## 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.

## 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).

## 2017

January 1, 2018

chart 1. SmallTrades Portfolio in 2017.

Chart 2 shows the diversification of ETFs as measured by percentages of year-end market values among ETF classes.

chart 2. Diversification of ETFs in 2017.

Chart 3 shows the diversification of stocks among 8 market sectors as measured by percentages of year-end market value for each stock sector and the ETFs.

Chart 3. Distribution of stocks and ETFs by market sectors.

Chart 4 shows the distribution of stocks according to market capitalization.

Chart 4. Combined market capitalizations.

### Performance

My investment goal is to outperform the “Benchmark” Standard & Poors 500 Total Return Index, yet my portfolio has never outperformed the Benchmark (chart 5).

Chart 5. Portfolio performance.

Chart 5 shows growth trends for the benchmark (blue dashed line) and portfolio (solid blue line) since 2007 [the benchmark represents a passively managed, buy-and-hold investment; my portfolio is an actively managed investment].  On the Y axis, a unit value of \$1.00 was assigned to both the total market value of the Portfolio and the Benchmark on December 31, 2007. Ratios of subsequent market- and benchmark values to the 2007 baseline are displayed line plots on the chart.

In 2014, my investment policy was modified to buy stocks of good companies and hold them for the long term. Chart 6 shows the result of my stock investments (red line) compared to the Benchmark Index (blue line) and ETF investments (red dashed line). The unit value of \$1.00 was calculated on December 31, 2013. Since then, the stock group clearly outperformed the Benchmark and ETFs.

Chart 6. Stock and ETF performances.

### Risk Management of ETFs

Broad-market index ETFs are primarily protected against stock losses by the passive management of investment portfolios which mimic the composition and performace of reputable market indices.

ETFs are secondarily protected by rebalancing significant allocation errors as described in the SmallTrades Portfolio’s strategies for risk management. In theory, a significant drift of asset classes occurs when one asset class surpasses a 24-28% allocation error. My preferred allocation of ETF market values is 30% stocks, 30% REITs, 20% bonds, and 20% gold bullion.

A perfect allocation of ETFs would result in 0% allocation error.  Furthermore, allocation errors would reflect disproportional gains or losses of market value.  Chart 7 shows the year-end allocation errors (blue bars) and error limits (red dashed lines) of my ETFs. There was growth of the Global Stocks ETF and decline of the remaining ETFs. Any allocation error that exceeds an error limit (red dashed line) should trigger trades that rebalance the ETFs to the preferred allocation.  My ETFs were not rebalanced in 2017.

Chart 7. ETF allocation errors in 2017.

### Risk management of Stocks

My stocks are primarily protected against risks of steep loss by diversification of the market sectors, as illustrated in the preceding chart 3. The second line of defense is stop-loss orders.  In keeping with the investment goal of holding good stocks for the long run, I set ‘stops’ at a wide margin to prevent recent market fluctuations from triggering an unwanted sale.

### Plan

The SmallTades Portfolio will continue to be actively managed for long term success. The ETFs will be rebalanced anytime there’s a 24% allocation error or a modification of the ETF holdings. In 2017, I failed to sell large cap stocks in order to buy good small cap and mid cap stocks. Consequently, 60% of the total market capitalization of my stock portfolio was in the Large Cap category.  In 2018, I would like to reduce the Large Cap category to 40% total market capitalization and boost the market capitalization of small- and mid cap stocks issued by good companies with potential growth of earnings.

