## 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.

## 2016

January 14, 2017

My SmallTrades portfolio holds stocks and four classes of exchange-traded index funds (ETFs).

chart 1

### Investment plan

The goal is to outperform a reputable benchmark, the Standard & Poors 500 Total Return Index, on a sustained basis.  The ETFs are diversified and rebalanced in order to partially offset the losses of a declining market. A small group of stocks are used to boost the investment returns.

### Performance

In FY2016 the portfolio’s market value increased by 8.3% due to a 9.1% gain in stock value and 8.1% gain in ETF value. Charts 2 and 3 illustrate the nominal (solid lines) and real (dashed lines) growth in unit value for shares of the portfolio, ETF group, stock group, and benchmark. The number of shares for each entity was the initial market value divided by \$1 of U.S. currency.  Assume that the initial unit value of \$1 was a real value unaffected by inflation.

Chart 2 shows the pattern of unit-value growth for the benchmark (black lines) and portfolio (blue lines) since December 31, 2007.

chart 2

The unit value of both entities declined in year 2008 and began to recover in year 2009. The benchmark (black lines) recovered in year 2011 while the portfolio (blue lines) is still struggling to recover [notes 1,2]. The effect of inflation was to devalue real growth (broken lines) compared to nominal growth (solid lines). The real unit value signifies the purchasing power of the investment. The investment has greater purchasing power than uninvested money when the real unit value exceeds \$1.

Chart 3 shows the result of implementing the current investment goal [note 2] with a small group of stocks (red lines) and large group of ETFs (blue lines). In chart 3, the initial unit value was re-calculated on December 31, 2013.

chart 3

Since 2013 the stock group clearly outperformed the benchmark (black lines) and ETF group. The success of the Stock group is attributed to investing in ‘good’ companies for the long term [note 3].

### Stock group

Chart 4 shows the market sector and market cap diversity of the stock group defined in chart 1.

chart 4

Several stock trades were made during FY2016 to improve the chance for success.
Closings:

• Alibaba Group (BABA), for 10% capital gain, to exit the Chinese market.
• Geely Automobile (GELYF), for 14% capital gain, to exit the Chinese market.
• Corning Inc. (GLW) for no gain.
• iRobot Corp. (IRBT) for 10% capital gain.
• ITC Holdings (ITC) for 14% capital gain, due to the stock’s delisting.
• Stericycle (SRCL) for 34% capital loss, to stop further loss.

Purchases:

• Biogen (BIIB), an innovative biotechnology firm.
• Cal-Maine (CALM), a leading producer of shelled eggs.
• Express Scripts Holdings (ESRX), a large mail order pharmacy
• Royal Bank of Canada (RY), a well-capitalized bank.

### ETF group

Chart 5 shows the distribution of asset classes among the ETFs. All asset classes drifted from an allocation plan of 30% stocks, 30% REITs, 20% bonds, and 20% gold [note 4].

chart 5

The SmallTrades portfolio’s primary strategy for risk management is holding a large group of diversified ETFs that are rebalanced to correct a significant allocation error. In theory, a significant drift of asset classes occurs when one asset class surpasses a 28% allocation error.  At the end of FY2016, the existing allocation errors (blue bars) were within 24% error limits (red dashed lines) as illustrated in Chart 6.

chart 6

Chart 6 reflects the portfolio’s response to an incline in equity markets compared to decline of the bond and gold markets. History has shown that a decline in equity markets tends to be offset by a rise in the bond and gold markets.

### Plan for FY2017

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. I would like to own fewer large cap stocks in favor of small- and mid-cap stocks issued by good companies with potential growth of earnings.

### Notes

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 the Roth account. During 2007-2010 the mutual funds were traded for stocks in an attempt to earn a 30% annual return by process of turning over short term ‘winners’. Several mistakes led to a big loss:  A) after a couple of short term capital gains from Lehman Brothers Inc., I ignored the dangers of that company’s large debt and lost \$45,000 during its decline to bankruptcy.  B) substantial long term profits from good companies were lost by selling holdings for short term profits. I was trying to earn a quick 30% annual rate of return and immediately re-invest in the next set of winners. It was too difficult to identify the next winners.  C) day trading also prevented a 30% return.  It was a game of chance that I played without a strategy and I was fortunate to break even.  D) a trial of investing in leveraged ETFs resulted in losses due to negative compounding.  Leveraged ETFs were very high-risk investments that I made without a sound strategy.
2. I abandoned the goal of a 30% annual rate of 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 ETFs and 20% stocks for the long term.
3. ‘Good’ companies attract and retain investors for many years. I search for profitable companies with growth potential that are undervalued by the stock market. My search methods include reading reputable sources of business news, participating in investment club discussions, using stock screeners, and attending investor conferences.  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.
4. Prior to March, 2016, five ETFs were allocated to four asset classes with each asset class holding 25% of the combined market value. Since I don’t depend on making withdrawals from the SmallTrades Portfolio, I increased my exposure 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.

## R-squared, the linearity of investment returns.

December 24, 2016

[updated 12/25/2016: R2 is a useful measure of indexing]

The R-squared (R2) statistic describes a pattern of plotted data with respect to a straight line. R-squared is called the coefficient of determination (ref 1,2).

The black dots in figure 1 represent investment returns that are poorly related to market returns. There is a random distribution of investment returns with respect to market returns. The blue line is an inadequate representation of the relationship simply because there is no relationship. The R2 score for this distribution is 0.03. Conversely, the black dots in figure 2 show the ‘herding’ of data around a straight line.

Figure 2’s investment returns are highly related to market returns with an R2 of 0.997.

