividend: a cash reward paid to share holders from the company’s profits or cash reserves.
  • Delisting: removal of the stock from the stock market for various regulatory reasons, including bankruptcy of the company.    

Growth investing is a long term strategy for using the upward momentum of share prices to earn a capital gain. The capital gain is earned by simply holding the stock and reinvesting all dividends.  The rule of 72 estimates the holding period needed to double the purchase price of the stock at an assumed rate of annual return.  The growth investor uses a fundamental analysis of the company and market valuation to judge the fairness of the stock price.  The main risks of incurring a loss are due to deterioration of the company, decline in market value, and taxation of the returns.

  • Long term: after one year.
  • Momentum: an upward trend of share prices.
  • Rule of 72: [ Years to double the price = 72/percentage annual rate of return ] For example, a 15% annual rate of return will double the share price in 4.8 years. 
  • Annual rate of return: a constant percentage change in value every year that accelerates the growth of an investment; CAGR is an acronym for the annual rate of return.
  • Valuation: the art of judging if the price is low (discounted, undervalued) or high (expensive, overvalued). 

disclaimer: this article may not increase your investment profits.

Copyright © 2018 Douglas R. Knight


PE, PEG, and PEGY Valuation Ratios

June 19, 2017

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 standardizes the market value of a stock for ease of comparison with other stocks.
  • PEG refines the valuation of stocks by adjusting PE to the growth rate of company earnings. PE is in equilibrium with the growth of earnings at PEG = 1.
  • PEGY adjusts PEG to stocks with high yields of dividends.

PE

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.

  • Compare the stock’s PE to an average PE of the industry, market, or historical record (ref. 3).
  • Normalize the PE to the company’s rate of earnings growth, which generates the PEG ratio. By convention, the PE is fairly valued when PEG = 1 (ref 5,6).
  • The least practical method is a comparison to some theoretical PE that is not readily available to most investors (ref 1,4).

PEG

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):

  • The EPS growth forecast may be invalid.
  • Another variable besides PEG could add or subtract value to the investment. For example, PEG ignores the value of a cash-rich company.
  • An overvalued company, for example one with a PEG of 3.0, might still be a stable investment despite its low rate of earnings growth.
  • PEG is best suited for stocks that don’t pay dividends; otherwise, calculate the PEGY.

PEGY

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.

Payback period

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.

Conclusions

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).

Endnotes

Formula 1: PE = P / E

  • P is the current auction price for a share of common stock listed in the stock market. The auction price fluctuates often depending on when a trading order is filled at an agreeable price between buyer and seller. Analysts typically use the closing price of the latest trading day to calculate the PE.
  • E is one year’s accumulation of the company’s earnings per share of common stock [EPS]. EPS represents the company’s net income divided by its outstanding shares and fluctuates at quarterly intervals. Any guaranteed payments of dividends to shares of preferred stock automatically reduce the EPS before calculation of the PE. EPS depends on the analyst’s choice between GAAP- and non-GAAP earnings and choice between basic and diluted outstanding shares.

Formula 2: PEG = PE / G

  • PEG fluctuates with frequent changes of PE and infrequent changes of G.
  • G is the EPS growth rate, which is the compound annual growth rate of EPS for a time period of at least several years. Although G is measured as a percentage change of EPS per year, the common practice is to ignore the units of measurement when calculating PEG.
  • Trailing PEG is the trailing PE divided by the G for past earnings.
  • Forward PEG is the forward PE divided by the G for future earnings.

REFERENCES

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


Skim the profit?

February 7, 2017

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.

chart 1, Market values.  $1,000 was invested in a good growth stock that paid no dividends. A generous 15% annual return doubled the market value every 5 years. The HOLD strategy (black squares) was to avoid selling for 20 years. The SELL strategy (green circles) was to sell half the shares every time the market value doubled. There were no trading fees.

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.

chart 2. The cash balances of the strategies in chart 1 are illustrated in this chart using the same symbols for data points. After 20 years, all remaining shares are sold for cash. The end point of each graph is the final cash balance.

chart 2, Cash balances. The cash balances of both strategies in chart 1 are illustrated in this chart using the same symbols for data points. The proceeds from every sale were held in a cash account and allowed to accumulate for 20 years.  After 20 years, the remaining shares were sold for cash. The end point of each strategy is the final cash balance.

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.

