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.


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.


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 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

April, 2014, I joined an investment club

May 15, 2014

I enjoy seeking short term returns from stocks. Active trading gives me the excuse to place crafty trading orders and check the market every day. The goal is to realize a profit from every stock in less than a year, resulting in a portfolio turnover rate of at least 100%. Read the rest of this entry »

Hey Kids, money is important

April 16, 2014

Three reasons for liking money: The best is that it buys things you want at today’s prices. Another reason is that it will buy things in the future. And the third reason is that it represents the trading value of goods and services (1).


Most people aren’t given a lot of money. They have to earn it and invest it to get rich. They also have to protect it against ‘risk’. Think of risk as your chances of losing money. Here are some easy ways of losing money:

  1. Theft. People may steal your money unless you put it in the bank and keep your bank account’s password a secret.
  2. Overspending. Save money for things that you will need in the future. Otherwise, you are spending too much money. Another way of overspending is to borrow money to buy things that you don’t really need. The best way to avoid overspending is to plan a budget.
  3. Debt. Using a credit card or taking a loan are two different ways of borrowing money from somebody called a lender. Before borrowing the money, you must sign a contract that requires you to repay the lender on time with an extra amount of money called interest. All of the money that you owe is called debt and refusal to repay the lender may eventually prevent you from buying things. Don’t borrow money unless you need it for an important reason (such as education) and use a budget to manage your debt.
  4. Unemployment. Unemployment occurs when people can’t work for money. Avoid unemployment by getting a good education and learning good skills. Don’t drop out of high school before graduation.
  5. Disasters. Accidents, illnesses, wars, and severe weather conditions are disasters that require a lot of money to survive the damage. Adults can buy insurance that will help pay for illness, injuries, and property damage.
  6. Inflation reduces the purchasing power of money.
  7. Citizens are required to pay taxes on the money they earn.


Money’s ability to pay for things is called purchasing power. It’s no secret that the purchasing power of money changes over time. Today the price of a Big Mac™ hamburger is nearly five dollars. But 50 years ago, the price of a Big Mac™ hamburger was only 45 cents. What happened over 50 years? The prices of most things went up, including the price of hamburgers. The increase in prices over time is called ‘inflation’.

You can be sure that today’s money will buy less in the future due to inflation. The best way to protect against the effects of inflation is to start investing money as soon as possible.

Investing money

Think of  ‘investing’ as a good way of using money to earn more money. The money that you earn is called a profit or a return. Investing is a lifetime skill worth learning now.

The risk of investing is that you will lose money. If you don’t want to risk losing money, invest in U.S. Government Bonds. The government always repays your money plus a type of return called interest.

Stocks are risky investments that often pay a higher return than U.S. Government Bonds. When you buy shares of a good stock, you must sell them at a higher price to earn the type of return called a capital gain. Try to avoid losing money by selling the shares at a lower price than you paid; that kind of loss is called a capital loss. The longer you wait to sell shares, the better your chance of selling them at a higher price. Some good stocks also pay small amounts of cash called dividends.

Investors who don’t have the time or interest in selecting a good stock can earn the average return from a large group of stocks by purchasing shares of a stock index fund. Investing in a good stock index fund is less risky than investing in a good stock.


Investors must pay part of their returns to the Government by paying taxes. Employees are able to pay lower taxes on their returns by investing in tax-deferred and tax-free retirement accounts. If you earn wages as an employee, you may be able to invest in tax-deferred accounts known as the traditional individual retirement account [IRA] and the employer sponsored 401(k) account. Tax-deferred accounts protect you from paying taxes on returns until you start withdrawing money after retirement. You may also be able to invest in tax-free accounts known as the Roth IRA and the Roth 401(k). After you pay regular taxes on your wages, you never pay taxes on money that you withdraw after retirement. Employers, tax advisers, and librarians can provide information that you need to know before using these important retirement accounts.

Making the most of your money

Click into this money management website to get good advice on managing and growing your money.

Copyright © 2014 Douglas R. Knight


1. Free exchange. Money from nothing. The Economist, 3/15/2014.

ETF #scorecard: Market Vectors Morningstar Wide Moat Research ETF (MOAT:nyse)

July 19, 2012


MOAT’s primary investment strategy is to make at least an 80% investment in stocks that are selected by a replicate sample of the Index [Index ticker: MWMFTR].  The indexer is Morningstar®, a leading financial analysis firm.   The indexed stocks are selected from among 97% of all stocks traded in the U.S. market.  Morningstar uses a proprietary method to screen stocks with wide economic moats [an “economic moat”, or “competitive advantage”, is the company’s unique ability among competitors for earning profits over an extended period of time].  Morningstar uses an additional proprietary method to assign a fair value to each screened stock.  The top 20 stocks with greatest discount price relative to fair value are used in the Index.