### Significance

The R2 score represents the degree of alignment of data to a best-fit line as determined by regression analysis. The lowest possible score of 0 indicates a random pattern of data with absolutely no alignment. The highest possible score of 1 represents complete alignment.

The product of R2 X 100 represents the percent of variation in investment returns that are related to market returns (ref 1,2). In other words, R2 measures the relavance of the best-fit line to a set of data. Relavance increases as the R2 score varies from 0 to 1.

The lowest score of 0 defies any financial analyst to draw a meaningful line for investment returns as they relate to market returns. In figure 1, the incline (β) and Y-intercept (⍺) of the blue line are unreliable measurements of investment performance.

The highest R2 score of 1.00 identifies a straight line of near-perfect predictions of returns. Any R2 above 0.75 identifies a straight line for making predictions of returns. Lower scores represent increasingly random events. In figure 2, the incline (β) and Y-intercept (⍺) are reliable measurements of investment performance.

R-squared is an excellent measure of index fund performance.  Websites for index mutual funds and ETFs publish R2 as a measure of alignment between fund returns and the market index.   Funds that have an R2 score of nearly 1.00 track the index very closely.

### References

1.  Lain Pardoe, Laura Simon, and Derek Young. STAT 501, Regression Methods. 1.5- The coefficient of determination, r-squared. Pennsylvania State University, Eberly College of Science, Online courses. https://onlinecourses.science.psu.edu/stat501
2.  R-squared. 2016, Investopedia http://www.investopedia.com/terms/r/r-squared.asp?lgl=no-infinite

## 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.

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.

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.

## Book review: How to Make your Money Last. The Indispensable Retirement Guide. by Jane Bryant Quinn.

March 22, 2016

Jane Bryant Quinn, 2016, Simon & Shuster, New York. 366 pages.

### Synopsis

This book should be read by everyone who needs to plan for retirement from the workforce.  Author Jane Bryant Quinn is an acclaimed financial journalist with excellent credentials. In this book, she draws from credible research to describe principles and checklists for retiring with a practical financial plan. She speaks from firsthand experience about reinventing life after leaving the workforce: “once again the future is a blank slate” that needs to be filled with activities for a meaningful life (chapter 1). Those activities need the support of a dependable income managed by a practical financial plan.

In her opinion, your default plan is to maximize social security benefits and gradually increase the market value of your retirement portfolio (a.k.a. retirement savings) while maintaining a monthly paycheck for the duration of retirement. The financial core of a good retirement plan is based on 3 principles (chapter 12):

2. Maintaining a cash reserve throughout retirement (chapter 9)
3. Making safe withdrawals from your retirement portfolio (chapters 8, 9)

Quinn provides practical checklists for transforming various sources of retirement income to a homemade paycheck.  In addition to building a retirement portfolio by ‘bucket’ investing (chapter 9) are the supplemental sources of income from Social Security benefits (chapter 3), traditional pensions (chapter 5), simple annuities (chapter 6), and home equity payments (chapter 10).  She also provides practical checklists for securing retirement income with the help of spending rules (chapter 8). Quinn’s valuable checklists help manage the financial risks of inflation (chapters 2-4, 8), taxes (chapter 7), costs of healthcare (chapter 4), and spousal protection (chapters 3, 4, 6, 7, 10, 11).

### Janet Quinn’s Core principles

BUDGET GAP (chapter 2). The 3 important numbers in your retirement plan are its budget gap (chapter 2), cash reserve (chapter 9), and safe withdrawal (chapter 9). Calculate your budget gap before retirement. It is the difference between future income and expenses. The future gap can be minimized by staying in the workforce (to build a larger retirement portfolio) and spending less money.  Significant adjustments to financial assets and regular income may be necessary to support your desired level of spending later on. Estimate the future annual amount of money you can safely spend by using the following formula (chapter 2):

safe spending = (0.04*financial assets) + regular annual income – estimated taxes

CASH RESERVE (chapter 9). Create a cash reserve at the start of retirement. It will be an important source of money to pay for any budget gap that develops during 2 years of decline in the financial markets.

SAFE WITHDRAWAL (chapter 9). The “safemax” is a percentage of your retirement portfolio that you can safely withdraw in the first year of retirement (chapter 8;“safe’ means “as far as we can tell”). The amount withdrawn, plus an adjustment for inflation, practically dictates how much you can withdraw every year to ensure the 30-year longevity of your retirement portfolio.

Here’s the 4% rule (chapter 8): Withdraw 4% of your retirement portfolio at the start of the first year and safely store the money to pay bills throughout the year. At the start of the second year, withdraw the previous year’s amount adjusted for inflation. For example, assume your retirement portfolio holds a \$50,000 investment in stocks and \$50,000 investment in bonds for a total of \$100,000. Even if you make no more contributions to the porfolio, the following annual withdrawals could be sustained for 30 years when adjusting the previous year’s withdrawal for a 3% rate of inflation and rebalancing the portfolio to maintain a mixture of 50% stocks and 50% bonds:

year 1- \$100,000 * 0.04 = \$4,000 withdrawal
year 2- \$4,000 * 1.03 = \$4,120 withdrawal
year 3- \$4,120 * 1.03 = \$4,244 withdrawal
legend- \$100,000 is the portfolio’s initial value, 0.04 is the safemax, \$4,000 is the first annual withdrawal, 1.03 is the inflation factor, and \$4,120 is the second annual withdrawal.  there is no adjustment for taxes in this calculation.

NOTE: The amount withdrawn by the 4% rule is directly related to the initial market value of the retirement portfolio. For example in year 1, the amount safely withdrawn from a \$200,000 portfolio would be \$8,000, etc.

Protect yourself from the hidden risks of greedy salespeople as you get older and less interested in managing your accounts. Appoint a trustworthy person as your durable power of attorney and use a written investment plan.