Alternate conditions

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.

Conclusion

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.

Appendix: Tables of cash balances

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 3.

chart 3, Rate of return.  $1,000 was invested in a good growth stock that paid no dividends. No shares were purchased after the original investment. The 20-year cash balance (cells) was only affected by the annual rate of return (rows) and liquidation strategy (columns).  The HOLD strategy did not sell shares for 20 years.  The SELL strategy sold half the shares whenever the market value doubled in size during the 20 year period.  The 7% rate permitted 1 selling period and the 15% rate permitted 4 selling periods. 

Chart 4 illustrates the effect of skimming 50%, 100%, or 150% increments of market value.

chart 4.

chart 4, Increments of market value. $1,000 was invested in a good growth stock that paid no dividends. The investment’s annual rate of return was 15% and no shares were purchased after the original purchase. The cash balances (cells) accumulated every time period (rows) among 3 different increments of market value (columns). The HOLD strategy did not sell shares for 20 years. The ‘rule’ for the SELL strategy was to sell a portion of shares when the market value grew by approximately 50% every 3 years ($521), 100% every 5 years ($1,011), or 150% every 7 years ($1,660).

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.

chart 5.

chart 5, Dividends. $1,000 was invested in a good growth stock that paid a 2% dividend on every share. No shares were purchased after the original investment unless the dividends were automatically reinvested. The cash balances (cells) accumulated with the passage of  time (rows) among 3 types of investments (columns). The HOLD strategy did not sell shares for 20 years. The SELL strategy removed half the remaining shares every 5 years.

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


Alpha is a point on a straight line, plus more.

December 22, 2016

{update on 12/23/2016: the significance of technical and operational alpha}

Alpha (⍺) is the cherished -but overrated- measurement of superior investment. Here are several interpretations:

  • A measurement of how well an investment outperforms its market index (ref 1).
  • The observed characteristic of a mutual fund that predicts higher fund performance (ref 2).
  • A portfolio’s return that’s independent of market returns (ref 3).
  • The excess (or deficit) return compared to the market’s return. Used this way, ⍺ is called Jensen’s Alpha.

Alpha represents a unique risk of outperforming the market’s returns. It is classically calculated as the “Y intercept” of a straight line attributed to the CAPM model (see appendix). In the last century, famous investors outperformed the market either by choosing exceptional investments or by investing in exceptional market sectors. The investment could be a single security (e.g., a stock) or a portfolio of capital assets (e.g., a mutual fund) (footnote 1, refs 1, 2). Now in this century, those alledged ‘alpha’ strategies are increasingly difficult to achieve. There’s an emerging sentiment among investors to avoid wasting time and money on attempting to outperform the market, the so called “loser’s game”. The current “winner’s game” is to seek ‘beta’ (refs 1, 2, 4, 5).

‘Beta’ is the portfolio’s return generated by market returns. Therefore, beta represents the risk of earning the market’s returns. The beta statistic, β, is currently calculated and reported by financial research firms as a coefficient for the incline of a straight line attributed to the CAPM model (see appendix).

Straight line of imaginary returns

(refs 5-8)

A straight line of imaginary returns presumably offers the best possible comparison of investment returns to a market index (footnote 2). ‘Returns’ and ‘performance’ are interchangeable terms that indicate the direction and movement of prices over time. An investment’s rate of return is calculated as the percentage change in price at regular intervals of time [likewise, the market’s rate of return is a percentage change in value of the market’s index at regular intervals of time]. Any rate of return is easily converted to a risk premium by subtracting the guaranteed interest rate for a Treasury bill (“T bill”). The risk premium is an investor’s potential reward for purchasing a security other than the T bill.

The straight line is drawn on a graph that shows actual measurements of investment returns plotted against market returns. The returns may either be measured as the rate of return or the risk premium depending on the goal of analysis. In the following chart, black dots represent a series of investment returns plotted against corresponding market returns.

alpha2

The blue line of imaginary returns is the best possible comparison of investment returns to market returns. The position of the line on the graph is governed by its incline (β) and intersection (⍺+ε) with the vertical axis.

⍺, the intersection

(refs 1-3, 5-8)

Alpha resides at the intersection of the theoretical line with the vertical axis for investment returns (chart). Since the vertical axis crosses the horizontal axis at 0% market returns, ⍺ is the theoretical investment return at 0% market returns. A positive value for ⍺ implies that the investment tends to outperform its market index. Likewise, ⍺ = 0 implies no inherent advantage of the investment and a negative value for ⍺ implies that the investment tends to move less than the market index.

