They need protection from the ‘streets’, a decent eduction, and financial skills.

## 2016

January 14, 2017My *SmallTrades* portfolio holds stocks and four classes of exchange-traded index funds (ETFs).

### 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.

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.

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.

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].

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 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

- 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.
- 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.
- ‘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.
- 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.

Copyright © 2017 Douglas R. Knight

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

December 24, 2016[updated 12/25/2016: R^{2} is a useful measure of indexing]

The R-squared (R^{2}) 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 R^{2} 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 R^{2} of 0.997.

### Significance

The R^{2} 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 R^{2} X 100 represents the percent of variation in investment returns that are related to market returns (ref 1,2). In other words, R^{2} measures the relavance of the best-fit line to a set of data. Relavance increases as the R^{2} 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 R^{2} score of 1.00 identifies a straight line of near-perfect predictions of returns. Any R^{2} 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 R^{2} as a measure of alignment between fund returns and the market index. Funds that have an R^{2} 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.

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

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

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

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

### APPENDIX: models for pricing assets and managing portfolios

#### (refs 1-3, 5-8)

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

I = ⍺ + ε+ βmM, equation 1, CAPM

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

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

⍺ is the excess risk premium attributable to skillful management of the Fund.

ε is the model’s error

βm, βs, βv, and βu are portfolio loading factors assigned by the Fund’s manager

The four-factor model offers a spectrum of possibilities.

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

Copyright © 2014 Douglas R. Knight

## Beta is the incline of a straight line

December 10, 2016Beta (which is symbolized as β) is the incline of a straight line. Mathematicians would say the same thing another way, that beta is the slope of a regression line. Either way, β describes the tendency of investment returns to move with market returns. The investment is a security (e.g., stock, bond, mutual fund) that has a unit price. The market is a trading place for a large group of securities. The combined value of all securities is measured by a market index.

### Returns

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

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

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

### Beta (β)

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

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

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

### Significance

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

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

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

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

### Risk

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

### Summary and advice

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

Copyright © 2016 Douglas R. Knight

## Why we need stocks and bonds

October 20, 2016* Believe it or not, Society is coming to the point where all capable people need to invest in stocks or bonds.* So what are stocks and bonds, and why do we need them?

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

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

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

Copyright © 2016 Douglas R. Knight

## Choosing an ETF

August 16, 2016Investing in an exchange-traded fund (ETF) begins with screening many funds to identify a few candidates, then rating the candidates. My preferred open-source screeners are XTF.com and ETF.com, both of which have inclusion criteria for selecting desirable ETFs and exclusion criteria for rejecting undesirable ETFs. Aim to find a reputable low-cost ETF that best matches the performance of its category.

### Asset class

Assets are potential sources of income to investors. Consequently, an *asset class* is a group of assets that earn income the same way. The ETF portfolio holds assets consistent with the fund’s investment strategy, which is either to copy a market index by process of passive management or compete with a market index by process of active management. The index measures the performance of an asset market.

Competing ETFs are typically grouped in one of the following asset classes:

- EQUITY is a share of ownership claimed through the purchase of a company’s stock. Equity ETFs earn capital gains and dividends from stocks.
- REIT. The real estate investment trust (REIT) is a company that owns and manages income-producing real estate. The REIT earns money from rent, mortgage interest, or other real estate investments. At least 90% of the REIT’s taxable income must be given to shareholders in the form of dividends. REIT ETFs earn capital gains and dividends from REITs.
- FIXED INCOME securities pay an expected amount of interest (e.g., bonds) or dividends (e.g., preferred stock).
- COMMODITIES are raw materials sold in markets for use in making finished products. Commodities are sold for cash or traded in futures contracts.
- CURRENCY is a system of money in the form of cash or notes. The currency market trades different currencies to profit from trading fees and differences in interest rates.

### Inclusions

The following inclusion criteria direct the search for reputable candidate funds desired by most individual investors:

- Passively managed ETFs typically charge lower fees than actively managed ETFs and likely outperform actively managed funds over long time-periods.
- U.S. listed ETFs comply with SEC regulations, U.S. stock exchange rules, and the U.S. tax code.
- One of these Asset classes: Equity (stocks), REIT (real estate), or Fixed Income (bonds).

Refine your inclusion criteria by selecting reputable indices and desired market categories.

### Exclusions

The following criteria should be excluded by all but the most adventurous investors!

- Exchange-traded notes (ETNs) are not ETFs.
- Closed-end funds (CEFs) are not ETFs.
- Leverage and inverse ETFs are very tricky investments.
- Actively managed ETFs charge higher fees in order to create porfolios that outperform or underperform a market index.
- These asset classes:

Alternatives (imitation hedge funds)

Asset Allocation (actively managed mix of assets)

Multi-Asset/Hybrid (diversified asset classes)

Volatility (exposure to volatile market)

Commodities (potential tax burdens)

Currency (potential tax burdens)

### Reputable index

All ETFs compete on the basis of an Index they use to design an investment portfolio. Some Indices make better measurements of market performance than others. Beware that some Indices measure untested markets. Generally speaking, the best-in-class ETFs use reputable market indices. One way of choosing a reputable index is by selecting a long-standing, oft-quoted Index provider or Index name.

Index providers are companies that specialize in measuring market performance and selling the information to financial institutions. Table 1 provides a sample of reputable Index providers.

### Category and Index names

Asset Classes have unique categories. Each category may be measured in a variety of indices listed in Tables 2-4.

### Rating the candidates

By now you should have several ETFs that could satisfy your investment goal. Verify that they belong to the same category, then assess their suitability based on the following critera:

- Net assets, Total assets, Assets Under Management (AUM), or Market cap AT LEAST $1 BILLION.
- Inception date AT LEAST 5 YEARS AGO
- Expense ratio BELOW 1%, LOWER IS BETTER AMONG COMPETITORS
- Legal structure PREFERABLY “OEIC” OR “UIT” (table 5)
- Number of holdings CONSISTENT WITH THE MARKET INDEX.
- Tracking error, LOWER IS BETTER AMONG COMPETITORS
- Premium (Discount), LOWER IS BETTER AMONG COMPETITORS

### The finishing touch

It’s a good idea to review the *Annual Report* of your selected ETF. Your potential tax burden is determined by the ETF’s legal structure, its portfolio turnover, and your tax accountant’s hourly fees.

**Copyright © 2016 Douglas R. Knight**