Measuring the Beta - PowerPoint by wuyunyi

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									Measuring the Ex Ante Beta




            2039
Calculating a Beta Coefficient Using Ex
Ante Returns

   Ex Ante means forecast…
   You would use ex ante return data if historical rates
    of return are somehow not indicative of the kinds of
    returns the company will produce in the future.
   A good example of this is Air Canada or American
    Airlines, before and after September 11, 2001. After
    the World Trade Centre terrorist attacks, a
    fundamental shift in demand for air travel occurred.
    The historical returns on airlines are not useful in
    estimating future returns.
In this slide set

   The beta coefficient
   The formula approach to beta measurement
    using ex ante returns
    –   Ex ante returns
    –   Finding the expected return
    –   Determining variance and standard deviation
    –   Finding covariance
    –   Calculating and interpreting the beta coefficient
The Beta Coefficient

   Under the theory of the Capital Asset Pricing Model total risk is
    partitioned into two parts:
     –   Systematic risk
     –   Unsystematic risk
                        Total Risk of the Investment



                  Systematic Risk       Unsystematic Risk

   Systematic risk is the only relevant risk to the diversified
    investor
   The beta coefficient measures systematic risk
The Beta Coefficient – the formula
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.
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
The Formula Approach to Measuring
the Beta




 You need to calculate the covariance of the returns between the stock
    and the market…as well as the variance of the market returns. To
    do this you must follow these steps:
      • Calculate the expected returns for the stock and the market
      • Using the expected returns for each, measure the variance
         and standard deviation of both return distributions
      • Now calculate the covariance
      • Use the results to calculate the beta
Ex ante return data (a sample)

  An set of estimates of possible returns and their respective
                   probabilities looks as follows:
The Total of the Probabilities must
equal 100%

This means that we have considered all of the possible outcomes in
                 this discrete probability distribution
Measuring Expected Return on the
stock From Ex Ante Return Data

The expected return is weighted average returns from
                the given ex ante data
Measuring Expected Return on the
market From Ex Ante Return Data

The expected return is weighted average returns from
                the given ex ante data
Measuring Variances, Standard
Deviations from Ex Ante Return Data

Using the expected return, calculate the deviations away from the mean, square
   those deviations and then weight the squared deviations by the probability of
  their occurrence. Add up the weighted and squared deviations from the mean
                         and you have found the variance!
Measuring Variances, Standard
Deviations from Ex Ante Return Data

      Now do this for the possible returns on the market
Covariance

The formula for the covariance between the returns on the stock and the
   returns on the market is:




Covariance is an absolute measure of the degree of „co-movement‟ of
  returns. The correlation coefficient is also a measure of the degree of
  co-movement of returns…but it is a relative measure…this is why it is
  on a scale from +1 to -1.
Correlation Coefficient

The formula for the correlation coefficient between the returns on the
   stock and the returns on the market is:




The correlation coefficient will always have a value in the range of +1 to -
   1.
Measuring Covariances and Correlation
Coefficients from Ex Ante Return Data

 Using the expected return (mean return) and given data measure the
      deviations for both the market and the stock and multiply them
  together with the probability of occurrence…then add the products up.
The Beta Measured Using
Ex Ante Return Data

 Now you can plug in the covariance and the variance of the
      returns on the market to find the beta of the stock:




          A beta that is greater than 1 means that the investment is
  aggressive…its returns are more volatile than the market as a whole.
   If the market returns were expected to go up by 10%, then the stock
        returns are expected to rise by 18%. If the market returns are
  expected to fall by 10%, then the stock returns are expected to fall by
                                     18%.
Lets Prove the Beta of the Market is 1.0

 Let us assume we are comparing the possible market
       returns against itself…what will the beta be?




 Since the variance of the returns on the market is = .007425 …the beta
 for the market is indeed equal to 1.0 !!!
Proving the Beta of Market = 1

 If you now place the covariance of the market with
         itself value in the beta formula you get:
How Do We use Expected and
Required Rates of Return?

   Once you have estimated the expected and required rates of
    return, you can plot them on a SML and see if the stock is
    under or overpriced.
              % Return
                                                                    E(R) = 5.0%

                R(RX) = 4.76%
                                                                        SML
                 E(RM)= 4.2%



          Risk-free Rate = 3%




                                               BM= 1.0         BX = 1.464


                                Since E(r)>R(r) the stock is underpriced.
How Do We use Expected and
Required Rates of Return?

   The stock is fairly priced if the expected return = the required
    return.
   This is what we would expect to see „normally‟ or most of the
    time.
                % Return
           E(RX) = R(RX) 4.76%
                                                        SML
                   E(RM)= 4.2%



             Risk-free Rate = 3%




                                      BM= 1.0   BX = 1.464
Use of the Forecast Beta

   We can use the forecast beta, together with an estimate of the risk-
    free rate and the market premium for risk to calculate the investor‟s
    required return on the stock using the CAPM:
Conclusions

   Analysts can make estimates or forecasts for the
    returns on stock and returns on the market portfolio.
   Those forecasts can be analyzed to estimate the
    beta coefficient for the stock.
   The required return on a stock can be calculated
    using the CAPM – but you will need the stock‟s beta
    coefficient, the expected return on the market
    portfolio and the risk-free rate.

								
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