### Life-time income

Life-time incomes offset the risk of outliving your retirement portfolio. The reliable life-time incomes of retirement are Social Security, Pensions, and Annuities.

SOCIAL SECURITY (chapter 3). Social security benefits include a guaranteed income for life, protection against inflation, tax benefits, and protection of your spouse without the risk of market fluctuations and without paying investment fees. Beneficiaries can maximize their income by delaying the onset of benefits to age 70 instead of starting at age 62 (be sure to enroll in Medicare at age 65). A survivor’s benefit is based on the earnings-record of the deceased. The spousal benefit is automatically upgraded to a higher survivor benefit.

PENSIONS (chapter 5). Traditional pensions offer either a monthly lifetime payment or a lump sum payment that can be rolled over to an Individual Retirement Account (IRA). The rollover incurs an investment risk (investment risk is the possibility of incurring a loss from your choice of investment or the investment’s fluctuation in market value).  Government pensions (except municipal pensions) are reliable.  Most private pensions are protected by the Pension Benefit Guaranty Corporation (PBGC.gov). If you are ineligible for a pension, consider buying a lifetime annuity.

ANNUITIES (chapter 6). Annuities aren’t a do-it-yourself investment; they are a tool for managing the risk of outliving your portfolio. Find a good advisor who isn’t a salesperson and avoid buying variable annuities with living benefit guarantees. Simple annuities are purchased with a lump sum in return for monthly lifetime income.

1. The Single Premium Immediate Annuity (SPIA) pays benefits until death unless purchased with payments “Certain”. The SPIA is not designed to create a legacy fund. Its advantage is the payment of benefits that exceed the interest of bonds and dividends of stocks. The insurance company’s rating should be at least AA- (Fitch, S&P), A (AM Best), or Aa3 (Moody’s). [The tax deferred variable annuity can be converted to an SPIA. Find the best available benefit-payments in ImmediateAnnuities.com and switch companies.]
2. The Immediate Pay Variable Annuity pays monthly benefits that change with the market. The benefit is a percentage of the investment portfolio value. The assumed interest rate (air) is your selected rate of withdrawal from the investment portfolio. The investment risks are volatility and choice of investment portfolio.
3. The Inflation Adjusted Immediate Annuity pays monthly benefits adjusted to last year’s inflation. There is no inflation or investment risk. The monthly benefits are lower at the beginning than later on. This annuity is more appropriate for younger people with a longer life expectancy.
4. Fixed Increase Annuities pay monthly benefits that rise at a fixed rate of 1-5%.
5. With a Deferred-income Annuity (“longevity insurance”) there is a time delay to the initial benefit followed by monthly payments for life. The reasons for owning this annuity are 1) protection from outliving retirement portfolio, and 2) providing your spouse with guaranteed income after death.
6. Fixed-term Annuities start paying benefits immediately. This is desirable for people with illiquid investments such as delayed social security.
7. The Charitable Gift Annuity gives a lump sum to charity that guarantees a fixed monthly income for life.

The variable annuity is a pure investment that risks poor performance in the market. Its insurance company offers a guaranteed living-benefit rider (LBR) that provides a minimum lifetime income regardless of the investment’s performance. Taxes on the accumulating returns are deferred until withdrawal, then taxed as regular income (unless “qualified” in a Roth). The tax is proportional to the ratio of investment return to invested capital.  The goal of a variable annuity is to allow growth of your investment above the guaranteed minimum. Success depends on a 90% allocation of stocks in the investment, yet most insurance companies limit the stock fund to 65% stocks. Why? The insurance company is protecting itself by using fixed income from the portfolio to pay the LBR instead of the company’s own money. Living benefits are first taken from the investment portfolio while you continue to pay the annual fee! This seems unfair, so try to exercise your right to withdraw from the investment every year up to a fixed percentage amount. Even if you draw down to \$0, the company will continue to pay your benefit. Spouses are usually not covered by a variable annuity. Rather, the death benefit is an insurance payout that doesn’t replace the annuity’s investment return a survivor might lose. If you bought a variable annuity, it’s too late to extend to your spouse. But you can switch to a better annuity in a tax-free exchange or buy more insurance. Variable annuities often charge excessive management fees of 3-5%.  For a second opinion, consult the Marco Consulting Group at Annuity Review (AnnuityReview.com). They will analyze 2 variable annuities for a fee of nearly \$300.

HOME EQUITY (chapter 10). The equity of your home is a ‘piggy bank’ that can be used for income or passed to your heirs. There are several ways of squeezing income from your home equity:

1. take a Reverse Mortgage to create a 20-30 year spending plan
2. borrow to pay a large bill
5. take a boarder after first checking on possible restrictions imposed by homeowners associations, zoning laws, etc.
6. sell the house and lease it from the new owner (i.e., Sale/Leaseback). Consult a lawyer before selling the house.

The reverse mortgage is a loan against the equity of your home in which the lender makes tax-free payments to you because they are loans. You pay all maintenance costs. Don’t repay the loan while living in the house; proceeds of the sale will repay the loan. You keep the excess proceeds, but otherwise are not responsible for a loss on the sale.

The Home Equity Conversion Mortgage (HCEM) is issued by private lenders and insured by the FHA. The HCEM offers 3 types of payments:

1. lump sum at the beginning
2. monthly payments
3. borrowings from the principal

At your death and before selling the house, your heirs will have the option of buying or selling the house before foreclosure. Seek more information and advice from Jack Guttentag on his website, MtgProfessor.org.