### Portfolio history

1. On 12/31/2007, the portfolio held a group of actively managed mutual funds in a tax-deferred Roth account. Since then there have been no cash deposits or withdrawals and the portfolio still resides in a Roth account.
2. During 2007-2010 the actively managed mutual funds were traded for stocks in an attempt to earn a 30% annual return by process of turning over short term ‘winners’.  Four mistakes led to a big loss:
3. mistake #1: after a couple of short term capital gains from Lehman Brothers Inc., I ignored the dangers of the company’s large debt and lost \$45,000 during Lehman’s decline to bankruptcy.
4. mistake #2: substantial long term profits from good companies were lost by selling holdings for short term profits. My strategy was to earn a quick 30% in the first year and re-invest in the next winners. It was too difficult to identify the next winners.
5. mistake #3: day-trading was a game of chance that I played and managed to break even; meanwhile, good stocks grew in value.
6. mistake #4: a trial of investing in leveraged ETFs resulted in losses due to negative compounding.
7. I abandoned the goal of a 30% annual return in 2012 by adopting a more realistic, but still aggressive, goal of outperforming the benchmark. That same year, I changed my investment strategy to that of holding a mixed portfolio of 80% broad-market index ETFs and 20% stocks for the long term. ‘Good’ companies attract and retain investors for many years. I will search for profitable companies with growth potential that are undervalued by the stock market. My search methods include reading reputable sources of business news, partiicipating in an investment club, using stock screeners, and attending investor conferences. Then I include and exclude stocks by reading analyst reports, financial statments, SEC filings, and market analyses. Valuation critieria help me decide if the stock price is worth paying.
8. Prior to March, 2016, five ETFs were allocated to four asset classes with each asset class holding 25% of the combined market value. Since my retirement income didn’t depend on making withdrawals from the SmallTrades Portfolio, I increased my ETF exposures to global stocks and REITs by decreasing my exposures to investment-grade bonds and gold bullion. The new allocation rule was 30% stocks, 30% REITs, 20% bonds, and 20% gold. Any drift in allocation to a 24% error will be rebalanced.

## What is a good company?

December 15, 2017

Good companies attract investors.  They do so by selling a desirable product that sustains the company’s growth of sales and earnings.  The growth of sales is a good measure of market success.  Durable companies convert their sales invoices into cash and use the cash wisely.  Accounting items such as the free cash flow, sustainable growth rate, quick ratio, and debt-to-equity ratio are easy measures of the company’s health and durability.  Growth stocks should be assessed by the quality of the company.

## Book review: Make Your Kid a Money Genius (even if you’re not)

October 16, 2017

Beth Kobliner, Simon & Schuster, New York, 2017.

Beth Kobliner is an authority on personal finance for youth as shown by her successful publications of a NY Times best-seller book (Get a Fiancial Life), staff writer for Money Magazine, and contributing author to national newspapers. She served on President Obama’s Advisory Council on Financial Capability for Young Americans.

In this book she offers financial advice for 6 age groups: pre-school, elementary school, middle school, high school, college, and young adult. Much of her advice is based on academic studies. It’s not a textbook for children.

### relevant topics for children

Most parents will discuss any topic except money; yet parents are the principal influence on their kids’ financial behavior. Many of a child’s money habits are set by age 7. This book discribes useful ways (called “teachable moments”) for talking about money with children as they grow from age 3 to young adult. Here are the author’s general comments about relevant topics for all ages:

TRUST: Parents need to build the trust of their pre-school children by following through on parental promises.
PATIENCE: Some children are impulsive, others are patient. Patient people tend to save more money! Pre-schoolers can be taught to wait for things.
CHARITY: Raise a generous child. Sharing time and money allows children to feel grateful for what they have. They are ready to show kindness by age 4. Elementary school children begin to understand the needs of others. Teen volunteers can engage in community service for their school and community. Most college students won’t have spare money, but they can donate their time. It allows them to explore the nonprofit world. Parents should honor their child’s charitable work with the same committment as other achievements in life; but, don’t overpraise their charitable efforts.
ALLOWANCE: It doesn’t matter if you give your elementary school child an allowance, but if you do, don’t make household chores a pre-requisite for receiving the allowance, use the allowance to set spending rules, and give them control of their spending decisions.
WORK: Children need to do unpaid chores and do well in school. Advanced chores such as raking leaves and doing laundry are essential to raising a self-reliant child. Elementary school children want to earn money, in which case the parent decides whether or not to pay the child for special chores. Middle school children are able to earn money. Limit the high school student’s work week to 15 hours; school is more important.
DEBT: Start teaching the basic concepts of debt to pre-school children. Middle school children need to understand the minimum monthly payments of credit card debt and protect themselves from identity theft. High schoolers are interested in car loans and credit cards; prepare them for wise use of credit cards. Parents, don’t buy your child a car or cosign for a car loan! After college, adult children are likely to have student-loan debt, car debt, or credit card debt. Parents should neither dip into their own retirement savings nor cosign for a loan as ways of helping young adults manage debt!
SHOPPING: Children want to buy stuff without limits, so parents need to start setting spending limits on pre-school children and teach the concept of ‘living within your means’. Elementary school children how to avoid being victimized by advertising and peer pressure. Tweens should spend their own money, not their parents’. If a teen prefers to spend for personal items rather than save money, they should learn from mistaken purchases. The ‘money culture’ among college students with different incomes can produce embarassment, resentment, and other strong feelings. Emphasize that college-related expenses are essential and everything else is extra.
SAVING: Parents should not raid their child’s savings. Middle school children should have a supersafe account (e.g., savings account, money market account, or CD). High school students should save for college, it will boost their motivation. Young adults should have an emergency fund and make maximal 401K deposits.
INSURANCE: Insurance is necessary for financial protection against devastating expenses. Most bankruptcies result from unpaid medical bills. Teens should pay for their car insurance and minimize their insurance rate with a good driving record. College students must have health insurance for the rest of their lives.
INVESTING: Don’t postpone the habit of investing in stocks; it’s a good way to protect against inflation. Children should learn the fundamentals and start saving small amounts at a young age. When they are old enough to understand numbers and show an interest in how money ‘grows,’ provide them with numeric examples of compound interest. High schoolers should open a Roth IRA to begin growing money.
COLLEGE: Attending college is the best pathway to earning higher wages compared to entering the workforce with a high school diploma. Middle school is the time to start talking about college and high school is the time to prepare for the college admissions process. High schoolers are advised to save for college; their chores should give way to college prep and testing. Avoid large student loans by chosing a good, inexpensive college and doing a better search for grants and scholarships. There are 3 ways to save for college:

