Measuring the Beta using Historical Stock Prices

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Measuring the Beta using Historical Stock Prices

• 2039

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In this slide set

• The beta coefficient
• The linear regression approach to beta
  measurement using historical return data
• Normalizing the data
• Normalized holding period returns
• Running the regression using MS Excel
• Relevant regression statistics and their
  interpretation
• Different regression charts

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The Beta Coefficient

• Under the theory of the Capital Asset Pricing
  Model total risk is partitioned into two parts
• Systematic risk
• Unsystematic risk
• Systematic risk is the only relevant risk to the
  diversified investor
• The beta coefficient measures systematic risk

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The Term Relevant Risk

• What does the term relevant risk mean in the
  context of the CAPM?
• It is generally assumed that all investors are
  wealth maximizing risk averse people
• It is also assumed that the markets where these
  people trade are highly efficient
• In a highly efficient market, the prices of all
  the securities adjust instantly to cause the
  expected return of the investment to equal the
  required return
• When E(r) R(r) then the market price of the
  stock equals its inherent worth (intrinsic value)
• In this perfect world, the R(r) then will justly
  and appropriately compensate the investor only
  for the risk that they perceive as relevanthence
  investors are only rewarded for systematic
  riskrisk that can be diversified away ISand
  prices and returns reflect ONLY systematic risk.

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The Proportion of Total Risk that is Systematic

• Each investor varies in the percentage of total
  risk that is systematic
• Some stocks have virtually no systematic risk.
• Such stocks are not influenced by the health of
  the economy in generaltheir financial results
  are predominantly influenced by company-specific
  factors
• An example is cigarette companiespeople consume
  cigarettes because they are addictedso it
  doesnt matter whether the economy is healthy or
  notthey just continue to smoke
• Some stocks have a high proportion of their total
  risk that is systematic
• Returns on these stocks are strongly influenced
  by the health of the economy
• Durable goods manufacturers tend to have a high
  degree of systematic risk

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The Regression Approach to Measuring the Beta

• You need to gather historical data about the
  stock and the market
• You can use annual data, monthly data, weekly
  data or daily data.
• You need at least thirty (30) observations of
  historical data.
• Hopefully, the period over which you study the
  historical returns of the stock is representative
  of the normal condition of the firm and its
  relationship to the market.
• If the firm has changed fundamentally since these
  data were produced (for example, they have merged
  with another firm or have divested itself of a
  major subsidiary) there is good reason to believe
  that future returns will not reflect the pastand
  this approach to beta estimation SHOULD NOT be
  used.rather, use the ex ante approach.

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Historical Beta Estimation
In this example, we have determined the quarterly
returns on the stock and the market and using
Excelran a regression to produce the
accompanying chart.
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Characteristic Line

• The characteristic line is a regression line that
  represents the relationship between the returns
  on the stock and the returns on the market over a
  period of time.
• The slope of the Characteristic Line is the Beta
  Coefficient
• The degree to which the characteristic line
  explains the variability in the dependent
  variable (returns on the stock) is measured by
  the coefficient of determination. (also known as
  the R2 (r-squared or coefficient of
  determination)).
• If the coefficient of determination equals 1.00,
  this would mean that all of the points of
  observation would lie on the line. This would
  mean that the characteristic line would explain
  100 of the variability of the dependent
  variable.
• The alpha is the vertical intercept of the
  regression (characteristic line). Many stock
  analysts search out stocks with high alphas.

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Characteristic Line for Imperial Tobacco

• High alpha
• R-square is very low
• Beta is irrelevant

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High R2

• An R2 that approaches 1.00 (or 100) indicates
  that the characteristic (regression) line
  explains virtually all of the variability in the
  dependent variable.
• This means that virtually of the risk of the
  security is systematic.
• This also means that the regression model has a
  strong predictive ability. if you can predict
  what the market will dothen you can predict the
  returns on the stock itself with a great deal of
  accuracy.