### Portfolio management

SPENDING RULES FOR THE HOMEMADE PAYCHECK (chapters 8, 9). The basic rules are to make buy-and-hold investments in your portfolio, withdraw funds using the 4% rule, and rebalance the portfolio after you make an annual withdrawal. Based on Quinn’s research up to the year 2016, the 4% safemax may be modified in one of several ways:

• 4.5% if your stock allocation is 45-65%
• 5.5% if you reduce the withdrawal in declining markets
• 3% to ensure surviving the next 30 years
• adjustments to the Shiller PE Ratio
• 4% if P/E10 >20
• 5% if P/E10 = 12-20
• 5.5% if P/E10 <12
• 6% is too high and your portfolio may only last 15 years. Instead, borrow on your house through a reverse mortgage.

The amount of annual income withdrawn from your retirement portfolio is determined by your safemax rate of withdrawal (discussed above in the core principles). Be consistent in withdrawing from your portfolio except when the market is depressed. Then withdraw from your cash reserve to pay bills. When the market starts to recover, tap the investments to restore the cash reserve and resume withdrawing at the safemax.

Skip an annual withdrawal when you don’t need it. If the required minimum withdrawal from tax-deferred accounts exceeds your planned annual withdrawal, reinvest the excess amount. Here are 2 ways to preserve capital:

1. Withdraw from investments that have increased in value, otherwise from investments with the lowest potential return.
2. Withdraw from taxable accounts before tax-deferred accounts. Within the taxable accounts, withdraw a blend of gains and losses to minimize taxes.

PORTFOLIO INVESTMENTS (chapters 8, 9). Bucket investing is done by putting money into different funds (‘buckets’), each having a specific purpose. First, create a cash reserve (‘cash bucket’) that will pay bills for 2 years when added to pension checks. 90% of the remaining retirement portfolio is allocated to investments and 10% to a discretionary bucket. Allocate 40-65% of the investments to stocks and the remainder to bonds [the author discussed additional guidelines for adjusting your allocation of stocks and bonds according to age (chapter 8)]. The discretionary bucket is used for big, extra items (e.g., new car).

Your allocation of bonds and stocks depends on your capacity for risk, not your tolerance for risk. The capacity for risk depends on how well you are funded and able to pay bills with pension funds. If your risk capacity is low, don’t risk too much on incurring a loss in the stock market. Do you need to risk a stock investment? Not if all your expenses, including health, are covered for life. People older than 80 tend to fall into this category. Younger people with at least a 10 year horizon have more time to survive market fluctuations. The S&P500 Total Return index has never declined over 15 years. Otherwise, you need to invest in stocks if all expenses are not covered for life. The reasons for investing in stocks are to hedge inflation (low allocation of 20-30%) or create a legacy fund for heirs (high allocation of 40-80%).

There are several important advantages to investing in index funds instead of individual stocks and short-term bonds.

• index funds are easier to rebalance each year
• you will earn the return of the whole market
• you will own a portfolio of diversified investments
• index funds are easily converted to cash
• short term bond prices aren’t as volatile as long term bond prices

What if you don’t want to rebalance the retirement portfolio?

• invest in a target-date fund
• use a rebalancing program
• pay a low-cost online advisor (e.g., betterment.com )
• hire a good fee-only financial advisor and avoid paying high fees. consult FINRA.org for help finding a reputable financial advisor.

### Risk management

TAXES (chapter 7). The main categories of tax-deferred retirement savings accounts are employer-sponsored plans and personal IRAs. The typical employer-sponsored plan allows investments in mutual funds. After leaving an employer you can keep the plan, merge it into that of a new employer, or convert it to a rollover IRA. Personal IRA’s expand your investment choices, some of which require a trustee to make the transactions (e.g., precious metal trust, real estate trust). Be aware of the costs of converting a traditional IRA to a Roth IRA. At the time of conversion you must pay regular income tax on the investment returns. You may also incur a higher medicare premium and pay possible tax on unearned income. To minimize taxes when you withdraw funds to pay bills, withdraw from the taxable portion of your portfolio first, the traditional IRA second, and the Roth IRA last.

If you inherit an IRA from your spouse, your choices are these:

• ask the trustee to name you as owner
• rollover to a new IRA owned by you
• rollover to an IRA already owned by you
• create an inherited IRA if you are younger that 59 1/2 years.

If you inherit an IRA from someone else, your choices are these:

• take your full inheritance now and lose the tax shelter
• retitle it as an inherited IRA to keep the tax shelter

HEALTH INSURANCE (chapter 4).  The Affordable Care Act guarantees your eligibility for health insurance irrespective of your state of health. There are 3 general healthcare plans: HMO (Health Maintenance Organization), POS (Point of Service), and PPO (Preferred Providers Organization).  In each plan, your cost share is capped by the annual maximum out-of-pocket payment.

The government’s Medicare program is comprised of part A for hospitalization, part B for outpatient services, part C for extra benefits plus prescriptions, and part D for prescriptions. You pay premiums for parts B-D, but not for part A. There are cost-sharing charges for services in parts A-D. Medigap is a private healthcare insurance designed to supplement Medicare and used to replace Part C of Medicare. Don’t miss the enrollment dates or else pay a higher premium!

LONG TERM CARE (chapter 4). If you become incapacitated and require long term healthcare outside the hospital, your costs may exceed \$85,000 per year. Consider purchasing long term care insurance, but don’t spend more than 5% of your retirement income on insurance premiums for long term care. Group policies are cheaper. Minimize your premiums by choosing a 3-year benefit period (instead of 5 years), avoid paying for inflation adjustments later in life, insure 50-75% of your expected cost, and extend the waiting period to 6 months. The alternatives to long term care insurance are:

1. join a continuing care retirement community that offers a nursing home benefit.
2. self insure by selling your home
3. use Medicaid as a safety net.