1. 529 Savings Plan. the earnings are tax-free for educational purposes and there is no income cap for donations. If your child rejects the plan’s participating schools, then rollover the savings to another education account, change the beneficiary to another child, or withdraw the savings with penalties.
2. Coverdell Account. the earnings are tax-free for educational purposes, but the annual contribution is limited to \$2,000 when a married couple earns less than \$220,000 annually. The savings can be used for elementary school and high school educational purposes.
3. Custodial accounts are available at banks and mutual funds. If the child’s earnings exceed \$1,050, they are taxed at the child’s tax rate for the next \$1,050, then at the parent’s tax rate for higher amounts until age 19 (age 24 for full time students). Colleges count the account balance as the child’s asset and expect 20% of the balance to go toward college expenses. That means less aid for the family.

The college student’s priorities are studies, a paying job [working students feel more invested in their education!], and employment after college. Does your college graduate want to start a career or go to grad school? Parents, don’t jeopardize your financial security to pay for their grad school.

### the author’s curriculum and activities for pre-school children

Curriculum

EXPLAIN PATIENCE.  Patience, trust, and generosity are personal traits that facilitate financial success; pre-school training should help develop those traits.  Impulse buying reduces funds for tomorrow’s purchase! Always consider tomorrow’s purchases before buying on impulse.
Teach your children to perservere. Explain that you can’t always get what you want! Advise them to be patient (‘self control’) and wait for something.

EXPLAIN WORK.  Instill a work ethic; chores are a part of life.  Explain how you work to earn money  Convey the idea that a job is a source of pride and dignity

EXPLAIN SHOPPING.  Explain that you have to pay for things in cash (money, check) or card (debit, credit); the credit card is one way to pay (at the risk of incurring debt!).  Teach them to distrust advertising!   Explain how ads are produced with actors, scripts, colors, etc.  Explain the risks of materialism

DISCUSS CHARITY.  Be respectful of families with different levels of household income by explaining that “some people have plenty and others not enough”. Help bring your child closer to people of need by avoiding the terms “poor” and “rich” when discussing family wealth.
Worthy causes? Maybe your child needs guidance. What would they like to change in the world? Who would they like to help?

DESCRIBE THE HISTORY OF INSURANCE.  Ancient shipowners created a fund to pay for losses from shipwrecks. Their bookkeeper became the insurance company.

INTRODUCE INVESTING.  The basic concept of investing is to spend time and effort to produce something good (e.g., turning flour into bread).

Activities

PRACTICE PATIENCE.  Encourage them against skipping to the head of the line.  Discuss a communal effort (e.g., family savings pot) to save for a family reward (pizza, water park, etc.)

LEARN ABOUT WORK.  Perform household chores.  Discuss the jobs of people you know.

DISCUSS CHARITY.  Consider these charities: heifer.org , nokidhungry.org , kaboom.org , nature.org , pencilsofpromise.org , donorschoose.org.

### general goals after pre-school

ELEMENTARY SCHOOL. Continue the development of personal traits by adding an adult perspective on respect for other people. School children need to start managing their money and protecting it. They are vulnerable to harmful attack from many directions, including identity theft from their online accounts. Give parental guidance.

