Risk, Return, and Capital Budgeting

1
Chapter 10

Risk, Return, and Capital Budgeting
(??????????)
2
Topics Covered

• Measuring Beta (How to measure the market risk of
  a security?)
• Portfolio Betas (How to measure the market risk
  of a portfolio?)
• CAPM and Expected Return (Relate the risk and
  return of a security)
• Security Market Line
• Capital Budgeting and Project Risk (Find the
  opportunity cost of capital)

3
Measuring Market Risk

• Market Portfolio - Portfolio of all assets
  (stocks, bonds, foreign securities, real estate,
  and so on) in the economy. In practice a broad
  stock market index, such as the SP Composite, is
  used to represent the market. We can track the
  rate of return of a market portfolio to know the
  impact of macro risk changes. If the market is
  up on a particular day, then the net impact of
  macroeconomic changes must be positive.
• Beta measure of the individual stocks.
  Sensitivity of a stocks return to the return on
  the market portfolio.

4
Measuring Market Risk

• Example - Turbo Charged Seafood has the following
  returns on its stock, relative to the listed
  changes in the return on the market portfolio.
  The beta of Turbo Charged Seafood can be derived
  from this information.

5
Measuring Market Risk

• Example - continued

Avg.0.8
Avg.-0.8
6
Measuring Market Risk
Example - continued

• When the market was up 1, Turbo average change
  was 0.8
• When the market was down 1, Turbo average
  change was -0.8
• The average change of 1.6 (-0.8 to 0.8) divided
  by the 2 (-1.0 to 1.0) change in the market
  produces a beta of 0.8.

7
Measuring Market Risk

• Example - continued

The Market Model
Slope0.8
8
Measuring Market Risk

• Aggressive stocks have high betas gt1 defensive
  stocks have low betas lt1 the average beta of all
  stocks is - no surprise here 1.0 exactly (e.g.,
  see figure 10.2 and page 292 for how to find the
  beta).
• We can break down common stock returns into two
  parts the part explained by market returns and
  the the firms beta, and the part due to news
  that is specific to the firm. Fluctuation in the
  first part reflect the market risk in the second
  part reflect unique risk. Compare the risk
  measures in Table 9.6 (p. 273) and Table 10.1
  (p.294) for again the illustration of the
  different measurements of risk

9
Portfolio Betas

• Diversification decreases variability from unique
  risk, but not from market risk.
• The beta of your portfolio will be an average of
  the betas of the securities in the portfolio.
• If you owned all of the SP Composite Index
  stocks, you would have an average beta of 1.0

10
Measuring Market Risk

• Market Risk Premium - Risk premium of market
  portfolio. Difference between market return and
  return on risk-free Treasury bills.

Market Portfolio
Risk-free Assets
11
Measuring Market Risk

• CAPM (????????)- Theory of the relationship
  between risk and return which states that the
  expected risk premium on any security equals its
  beta times the market risk premium.

12
Measuring Market Risk

• Security Market Line - The graphic representation
  of the CAPM the relationship between expected
  return and beta (risk).

Lending Portfolio
Borrowing Portfolio
13
Beta and Unique Risk
Covariance with the market
Variance of the market
See the example 10.3 and Figure 10.4b in
p.297-299 for illustrating the relation between
expected returns and betas.
14
More about the CAPM

• According to the CAPM, the expected returns
  (required returns) demanded by investors depend
  on two things (1) compensation for the time
  value of money (the risk free rate), and (2) a
  risk premium, which depends on beta and market
  risk premium.
• Why the CAPM works? The CAPM assumes that the
  stock market is dominated by well-diversified
  investors who are concerned only with market
  risk. That makes sense in a stock market where
  trading is dominated by large institutions and
  even small fly can diversify at very low cost.
  Does it work in Taiwan?