LIFE INSURANCE (chapter 11). Don’t buy any if you are a single retiree without dependents. You’re better off investing the saved-premiums. Consider owning life insurance if you have dependents and want to leave a legacy fund or charitable gift. Chapter 11 describes how to extract more value from a life insurance policy.

SHELTER (chapter 10). Younger retirees like living in an active community and older retirees like their “independent living” in a more secure location. The choices for independent living are to remodel your existing home as needed to compensate for a handicap (e.g., wheelchair) or change homes. For example, move to an active adult community (consult 55Places.com; ensure that you will continue to receive healthcare).

Retirees seek “assisted living’ when they need help with the basic functions of living.  The choices for assisted living are to receive in-home healthcare or move into an assisted living facility (consult ALFA.org for choices).

Downsize to make life easier!

## Websites for retirement-planning

February 19, 2016

### Resources

http://DOL.GOV/EBSA/PDF/RETIREMENTTOOLKIT.PDF , federal programs and retirement calculators
http://SOCIALSECURITY.GOV , benefits & ‘retirement estimator’
http://MEDICARE.GOV health insurance for retirees
http://WISERWOMEN.ORG Women’s Institute for a Secure Retirement
http://HHS.GOV/AGING , health- and legal information
http://USA.GOV/BENEFITS-GRANTS-LOANS , federal benefits
http://AGING.OHIO.GOV , quality of life
http://economiccheckup.org , to plan retirement, reduce debt, find work, and cut spending.

### Money management (‘financial planning’)

http://DOL.GOV , search for “Taking the mystery out of retirement planning” and download this excellent pamphlet of useful advice.
http://MYRA.GOV , A safe, affordable Roth savings account for wage earners.
http://WESTERVILLELIBRARY.ORG , search for “Investments 101”

### Portfolio management

http://apps.finra.org/Calcs/1/RMD , find link to “required minimum distribution”
http://BANKRATE.COM , click on “RETIREMENT” tab, then on “Retirement Calculators” subtab, then on “Asset allocation calculator”
http://53.COM, click on “Financial calculators”, then click on the “Retirement Planning” tab, then click on the “Retirement Income Calculator” to estimate your longevity of savings; click on the “Retirement Account Calculator” to compare retirement savings accounts.

### Risk management

http://IRS.GOV , search “identity protection”, about Identity theft
http://FINRA.ORG (securities help line for seniors, 844-574-3577), Check the credentials of a broker or financial advisor; about Investor protection; http://apps.finra.org/meters/1/riskmeter.aspx to assess your risk for Financial fraud
http://LONGTERMCARE.GOV , about LTC health insurance
http://PBGC.GOV ,  to assess pensions
http://immediateannuities.com , to shop for simple annuities
http://annuityreview.com , obtain a second opinion about variable annuities

## 2015

January 17, 2016

The investment goal of the Small Trades Portfolio is to outperform its benchmark index, the Standard & Poor’s 500 Total Return.  Regretfully, this has not happened (chart).

The chart compares the growth of \$1.00 invested in the portfolio to a theoretical investment in its benchmark index and the inflation of U.S. consumer prices.  A decline of the benchmark during the 2008 Recession recovered in 2012 and grew to \$1.66 (66% above baseline) by the end of 2015.  But the portfolio declined and never fully recovered.   Revised operations after the Recession managed to stabilize the portfolio by reallocating 80% of the portfolio’s principal to exchange-traded funds (ETFs).  The ETFs are invested in underperforming asset classes that will eventually recover.

There are encouraging signs of investment performance found in the trends of compound annual growth rates (next chart) and stock performance (subsequent chart).

The compound annual growth rates of the benchmark index are leveling off while those of the portfolio are rising.

Revisions in my investment philosophy for stocks also show an encouraging response.  For every \$1.00 invested in the portfolio on 12/31/2013,  the portfolio’s stocks outperformed the benchmark index and portfolio ETFs for two successive years.

### Discussion

The portfolio is intentionally overweighted by index ETFs.  Among these, the equities ETF (ticker: VT) has 75% of holdings in developed markets and 25% in emerging markets. The returns from emerging markets were disappointing due to economic and political factors in foreign countries. The 2015 decline of gold prices was expected, given the global deflation of prices.

### Strategy

I prefer to invest in healthy emerging markets and when that occurs, I will trade the world-market ETF (ticker: VT) to a riskier emerging-market ETF (ticker: VWO). A continued decline of gold prices will likely cause me to rebalance the ETFs to equal portions of 25% among four asset classes of emerging markets equities, U.S. real estate, U.S. bonds, and gold bullion.  25% allocations of emerging markets equities, U.S. real estate, gold bullion, and U.S. bonds collectively impose a higher risk-return quality to the ETF portfolio compared to a 60:40 allocation of U.S. stocks and bonds.

My investment strategy for stocks is evolving from placing conditional trading orders on cyclic stocks to buying good growth stocks for the long term.

Douglas R. Knight

## Lead article: Stock Index Funds

January 16, 2016

The only way an individual investor can quickly invest in hundreds of different stocks is to buy shares of a stock index fund. The tremendous advantage is an immediate ownership of a diversified portfolio in one affordable investment. It’s the surest way of earning the stock market’s returns provided the correct investment is held through a series of ‘bull’ and ‘bear’ markets. Selecting the ‘correct’ fund requires only a few hours of easy research based on the following information:

INDEX. Stock index funds are passively-managed investment funds designed to imitate a stock index. The index measures the investment performance of a hypothetical portfolio of stocks. Some indices are riskier than others by virtue of the underlying securities in the hypothetical portfolio. For example, micro-cap stocks are riskier than all stocks combined by virtue of differences in turnover, liquidity, and diversification.