MIDDLE SCHOOL. Tweens are vulnerable to marketing campaigns, overspending, and credit card debt. Give parental guidance.

HIGH SCHOOL. Reduce the time spent on household chores. The teen’s main job is graduating from high school with a good education. Teen’s also need to prepare for higher education or entering the workforce. Give parental guidance.

### conclusion

Kobliner’s book contains credible advice for the homeshooling of children in financial matters. There is much more information in her book than I’ve been able to summarize in this article. Be sure to visit her web site, “Money as You Grow”, for additional help and perspective (https://www.consumerfinance.gov/consumer-tools/money-as-you-grow/.

## Pictures from financial statements

July 4, 2017

These 20 graphs form a pictorial essay of  a company’s financial statements.  This large company survived the Recession of 2007-8!

## 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 .
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

## The Physics of Wall Street, by James Owen Weatherall

April 25, 2017

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.

### The evolution of market models

• Bechelier made the first price-distribution model of stock markets. His normal distribution only worked in the Paris Bourse where there was little variation of prices.
• Osborne postulated that returns, not prices, are normally distributed. His model of the ‘random walk hypothesis’ expanded the understanding of price variation.
• Mandelbrot claimed that distributions of financial markets are more variable than previously thought.
• Thorp, Black, and Scholes converted price-distribution models to algorithms for daily trading. Their options pricing model was adapted from Osborne. Black later described the shortcomings in his paper “The holes in Black-Scholes”.
• The Prediction Company of Farmer, Packard, and McGill used black box models to improve the Black-Scholes model. They capitalized on short-term inefficiencies in the market.
• Didier Sornette predicted market catastrophes.

Today’s market models are still imperfect!

### Early Probability Theory, 16th-17th centuries

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?

• mathematical odds: 3 outcomes in 36 tries, or 1 in 12.
• betting odds: 33 to 3, or 11 to 1. Bet \$1 and either lose it or win \$11 plus the refunded \$1.

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].

### Random behavior of market prices, 19th-20th centuries

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.

• 1947: Samuelson published “Foundations of Economic Analysis”.
• 1964: Paul Cootner published Bechelier’s thesis in “The Random Character of Stock Market Prices”.

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.

### Hedging

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.

### Forecasting

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.

### Reform

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.

### Author’s Conclusions

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!

## Finance for Nonfinancial Managers, 2nd Ed., by Gene Siciliano.

April 6, 2017

### Book Review

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.

### Accounting

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:

1. Balance sheet
2. Income statement
3. Cash flow

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.

### Finance and Management

The remaining chapters are devoted to these topics:

• Key performance indicators (KPIs) for evaluating financial statements.
• Cost accounting, the analysis of manufacturing productivity.
• Finance of new projects by previewing the return on investment (ROI), weighted cost of capital (WACC), and internal rate of return (IRR). Never invest in a project that has a negative IRR.
• Breakeven point, to determine such things as the price of a product’s launch and risk assessment.
• Creating a business plan to guide business operations and attract financial resources.
• Annual budget, part of the business plan.
• Financing the company by getting a loan (debt) or selling shares (equity).
• Entrepeneurship.

## Stop losing value from a declining price

March 4, 2017

### background

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:

1. Company performance. ‘Good’ companies attract investors. Conversely, ‘distressed’ companies repel investors.
2. Industry performance. Business cycles can affect the sales of products from an entire industry. For example, sales of new automobiles declined during the Recession of 2008.
3. Market cycles. Aside from business performance, the entire stock market is subject to periods of declining prices due to massive selloffs by investors.

The risk of an extreme loss can be prevented by setting a stop-loss price (“stop”) to sell part or all of your shares.

### ways of setting the stop

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:

1. Absolute loss. Suppose you invest \$5,000 in 100 shares of stock (i.e., \$50/share) and you can tolerate a loss of \$1,000 should the price start to fall. Regardless of future prices, you choose to stop the decline at \$1,000 below the original \$5,000 value. In this example, the stop would be \$40/share [stop = (value – loss)/shares = (\$5,000 – \$1,000)/100].
2. Fraction of value. Suppose you can tolerate a 10% loss from an investment originally valued at \$5,000 for 100 shares.  Ten percent is one-tenth of 100, which is equivalent to a decimal number of 0.10. The stop would be \$45/share [stop = (1.00 – decimal)*value/shares = (1.00 – 0.10)*\$5,000/100].

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.

### add a limit price (“limit”) for extra protection

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.

### who should worry about an extreme 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.

### conclusion

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.