## 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.

Copyright © 2017 Douglas R. Knight

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## Skim the profit?

February 7, 2017

Selling all or part of a profitable investment is a tough choice to make.  On one hand, holding the investment allows time to accumulate a high return, but at the risk of losing profit in the market’s next big decline. On the other hand, selling portions of the investment to ensure a profit today will diminish the future return.

Both choices are easy to illustrate by imagining a stock investment that pays no dividends.  Assume there is a consistent growth of stock price and that no additional shares are purchased after the original purchase. The profit is skimmed by selling part of the investment when its market value grows to twice the original purchase.  Repeat the process every time the market value doubles until the investment is closed.  Chart 1 illustrates the skimming of a \$1,000 investment.

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

After 5 years, the investor could claim a profit of \$1,000 on the original \$1,000 investment. Then the choices would be to close the investment at \$2,000, withdraw only the \$1,000 profit and wait for more (green circles), or withdraw nothing and wait for a bigger profit (black squares). The largest profit is made by waiting 20 years.

Chart 2 illustrates the accumulated cash balances of the HOLD and SELL strategies.

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

After closing the investment in 20 years, the accumulated cash balance would be \$16,367 from the HOLD strategy and \$5,045 from the SELL strategy.

### Alternate conditions

The accumulated cash balance will vary according to the annual rate of return (appended chart 3), the amount skimmed (appended chart 4), and the payment of dividends (appended chart 5).  In every condition, the total profit of the HOLD strategy exceeds the total profit of the SELL strategy.

### Conclusion

On the question of whether or not to skim profits, skim if you need cash in the next 5-10 years. Otherwise, don’t sell without reassessing the investment or using a risk management scheme.  The question of selling for a loss was excluded from this discussion; that’s a different topic.

### Appendix: Tables of cash balances

Charts 3-5 are tables of cash balances that represent profits from an imaginary investment of \$1,000. The choices for taking a profit were to HOLD the investment for 20 years before liquidating the account or to SELL profitable portions of the investment.  Assume there were no trading fees.

Chart 3 shows that a 15% annual rate of return earned a bigger profit than a 7% annual rate of return.  Furthermore, the HOLD strategy earned a larger profit than the SELL strategy at both rates of return.

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

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

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

The HOLD strategy outperformed the SELL strategy. With the SELL strategy, waiting longer to skim bigger profits accumulated a larger cash balance after 20 years. Why? The bigger profits were less frequent, which had the effect of preserving the investment’s principal for longer time periods.

Chart 5 reveals a surprising effect for skimming profits from reinvested dividends.

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

There were no surprises in the HOLD strategy. Reinvested dividends accumulated the largest cash balance over 20 years. However, reinvested dividends accumulated the lowest cash balances in the SELL strategy. Why? Slightly more shares were sold every 5 years from ‘reinvested dividends’ compared to ‘no dividends’. Yet the same number of shares were sold from ‘cash dividends’ compared to ‘no dividends’. The cash dividends directly augmented the cash balances.

Copyright © 2017 Douglas R. Knight

## Young lives matter

January 25, 2017

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

## 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.

Copyright © 2017 Douglas R. Knight

## 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.

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

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

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

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

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

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

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

I = ⍺ + ε+ βmM,     equation 1, CAPM

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

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

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

The four-factor model offers a spectrum of possibilities.

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

Copyright © 2014 Douglas R. Knight

## Beta is the incline of a straight line

December 10, 2016

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

### Returns

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

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

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

### 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