FUND MANAGEMENT. The investment fund is an actual portfolio of stocks that are managed for the benefit of the fund’s shareholders. Passive management is an investment style that imitates the performance of the selected index. Active management intentionally avoids imitating the index and is a more costly endeavor.

The legal structure of an index fund regulates its style of management. A unit investment trust (UIT) is bound by a trust agreement to manage a portfolio of fixed composition. The UIT has an unmanaged portfolio because there is no allowance for adjustment of composition by the manager. The open-end investment company (OEIC) operates a managed portfolio of adjustable composition. The OEIC is bound by its investment strategy to operate either a passively or actively managed fund. OEIC managers of an index fund are bound to passive management but have leeway to supplement the fund’s income by revising, lending, or borrowing a minor portion of the portfolio. These operations may increase the risk and tax burden of investment.

PRICING. The pricing mechanism of an index fund is closely regulated. Mutual funds are OEICs that trade shares at net asset value (NAV); in other words, they are priced at the fund’s net worth-per-share. The mutual fund’s share price is not quoted until the next day because the NAV is determined after trading hours from closing prices of the underlying stocks. Mutual funds are marketed through an authorized broker and guaranteed to be priced at the NAV. Exchange-traded funds (ETFs) are OEICs or UITs that trade the fund’s shares in the stock market, which means that the share price is quoted by public auction during trading hours. ETFs are traded the same way as stocks. The intraday net asset value (iNAV) and share price are continually updated and reported by the stock market. The fund’s share price is linked to the fund’s iNAV by arbitrage. Individual investors can neither participate in arbitrage nor redeem ETFs at NAV.

FEES. Managers of investment funds are compensated by charging an annual expense ratio that diminishes the NAV. Competition has decreased the expense ratio of stock index funds to only a few basis points (1 basis point = 0.01%), but beware that the expense ratios of bond index funds and actively managed mutual funds are typically higher; read the prospectus. Mutual funds are notorious for adding special fees to trades and imposing minimal holding periods; check with the broker and read the prospectus. New, small index funds are at risk for early termination when the NAV fails to grow above an estimated fifty million dollars. The expense ratios of small funds generate insufficient compensation for the fund sponsors, so they close shop.

TAXES. OEICs and UITs are registered Investment companies (RICs) that pass all income taxes to the shareholders. The amount of tax depends on dividends and capital gains earned by the fund. Managed portfolios incur a higher tax burden due to the more frequent turnover of portfolio securities. Consequently, mutual fund shareholders pay taxes on unrealized capital gains that ETF shareholders don’t have to pay. In theory, UITs are more tax efficient than OEICs.

INVESTMENT PERFORMANCE. During the 10 year period of 2006-2015, the compound annual growth rate of Standard and Poor’s 500 Total Return Index was 7.2%. In comparison, the growth rates of an index ETF (ticker: SPY) and an index mutual fund (ticker: VFINX) were 7.1% and 7.0% respectively. The slight differences in performance were due to an expense ratio, tracking error, and pricing error of the investment funds compared to the index.

OTHER INDEX FUNDS. There are indices to measure the investment performance of bonds, commodities, precious metals, and other assets. Likewise, there are mutual funds and ETFs that track the various indices. Bond index funds are managed by OEICs and require frequent turnover of the underlying bonds. The index funds for commodities, precious metals, and other assets are structured as grantor trusts, partnerships, or debt instruments. Stock index funds are generally less expensive, taxed at lower rates, and less risky than other index funds. Leveraged ETFs are exceptionally risky investments designed for same-day trading.

CONCLUSION. A broad-market stock index fund is the correct investment for earning returns from the entire stock market or a sector of the stock market. Simply choose an established, reputable index for the particular market that interests you. Then choose an established, reputable mutual fund or ETF that imitates the index. Use screeners or reputable fund families to select appropriate funds. Verify the fund’s expense ratio, extra fees (if any), NAV, longevity, and passive management by reading the prospectus and/or research reports. XTF.com is a free and excellent rating service for screening and assessing ETFs. Cross check your research with a trusted broker.

## What is a good growth stock?

December 22, 2015

### Theme

—profitable companies attract investors—

A good growth stock represents the profitable company that sells desirable products. The company’s business earnings should grow nearly 6% annually so as to match the growth rate of the U.S. Economy (about 3.5%) and compensate the rate of U.S.Inflation (about 2%); otherwise, the company might do well to liquidate its business and reinvest in securities.

Growth stock investors seek an annual rate of return that exceeds the U.S. Stock Market’s historical 8-10% annual rate of return. The basic approach is to buy stocks at a low price and sell them at a high price, but that is easier said than done. Investors can help realize high returns by selecting stocks from well managed companies, holding the stocks through an adequate growth period, to offset price volatility, and diversifying their stock portfolio.

### Evaluating the company

Does the company earn respectable profits with a sustainable business? The answer is yes if the company has a:

• growth rate of earnings that surpasses 6% annually.
• future growth rate of earnings that surpasses 6% annually.
• durable business with a sustainable growth rate.

Growth rate. The company that recognizes and satisfies the needs of customers will accumulate sales with the demand for its product. Profitability is the combination of sales growth coupled with efficient management of business expenses. In other words, the profitable company has a respectable growth rate of sales with respect to time, respectable rate of earnings with respect to sales, and consequently, a respectable growth rate of earnings with respect to time.

Earnings are the net income from sales after payment of expenses. The growth rate of earnings matches the growth rate of sales when the company runs its business in a consistent manner. Both sales and earnings should grow annually by at least 6% to outperform the national economy and compensate for the effect of inflation. Growth investors typically monitor the company’s earnings per share (EPS) on a quarterly basis. The EPS should grow at a compound annual growth rate of 6%, or more, as determined from at least 5 years of historical data. When evaluating a company’s earnings, consider the possibility that management is manipulating the EPS to earn higher compensation.