It’s too early to evaluate the fund’s annual yield, portfolio turnover rate, and investment performance.  Therefore, watch the fund before committing to a long-term investment.  Expect the future turnover rate to be less than 100% if the stocks have competitive advantages that favor long term investment. However, quarterly fluctuations in discount price could increase the Index and Portfolio’s turnover rates.  The articles Scorecard appraisal and  scorecard App provide additional information on ETF risk-benefit analysis.

MOAT’s historical index is compared with SPY’s historical index in the following Bloomberg Chart:

It appears that MOAT’s index outperformed SPY’s by 5.24% during the last 12 months.


The fund’s underlying assets are solid, but only time will tell if the fund is wisely managed.

Copyright © 2012 Douglas R. Knight 

ETF #scorecard: iShares FTSE NAREIT Mortgage Plus Capped Index Fund (nyse: REM)

June 25, 2012


REM invests in mortgage REITs to earn an income stream of about 10% annual yield.  That income is distributed to shareholders in quarterly payments.  The benefit of exposure to REM’s portfolio outweighs the risks of management error and exposure to mortgage REITs as long as the Fed keeps interest rates low in the U.S. Economy and the REITs maintain market value.



About mortgage REITs

All REITs avoid paying corporate income tax by investing in the real estate market and distributing at least 90% of the income to shareholders.  Mortgage REITs invest in residential or commercial mortgages and mortgage-backed securities (MBSs).  The residential mortgages may be agency-guaranteed or unguaranteed.  Agency-guaranteed mortgages protect the principal, but the principal of unguaranteed mortgages carries the risk of default.  Owners of MBSs risk loss if the security is overvalued and the underlying mortgages default1.

Profit scheme.  Suppose a building loan pays 4% on the principal (i.e., 4% yield).  The REIT may buy the mortgage with its own cash to earn the 4% yield or leverage the purchase with borrowed cash to seek a higher yield.  The following table illustrates the financing of a mortgage (or MBS) for increased returns2:

LEGEND: Unleveraged return = (mortgage yield * own cash).  Leveraged return = (mortgage yield – short term yield) * borrowed cash.  Return on equity = 100 * (unleveraged return + leveraged return) / own cash

Risk.  Interest rate spread is the difference between short-term interest rate paid by the firm (i.e., REIT) to buy the mortgage and the long-term interest rate collected from the mortgage by the firm.  Fed policy is the biggest driver of short-term interest rate3.  The book value of MREITs is the balance of mortgages and MBSs owned by the firm less all liabilities.  An increase in long term interest rate will lower the book value, increase leverage, and limit the ability to raise capital through secondary offerings4.

Risk management:  The 3 sell signals for mortgage REITs are 1) a quarterly interest rate spread less than 1.75%, 2) an increase in short term interest rates – especially above 4% –, and 3) a 15% decline in mortgage REIT stock prices below the 52 week high.  Consider using Annaly Capital Management (NLY) as a primary marker for the mortgage REIT industry 5.

Comments about REM.

The underlying Index measures the mortgage real estate (MREITs), mortgage finance, and savings association sectors of the U.S. equities mkt.  About 69% of the recent index mkt cap is concentrated in REITs.

The underlying assets.have the following risks:

  • MREITS risk default on payments, lower interest rates, and costs of leverage.
  • REITs risk landlord ownership of real estate.
  • Mortgage finance companies risk default on payments.
  • Savings associations risk losses from lending.

Investment strategy.  At least 90% assets are securities in the underlying index.  Less than 10% assets are not indexed securities that include futures, swaps, and cash equivalents.  The fund may lend assets up to 30% total asset value.

Copyright © 2012 Douglas R. Knight



2.  How to Win Bernanke’s War on Savers with a 19% Yield January 18, 2012 by Martin Hutchinson, Global Investing Strategist, Money Morning Martin Hutchinson

3.  Mortgage REITs: A Look Inside tickerspy’s Highest Yielding Segment (AGNC, CIM, NRF, RSO, NLY, ANH) by Ryan Patel | September 3rd  |

4.  Mortgage REITs And Double-Digit Yields: What’s The Catch? January 15, 2012 by John D. Thomason.

5.  Common Sense Formula For Taking Profits On Your Mortgage REIT Investments, Tom Dyson and Nirav Desai.  Copyright 2011 by COMMON SENSE PUBLISHING,

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