There’s a degree of error (ε) involved in drawing the line of imaginary returns, which means that its intersection is defined by the term ⍺+ε. The ε declines when a series of returns lie close to the line. The chart shows plots for 2 different series of returns; one series of black dots and another series of white circles. Both series have an equally small ε as illustrated by the close alignment of data to each straight line. Alpha of the blue line is 0% return and ⍺ of the orange line is 5% return, both occuring when the market return is 0. The series of open-circle returns outperformed the series of black-dot returns by 5%.

Significance

(refs 1, 2, 4, 5)

Alpha measures how well an investment outperforms the market. Yesterday’s ‘technical’ ⍺, shown in the preceding chart, applied to measuring superior stock-picking skills.  Today, the technical ⍺ of stocks is not reported by the most popular financial websites.

Today’s ‘operational’ alpha is really a beta loading factor of multi-factor models (see appendix).  Operational alpha is more relevant to measuring the performance of actively managed mutual funds and investment portfolios. The investment goal of an actively managed mutual fund is to outperform its market index. Active management may be the “loser’s game” of paying excessive fees in contrast to passive management, which may be the “winner’s game” of paying minimal fees.

Footnotes

1. Capital assets are securities and other forms of property that potentially earn a long term capital gain(loss) for the owner.

2. The straight line has other names that precede my use of the term ‘imaginary returns’. The straight line is also called a regression line or security characteristic line (ref 6).

References

1. Larry E. Swedroe and Andrew L. Berkin. Is outperforming the market alpha or beta? AAII Journal, July 2015. pages 11-15.

2. Yakov Amihud and Rusian Goyenko. How to the measure the skills of your fund manager. AAII Journal, April 2015. pages 27-31.

3. Daniel McNulty. Bettering your portfolio with alpha and beta. Investopedia. http://www.investopedia.com/articles/07/alphabeta.asp#ixzz4SYJ0rN9q

4. John C. Bogle. The little book of common sense investing. John Wiley & Sons Inc., Hoboken, 2007.

5. Investing Answers. Alpha Definition & Example. 2016. http://www.investinganswers.com/financial-dictionary/stock-valuation/alpha-43

6. Professor Lasse H. Pederson. The capital asset pricing model (CAPM). New York University Stern School of Finance. undated. http://www.stern.nyu.edu/~lpederse/courses/c150002/11CAPM.pdf

7. MoneyChimp. Regression, Alpha, R-Squared. 2016. http://www.moneychimp.com/articles/risk/regression.htm

8. Invest Excel. Calculate Jensen’s Alpha with Excel. undated. http://investexcel.net/jensens-alpha-excel/

APPENDIX: models for pricing assets and managing portfolios

(refs 1-3, 5-8)

The original one-factor model was called the Capital Assets Pricing Model (CAPM). The single factor is market returns (M).  The investment returns (I) are predicted by a best-fit line with incline (βm) and intersection with the vertical axis (⍺ + ε) (equation 1).

I = ⍺ + ε+ βmM,     equation 1, CAPM

Subsequent series of three-factor and four-factor models were sequential upgrades of CAPM. Equation 2 is an example of a four-factor model for the risk premium of an investment fund (F) comprised of separate portfolios for the broad market (M), asset size (S), asset value (V), and asset momentum (U).

F = ⍺ + ε + βmM + βsS + βvV + βuU,     equation 2, four-factor model

⍺ is the excess risk premium attributable to skillful management of the Fund.
ε is the model’s error
βm, βs, βv, and βu are portfolio loading factors assigned by the Fund’s manager

The four-factor model offers a spectrum of possibilities.

  • During 1927-2014, the average annual returns of indices for the the four-factor model were 8.4% for the broad stock market, 3.4% for stock size, 5% for stock value, and 9.5% for stock momentum.  The sum of average annual returns, 26.3%, represented the alpha-threshold for superior fund returns (ref 1).
  • Passive management could be predicted by setting βm to 1.00, measuring the market index return, and setting the remaining loading factors to 0.  A market index fund would  be expected to generate a risk premium that matches the market index risk premium with an ⍺ of 0 and slight ε for tracking error.
  • Active management involves designing loading factors and portfolio assets to outperform the fund’s predicted returns.