Future growth rate. The earnings estimate is an analyst’s quarterly or annual forecast of the EPS. The estimate is more uncertain when the forecast extends to 3-5 years. Investors use the earnings estimate to track a company’s performance and to derive a future range of share prices. The growth investor should seek companies with earnings estimates above the 6% compound annual growth rate.

Durable business. Any company can be driven out of business by an economic disaster in the entire industry, strong competition, and a declining market for the company’s product. The durable company has sufficient financial strength to survive hard times coupled with the competitive advantages needed to maintain its market position. The sustainable growth rate is a measure of the company’s capacity for earnings growth, assuming there’s room for growth of sales in the product’s market. An analysis of market opportunity is used to estimate the future demand for the company’s product.

### Evaluating the stock

If a profitable company attracts investors, its stock price will rise with investors’ demand for shares. The attractive stock may be detected by a:

• favorable valuation
• price momentum
• projected annual return above 10%

Favorable valuation. Growth investors place a high value on the company’s EPS for the simple reason that EPS represents the net income that generates an investment return. The 2 sources of investment return are dividends and capital gains. If the company choses to pay dividends, they are derived from the net income. Capital gains are the amount of profit from an increase in share price generated by investor-demand.

The price of a growth-stock tends to increase with the rise in EPS. This relationship is measured by the price-to-earnings ratio (P/E or PE). The current P/E is today’s price divided by the EPS of the past 12 months. The current P/E reveals what investors are willing to pay for each dollar of company earnings. The relative P/E is a ratio of the current P/E to past P/Es or to some benchmark P/E such as the average P/E of the stock market. At parity, the relative P/E is 1.0. Stocks below parity are undervalued by market participants and may be trading at prices that favor buyers. Conversely, stocks above parity are overvalued and may be trading at prices that favor sellers. There are other ways of assessing the value of a stock such as the calculation of fair value performed by stock analysts.

Price momentum. Another characteristic of the growth stock is that its share price is likely to continue in the direction of an upward trend as long as there’s a demand for shares. A review of historical prices will reveal the direction of price momentum.

Projected annual return. The reason that growth investors should seek returns above the 8%-10% total return of the stock market is that an alternative investment in index funds will capture the market’s return. One way of projecting the stock’s annual return is to multiply the future EPS by a P/E ratio to obtain the future share price. The difference from today’s price represents the future capital gain. Factoring in the stock’s dividend yield will give the projected annual return.

### Risk management

The primary hazards of incurring a loss are,

• company risk
• market risk
• portfolio risk

Company risk. Poor management can weaken the company and reduce its profitability. A fundamental analysis of the company, which includes a review of the financial statements, can help reduce the possibility of investing in a poorly managed company. Periodic reviews of financial statements and company news are needed to reassess the company’s management efficiency and help prevent a serious capital loss from investment.

Market risk. Volatility is the moment-to-moment fluctuation in share price that results from trading activity in the stock market. Greater volatility produces greater upside and downside risks. Upside risk is the potential gain from an investment. It represents a reasoned guess of the future peak share price. Downside risk is the potential loss. Volatility, upside risk, and downside risk are calculated in several ways. Generally speaking, riskier investments should be held for longer time periods to improve the chance of earning an estimated return.

Portfolio risk. A concentrated portfolio has a large investment in one stock compared to others. Any capital loss from the largest holding could seriously degrade the investment return of the whole portfolio. The potential impact of capital loss from a large investment can be reduced by re-allocating the principal among stocks that are diversified with respect to industry and company size.

### Conclusions

A good growth stock outperforms the stock market because the company’s earnings grow faster than the Economy. One way detecting a good growth stock is to find the company that has a good sales record, bright future for earnings, and durability. Then determine what value other investors place on the stock in today’s market and future years. A potential capital gain of 10% or higher is a good growth investment.

March 20, 2015

## Preview

The simple rate-of-return ( R ) is a measure of your investment’s profitability for any chosen time interval.  By comparison, the CAGR and IRR are rates of return that measure your investment’s profitability as if it were an orderly process with respect to time.  CAGR is the acronym for “compound annual growth rate”.  It is the constant rate at which an investment’s market value grows every year in a cumulative fashion.  IRR is the acronym for “internal rate of return”, which describes the performance of all cash flows in a financial project such as the individual investor’s program of dollar-cost-averaging or an investment club’s program of portfolio management.  IRR is an annualized rate-of-return when all time intervals are measured in years.

## Return

Any profit from your investment is called a return.  There are 2 types of return: realized and unrealized.  Realized returns are cash payments from dividends, interest, and sales.  Unrealized returns are the market values of reinvested dividends and unsold holdings.

return = market value – cost  [equation 1]

Example 1: Suppose you invested \$100 and held the stock for 5 years until its market value grew to \$201.  From equation 1, you determine that your return is \$101.  If you sell it, it’s a realized return; otherwise, it’s an unrealized return.

## Simple rate-of-return

The simple rate-of-return ( R ) is a measure of your investment’s profitability for any chosen time interval, but time is not an essential factor in the calculation (equation 2).

R = return/cost [equation 2]

R is reported as a decimal number or a percentage.

Example 2: The cost of an investment was \$100 and 5 years later the return was \$101.  From equation 2, R = \$101/\$100 = 1.01.  Multiply the answer by 100 to find the percentage.  R = 100×1.01 = 101%.