15
Testing the CAPM How well does it works?
Beta vs. Average Risk Premium
Avg Risk Premium 1931-65
SML
30 20 10 0
Investors
Market Portfolio
Portfolio Beta
1.0
16
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium 1966-91
30 20 10 0
SML
Investors
Market Portfolio
Portfolio Beta
1.0
17
Setting up for the Estimation

• (1) Decide on an estimation period
• Services use periods ranging from 2 to 5 years
  for the regression
• Longer estimation period provides more data, but
  firms change
• Shorter periods can be affected more easily by
  significant firm-specific event that occurred
  during the period (Example ITT for 1995-1997).
• (2) Decide on a return interval - daily, weekly,
  monthly
• Shorter intervals yield more observations, but
  suffer from more noise.
• Noise is created by stocks not trading and biases
  all betas towards one.
• (3) Estimate returns (including dividends) on
  stock
• Return (PriceEnd - PriceBeginning
  DividendsPeriod)/ PriceBeginning
• Included dividends only in ex-dividend month
• (4) Choose a market index, and estimate returns
  (inclusive of dividends) on the index for each
  interval for the period.

18
Choosing the Parameters Boeing

• Period used 5 years
• Return Interval Monthly
• Market Index SP 500 Index.
• For instance, to calculate returns on Boeing in
  May 1995,
• Price for Boeing at end of April 27.50
• Price for Boeing at end of May 29.44
• Dividends during month 0.125 (It was an
  ex-dividend month)
• Return (29.44 - 27.50 0.125)/ 27.50
  7.50
• To estimate returns on the index in the same
  month
• Index level (including dividends) at end of April
  514.7
• Index level (including dividends) at end of May
  533.4
• Dividends on the Index in May 1.84
• Return (533.4-514.71.84)/ 514.7 3.99

19
Boeings Historical Beta
20
The Regression Output

• ReturnsBoeing -0.09 0.96 ReturnsS P 500
  (R squared29.57) (0.20)
• Intercept -0.09
• Slope 0.96

21
Analyzing Boeings Performance

• Intercept -0.09
• This is an intercept based on monthly returns.
  Thus, it has to be compared to a monthly
  risk-free rate.
• Between 1993 and 1998,
• Monthly Risk-free Rate 0.4 (Annual T.Bill rate
  divided by 12)
• Risk-free Rate (1-Beta) 0.4 (1-0.96) .01
• The Comparison is then between
• Intercept versus Risk-free Rate (1 - Beta)
• -0.09 versus 0.4(1-0.96) 0.01
• Jensens Alpha -0.09 -(0.01) -0.10
• Boeing did 0.1 worse than expected, per month,
  between 1993 and 1998.
• Annualized, Boeings annual excess return
  (1-.0001)12-1 -1.22

22
Estimating Boeings Beta

• Slope of the Regression of 0.96 is the beta
• Regression parameters are always estimated with
  noise. The noise is captured in the standard
  error of the beta estimate, which in the case of
  Boeing is 0.20.
• Assume that I asked you what Boeings true beta
  is, after this regression.
• What is your best point estimate?
• What range would you give me, with 67
  confidence?
• What range would you give me, with 95
  confidence?

23
Breaking down Boeings Risk

• R Squared 29.57
• This implies that
• 29.57 of the risk at Boeing comes from market
  sources
• 70.43, therefore, comes from firm-specific
  sources
• The firm-specific risk is diversifiable and will
  not be rewarded.

24
Beta Estimation in Practice Bloomberg
25
Estimating Expected Returns December 31, 1998

• Boeings Beta 0.96
• Risk-free Rate 5.00 (Long term Government Bond
  rate)
• Risk Premium 5.50 (Approximate historical
  premium)
• Expected Return 5.00 0.96 (5.50) 10.31

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Use to a Potential Investor in Boeing

• As a potential investor in Boeing, what does this
  expected return of 10.31 tell you?
• This is the return that I can expect to make in
  the long term on Boeing, if the stock is
  correctly priced and the CAPM is the right model
  for risk,
• This is the return that I need to make on Boeing
  in the long term to break even on my investment
  in the stock
• Both
• Assume now that you are an active investor and
  that your research suggests that an investment in
  Boeing will yield 25 a year for the next 5
  years. Based upon the expected return of 10.31,
  you would
• Buy the stock
• Sell the stock

27
How Managers Use this Expected Return

• Managers at Boeing
• need to make at least 10.31 as a return for
  their equity investors to break even.
• this is the hurdle rate for projects, when the
  investment is analyzed from an equity standpoint.
• In other words, Boeings cost of equity is
  10.31.
• What is the cost of not delivering this cost of
  equity?