Copyright © 2014 Douglas R. Knight


Beta is the incline of a straight line

December 10, 2016

Beta (which is symbolized as β) is the incline of a straight line. Mathematicians would say the same thing another way, that beta is the slope of a regression line. Either way, β describes the tendency of investment returns to move with market returns. The investment is a security (e.g., stock, bond, mutual fund) that has a unit price. The market is a trading place for a large group of securities. The combined value of all securities is measured by a market index.

Returns

Trading causes security prices to change during the passage of time, a process called price movement. Calculations of β require price movements to be measured as percentage returns. In table 1, the daily closing prices of a security and its market index are listed under the column heading “close”. Percentage daily changes in closing price are listed under the column heading “Return %”.   Equation 1 is the formula used to calculate a return:

Return % = 100 x (current price – past price) / past price  (equation 1)

Notice in table 1 that all prices are a positive number and that the market’s close is bigger than the investment’s close. However, the calculated returns are positive and negative numbers of similar size. The positive and negative returns represent up and down movements of prices. Table 1 has 3 pairs of investment and market returns with corresponding dates.

table-1

Beta (β)

β may be calculated directly from a table of returns, but it’s more meaningful to analyze a scatter plot of returns. The scatter plot in figure 1 has a solid blue line derived from 5 years of daily returns represented by more than a thousand black dots. Each dot has a pair of corresponding returns on each axis.

fig-1
The blue line offers the single-best comparison of investment returns to market returns. The incline of the blue line is β, which is calculated as a ratio of the lengths AC and BC of the dashed lines. Since AC and BC have equal point spreads of 5%, β is 1.00, which means that the investment and its market TENDED to move together at the same rate of return.

Notice that the black dots are closely aligned to the blue line, therefore excluding the random movement of returns. Consequently, the blue line is highly predictive of this particular investment’s past performance.

Significance

β is a measurement that literally means for every percent of market return, the percent investment return TENDED to change by the factor of β.  This is illustrated in figure 2.

fig-2
The colored performance lines in figure 2 represent different investments. Each line offers the single-best comparison of investment returns to market returns. For the sake of graphic clarity, a large cluster of paired returns was not plotted as data points.

At β = 1.00 (black dashed line) the investment and market TENDED to move together at the same rate. At β >1.00 (yellow line), the investment performance was amplified by trading activity in the market. The yellow line’s β infers that the investment’s return was 1.72 times the market’s return. At β <1.00 (green line), the investment performance was diminished by market activity. The green line infers that the investment’s return was 0.86 times the market’s return. At β <0 (red line), the investment performance was reversed by market activity. The red line infers that the investment’s return was -3.86 times the market’s return.

Thus, β is a ‘pretend’ multiplier of market performance. Higher β ‘amplified’ the market performance, lower β ‘diminished’ the market performance, and negative β ‘reversed’ the market performance.

Risk

Risk is the chance for a capital gain and capital loss. Betas greater than 1.00 tend to be riskier investments and those lower than 1.00 tend to be safer investments compared to performance of the market. Negative β infers a reversal of investment outcomes compared to market outcomes.

Summary and advice

β is a statistic for past performance that describes the tendency of investment returns to move with market returns. When comparing the β of different investments, be sure to verify the time periods and market index used by the analyst. β is typically measured with weekly or monthly returns for the past 3-5 years.

Copyright © 2016 Douglas R. Knight


Why we need stocks and bonds

October 20, 2016

Believe it or not, Society is coming to the point where all capable people need to invest in stocks or bonds. So what are stocks and bonds, and why do we need them?

They are valuable certificates purchased from businesses by investors. Businesses need investors’ money to build and sell products to customers for a profit. Investors need the certificate to retrieve their money with a bonus payment. That bonus payment is an enticement to invest in businesses.

Stock and Bonds are different from each other. Stocks represent part ownership in a business. The stock owner hopes to collect portions of business profits called dividends and to eventually sell the stock certificate for a bonus amount. Bonds are written promises to refund investors’ money with an extra amount called interest. Both potentially offer individuals an extra source of money.

Markets for stocks and bonds will grow and endure for future generations.  More individuals will become investors out of necessity.  The details of investing are interesting and challenging.

Copyright © 2016 Douglas R. Knight


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