## CAGR

The CAGR is a rate-of-return that measures your investment’s profitability as a growth rate.  Time is a factor in the calculation of CAGR (equation 3).

rate = (final/initial)(1/N) -1  [equation 3]

N is the number of events or time periods between

the initial and final values.

Example 3, simple R versus CAGR: The cost of an investment was \$100 and 5 years later its final value was \$201.  We know from example 2 that the simple R is 101%.  Using the growth rate formula from equation 3, we find that the CAGR is 15%.

Significance: CAGR is the acronym for “compound annual growth rate”.  It is the constant rate at which an investment’s market value grows every year in a cumulative fashion.

MATH: CAGR is a growth rate that describes the ‘future’ (or final) value of a single cash payment.  In contrast, the discount rate devalues a cash flow.  Both rates represent a common ratio that generates a geometric series of points aligned to a smooth curveref 1. Chart 1 illustrates the geometric series of an inflated and devalued investment.

Chart 1.  Geometric series.

In chart 1, the black circle represents a single investment.  The blue curve is a series of theoretical values related to the investment by a common ratio called the discount rate or the growth rate depending on the particular application.  The discount rate devalues the investment to lower values as a function of the time-period N.  The growth rate inflates the investment to higher values.  Both rates are calculated by the formula in equation 3.

## IRR

Equation 3 is also used to calculate the IRR, an acronym for the “internal rate of return”.  The IRR is used to measure the profitability of investments with multiple cash flows.  It is a discount rate that balances all devalued cash flows in a financial project.

MATH: In the field of Finance, a devalued cash flow is called the present value.  The present value is found by revising equation 3 to calculate the initial value for time period N at a given discount rate.  The net present value of the project is the sum of all present values.  The IRR is the discount rate that sets the net present value to zeroref 2.  It is the best-fit discount rate found by an iterative process of trial and error.  The significance of the IRR will be discussed after working through example 4.

Example 4, IRR:  An investor paid \$100 each year for 4 years to purchase and accumulate shares of a particular stock.  After 5 years the market value of all shares was \$735.  Since the purchases were multi year cash flows, the IRR is a good choice for analyzing this investment.  In this example, the trial discount rate is 13.1%.  Table 1 (below) illustrates the analysis:

Table 1.  IRR analysis of the investment in example 4.

Row 1, N displays the time period in years for factor N of equation 3.  Row 2, ACTUAL is the series of investments that began with a \$100 payment at time 0.  Additional \$100 payments were made at the end of years 1 through 4 for a total cash outflow of \$500.   The total market value of the investment was \$735 at the end of the 5th year.  To determine the IRR, the present value ref 2 of every cash flow was calculated with the trial discount rate of 13.1% after rearranging equation 3 to solve for the initial value.  Row 3, DISCOUNTED is the series of present values for each cash flow in row 2.  Notice that the total present value of all cash outflows equals the discounted cash inflow of \$396.65.  Therefore, the net present value is \$0 and the 13.1% discount rate is the investment’s IRRRow 4, PROJECTED is the final value for each present value in row 3.  The final value is predicted by rearranging the terms of equation 3 and using the IRR’s 13.1% as a growth rate for the remaining time.  It’s no accident that the sum of final values in row 4 equals the \$735 cash inflow in row 2.  Chart 2 (below) illustrates the growth curves for projected values.

Chart 2. Projected values for every cash outflow in example 4.

In chart 2, N is the time period in years.  Each black square depicts an investment of \$100.  Each blue curve shows the predicted growth of the investment.  Every point on a curve is a future value and the endpoint at year 5 is the final value.  The final values are listed in row 4 of table 1.  They decreased as the years progressed because there was less time remaining for growth.

Significance:  The IRR is a rate-of-return that describes the performance of all cash flows in an investment.  The IRR is an annualized rate-of-return when all time intervals are measured in years.

## Time distortion

A positive CAGR or IRR always shows a profit.  Conversely, a negative CAGR or IRR always shows a loss.  Higher CAGRs and IRRs imply more profitable investments, but beware that those with short holding periods may grossly misrepresent the long term performance of an investment.

Example 5, time distortion:  Suppose that four different \$100 investments grew to \$200 apiece.  From equation 1, we know that the return was \$100 for every investment.  If the holding periods were 10, 5, 1, and 1/5th years, what were the annualized rates of return?

Table 2.  Annualized- and Simple Rates of return

for different holding periods

Legend.  Equation 3 is used to calculate the annualized rate-of-return when the unit of time is in years.  For this equation, the “Holding period” is the value of N and “Final/Initial” is the quotient of \$200 divided by \$100.  The 4th column is the annualized rate-of-return calculated by equation 3.  The 5th column is the simple rate of return calculated by equation 2.

High annualized rates are desirable, but don’t feel exuberant about an exceptionally high annualized rate-of-return.  As shown in table 2, the annualized rate-of-return might temporarily be inflated by a brief holding period.  It’s unlikely that a short term investment could sustain the 3,100%, or even 100%, annualized rate-of-return in the long run.

Significance:  The passage of time decreases an annualized rate-of-return when cash flows are static.  ANY increase in the CAGR or IRR over time indicates a profitable increase of cash inflow relative to cash outflow.  It’s always wise to verify this impression by checking the payout of the project.

## Conclusions

In the investment world, rates of return are measurements of profitability.  Positive rates indicate profits and negative rates indicate losses.  All rates of return are sensitive to the volatility of market prices; they rise and fall with the market.  The annualized rates of CAGR and IRR are exquisitely sensitive to short time periods; don’t get exuberant about high annualized rates before checking the time period and potential payout.  In the long term, annualized rates tend to decline unless supported by dividend payments and capital gains.  An IRR that is holding steady during the passage of time is revealing an underlying growth in market value.