28
Testing the CAPM Anomalies
Company Size vs. Average Return
Average Return ()
Company size
Smallest
Largest
29
Testing the CAPM Anomalies
Book-Market vs. Average Return
Average Return ()
Book-Market Ratio
Highest
Lowest
30
Capital Budgeting SML

• The security market line provides a standard for
  project acceptance. If the projects return lies
  above the SML, the the return is higher than
  investors could expected to get by investing
  their funds in the capital market and therefore
  is an attractive investment opportunity(see
  example 10.4 in p.303-304 for illustration).
• Two problems about the above argument. (1) If
  the firm has issued securities other than equity
  and (2) if the project risk is significantly
  different from the companys existing business.
  Have to be solved latter.

31
Capital Budgeting Project Risk

• The project cost of capital depends on the use to
  which the capital is being put. Therefore, it
  depends on the risk of the project and not the
  risk of the company. If a company invests in a
  low-risk project, it should discount the cash
  flows at a correspondingly low cost of capital,
  and vice versa.
• Expected cash-flow forecast should already
  reflect the possibilities of all possible
  outcomes, good or bad. If the cash-flow
  forecasts are prepared properly, the discount
  rate should reflect only market risk of the
  project. It should not have to fudged to offset
  errors or biases in the cash flow forecast.

32
Capital Budgeting Project Risk

• Example - Based on the CAPM, ABC Company has a
  cost of capital of 17. (4 1.3(10)). A
  breakdown of the companys investment projects is
  listed below. When evaluating a new dog food
  production investment, which cost of capital
  should be used?
• 1/3 Nuclear Parts Mfr.. B2.0
• 1/3 Computer Hard Drive Mfr.. B1.3
• 1/3 Dog Food Production B0.6
• AVG. B of assets 1.3

33
Capital Budgeting Project Risk

• Example - Based on the CAPM, ABC Company has a
  cost of capital of 17. (4 1.3(10)). A
  breakdown of the companys investment projects is
  listed below. When evaluating a new dog food
  production investment, which cost of capital
  should be used?
• R 4 0.6 (14 - 4 ) 10
• 10 reflects the opportunity cost of capital on
  an investment given the unique risk of the
  project.

34
Determinants of Project Risk Some Thoughts

• Operating leverage increases the risk of a
  project. When a large fraction of your cost is
  fixed, any change in revenues can have a dramatic
  effect on earnings. Therefore, projects that
  involve high fixed costs tend to have higher
  betas.
• Many people intuitively associate risk with the
  variability of earning. But much of this
  variability reflects diversifiable risk. Some
  investments may have high standard deviation but
  a low beta (definition of risk).
• Cyclical business with revenues and earnings
  strongly depended on the state of the economy,
  tend to have high beta and cost of capital.
  While business such as food, beer, cosmetic are
  less affected by the state of the economy and
  tend to have low betas.

35
????????
1. ????
(1) ???????
???? ks 7 (12-7) ? 1.2 13?
????? 40,?? 8,???? 25 ?
???????? (WACC)
WACC wd?kd?(1 - t) ws?ks
0.4 ? 8 ? (1-25) 0.6 ? 13
10.2?
36
(2) ???????

• ????
• ??????? 1.6 (kproj 16)
• ?????????? 20
• ?????????????????

bold proj 0.8 ? 1.2 0.2 ? 1.6 1.28,
ks 7 (12 - 7) ? 1.28 13.4?
????????????? (WACC)?
WACC 0.4 ? 8 ? (1-25) 0.6 ? 13.4
10.44?
37
2. ?????????

• ???????????????????,????????,??????????????

• ????????????????????

38
? ???????????????
? C ????? B ????????
C ?????? 50,???? 20,bc 1.8?
B ?????? 33,???? 20?