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Measuring the Beta using Historical Stock Prices

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**1. **Measuring the Beta using Historical Stock Prices 2039

**2. **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

**3. **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

**4. **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 relevant…hence investors are only rewarded for systematic risk…risk that can be diversified away IS…and prices and returns reflect ONLY systematic risk.

**5. **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 general…their financial results are predominantly influenced by company-specific factors
An example is cigarette companies…people consume cigarettes because they are addicted…so it doesn’t matter whether the economy is healthy or not…they 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

**6. **The Regression Approach to Measuring the Beta

**7. **Historical Beta Estimation

**8. **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.

**9. **Characteristic Line for Imperial Tobacco

**10. **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 do…then you can predict the returns on the stock itself with a great deal of accuracy.

**11. **Characteristic Line General Motors

**12. **An unusual Characteristic Line

**13. **Diversifiable Risk(non-systematic risk) Examples of this type of risk include:
a single company strike
a spectacular innovation discovered through the company’s R&D 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.

**14. **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)

**15. **Demonstration Through Example The following slides will be based on Alcan Aluminum (AL.TO)

**16. **Five Year Stock Price Chart for AL.TO

**17. **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 button…and get 30 months of historical data
Use the download in spreadsheet format feature to save the data to your harddrive

**18. **Spreadsheet Data From Yahoo The raw downloaded data should look like this:

**19. **Spreadsheet Data From Yahoo The raw downloaded data should look like this:

**20. **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.

**21. **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 S&P/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.

**22. **Raw Company Data

**23. **Normalizing the Raw Company Data

**24. **Calculating the HPR on the stock from the normalized data

**25. **Now Put the data from the S&P/TSX Total Return Composite Index in

**26. **Now Calculate the HPR on the Market Index

**27. **Regression In Excel If you haven’t already…go to the tools menu…down 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.

**28. **Now Use the Regression Function in Excel to regress the returns of the stock against the returns of the market

**29. **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.

**30. **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.