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Characteristic Line General Motors

• Positive alpha
• R-square is very high
• Beta is positive and close to 1.0

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An unusual Characteristic Line
Returns on a Stock
Characteristic Line for a stock that will provide
excellent portfolio diversification (high R2)

• Positive alpha
• R-square is very high
• Beta is negative and lt 1.0

Returns on the Market (TSE 300)
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Diversifiable Risk(non-systematic risk)

• Examples of this type of risk include
• a single company strike
• a spectacular innovation discovered through the
  companys RD program
• equipment failure for that one company
• management competence or management incompetence
  for that particular firm
• a jet carrying the senior management team of the
  firm crashes
• the patented formula for a new drug discovered by
  the firm.
• Obviously, diversifiable risk is that unique
  factor that influences only the one firm.

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OK lets go back and look at raw data gathering
and data normalization

• A common source for stock of information is
  Yahoo.com
• You will also need to go to the library a use the
  TSE Review (a monthly periodical)
• You want data for at least 30 months.
• For each month you will need
• Ending stock price
• Number of shares outstanding for the stock
• Dividend per share paid during the month for the
  stock
• Ending value of the market indicator series you
  plan to use (ie. TSE 300 composite index)

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Demonstration Through Example

• The following slides will be based on Alcan
  Aluminum (AL.TO)

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Five Year Stock Price Chart for AL.TO
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Spreadsheet Data From Yahoo

• Process
• Go to http//ca.finance.yahoo.com
• Use the symbol lookup function to search for the
  company you are interested in studying
• Use the historical quotes buttonand get 30
  months of historical data
• Use the download in spreadsheet format feature to
  save the data to your harddrive

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Spreadsheet Data From Yahoo

• The raw downloaded data should look like this

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Spreadsheet Data From Yahoo

• The raw downloaded data should look like this

Volume of trading done in the stock on the TSE in
the month in numbers of board lots
Opening price per share, the highest price per
share during the month, the lowest price per
share achieved during the month and the closing
price per share at the end of the month
The day, month and year
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Spreadsheet Data From Yahoo

• From Yahoo, the only information you can use is
  the closing price per share and the date. Just
  delete the other columns.

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Acquiring the Additional Information You Need

• In addition to the closing price of the stock on
  a per share basis, you will need to find out how
  many shares were outstanding at the end of the
  month and whether any dividends were paid during
  the month.
• You will also want to find the end-of-the-month
  value of the SP/TSX Total Return Composite Index
  (look in the green pages)
• You will find all of this in The TSE Review
  periodicals (HG 5160.T6T6) found on the second
  floor of the library.

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Raw Company Data
Number of shares doubled and share price fell in
half this is indicative of a 2 for 1 stock
split.
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Normalizing the Raw Company Data
The adjustment factor is just the value in the
issued capital cell dividend by 321,400,589.
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Calculating the HPR on the stock from the
normalized data
Use 59.22 as the ending price, 57.90 as the
beginning price and during the month of May, no
dividend was declared.
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Now Put the data from the SP/TSX Total Return
Composite Index in
You will find the Total Return SP/TSX Composite
Index values in TSE Review found in the library.
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Now Calculate the HPR on the Market Index
Again, you simply use the HPR formula using the
ending values for the total return composite
index.
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Regression In Excel

• If you havent alreadygo to the tools menudown
  to add-ins and check off the VBA Analysis Pac
• When you go back to the tools menu, you should
  now find the Data Analysis bar, under that find
  regression, define your dependent and independent
  variable ranges, your output range and run the
  regression.

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Now Use the Regression Function in Excel to
regress the returns of the stock against the
returns of the market
R-square coefficient of determination
Alpha
Beta
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Finalize Your Chart

• You can use the charting feature in Excel to
  create a scatter plot of the points and to put a
  line of best fit (the characteristic line)
  through the points.
• Finally, you will want to interpret the Beta
  (X-coefficient) the alpha (vertical intercept)
  and the coefficient of determination.

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The Beta

• Obviously the beta (X-coefficient) can simply be
  read from the regression output.
• You will want to interpret it in the context of
  the firms, its products and the likely
  relationship that they hold with the health of
  the overall market.