Principles of Corporate Finance

1
Risk and Return
To risk or not to risk, that is the question
2
Standard deviation and normal distribution

• normal distribution is completely defined by
• its mean and standard deviation
• the probability of abnormally high or low
  returns
• depends on the standard deviation
• Std Devs. Cumulative
• from mean probability
• -3 0.1
• -2 2.3
• -1 15.9
• 0 50.0
• 1 84.1
• 2 97.7
• 3 99.9

3
Markowitz Portfolio Theory

• Price changes vs. Normal distribution
• IBM - Daily change 1986-2006

Proportion of Days
Daily Change
4
Calculating mean (or expected) return

Probability
Probability Return
x return .20
-10 -2
.50 10
5 .30
30 9
Total
12
Mean or

expected

return
5
Calculating variance and standard deviation

Deviation Probability
from mean
x squared Probability Return
return deviation .20
-10 -22
96.8 .50 10
- 2 2.0
.30 30
18 97.2
Total
196.0

Variance Standard deviation square root of
variance 14
6
Calculating variance and standard deviationof
Merck returns from past monthly data

Deviation
from mean
Squared Month
Return return
deviation 1
5.4 2.6
6.76 2
1.7 - 1.1
1.21 3
- 3.6 - 6.4
40.96 4
13.6 10.8
116.64 5
- 3.5 - 6.3
39.69 6
3.2
0.4 0.16
Total 16.8
205.42
Mean 16.8/6 2.8 Variance
205.4/6 34.237 Std dev
Sq root of 34.237 5.851 per month
Annualised std dev 5.9 x square root (12)
20.3
7
Mean and standard deviation

• mean measures average (or expected return)
• standard deviation (or variance) measures the
• spread or variability of returns
• risk averse investors prefer high mean low
• standard deviation

20
15
better
expected
10
return
5
0
5
10
15
20
standard deviation
8
Expected portfolio return
Portfolio
Expected Proportion x
proportion (x) return (r)
return (xr) Merck
.40 10
4 McDonald .60
15
9 Total 1.00
13
Expected
portfolio
return
9
Calculating covariance and correlation

Deviation from Probability
Return on mean
return x product of Prob.
A B A
B deviations .15
-10 -10 -22 -22
72.6 .05 -10
10 -22 - 2
2.2 .45 10 10
- 2 - 2
1.8 .05 10 30
- 2 18 - 1.8
.25 30 30 18
18 81.0 .05
30 -10 18
-22 - 19.8 Mean 12
12 Total
136 Std dev 14 14


Covariance Correlation

.6944 coefficient
(sd A) x (sd B) 14 x 14
covariance
136
10
Calculating covariance and correlation
betweenMerck and McDonald from past monthly data

Deviation
Product
Return from
mean of Month
Merck McD Merck
McD deviations 1
5.4 10.7 2.6
8.9 23.2 2
1.7 - 8.4 - 1.1
-10.2 11.2 3
- 3.6 1.6
- 6.4 - 0.2
1.2 4 13.6
10.2 10.8 8.4
90.9 5 - 3.5
4.4 - 6.3
2.6 -16.5 6
3.2 - 7.8
0.4 - 9.6 - 3.8
Total 16.8 10.7

106.1 Mean 2.8
1.78 Covariance 106.1/6
17.7 Std dev Merck 5.9 Std dev McD
7.7 Corr. co-effic Cov/(sdMe .
sdMcD ) 17.7/(5.9 x
7.7) .39
11
Effect of changing correlations Portfolio of
Merck McDonald
12
Mean standard deviation Portfolio of Merck
McDonald
13
The set of portfolios
Expected return
B
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
A
x
x
x
x
x
Standard deviation
The set of portfolios between A and B
are efficient portfolios
14
Adding a riskless asset to the efficient frontier
tangency portfolio
riskless rate
15
Portfolio composition with a riskless asset

• Regardless of the investor's attitude to
• risk, he should split his portfolio between
• the tangency portfolio and the riskless asset.
• - the tangency portfolio provides the
• maximum reward per unit of risk
• - the riskless asset adjusts the level of
  risk

16
Two basic ideas about risk and return
1. Investors require compensation
for risk 2. They care only about a stock's
contribution to portfolio risk
17
Capital asset pricing model
Expected
return
Expected
market
return
Risk
free
rate
0
.5
1.0
Beta
r rf
(rm - rf )
18
Capital asset pricing model - example
If Treasury bill rate 5.6 Bristol
Myers Squibb beta .81 Expected
market risk premium 8.4 r
rf beta (rm - rf ) 5.6 .81
(8.4) 12.4
19
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium 1931-2005
30 20 10 0
SML
Investors
Market Portfolio
Portfolio Beta
1.0
20
Testing the CAPM
Return vs. Book-to-Market
Dollars (log scale)
High-minus low book-to-market
Small minus big
http//mba.tuck.dartmouth.edu/pages/faculty/ken.fr
ench/data_library.html
21
Validity of capital asset pricing model
EVIDENCE IS MIXED 1. Long-run average
returns are significantly related to
beta. 2. But beta is not a complete
explanation. Low beta stocks have
earned higher rates of return than
predicted by the model. So have small company
stocks and stocks with low price to book
value ratios.
22
Capital asset pricing modelis attractive
Because 1. It is simple and usually
gives sensible answers. 2. It
distinguishes between diversifiable
and non-diversifiable risk.
23
CAPM is controversial
BECAUSE 1. No one knows for sure how to
define and measure the market
portfolio -- and using the wrong market index
could lead to the wrong answers. 2.
The model is hard to prove -- or disprove.
3. The model has competitors.
24
The Consumption CAPM

• In standard CAPM, investors are concerned with
  the level and uncertainty of their wealth.
  (Consumption is outside the model)
• In the Consumption CAPM, investors are concerned
  with the level and uncertainty of their
  consumption. Stocks that provide low consumption
  (those with low consumption betas) should have
  low expected returns.
• Is the Consumption CAPM useful?
• It has the advantage that you dont have to
  identify the market portfolio.
• Unfortunately consumption is difficult to
  measure (especially total consumption for
  everyone).
• Consumption CAPM is difficult to apply for
  practical use.

25
Arbitrage Pricing Theory (APT)

• APT assumes that
• r a b1 (rfactor 1 ) b2 (rfactor 2 )
  .... noise
• Suppose that a diversified portfolio has no
  exposure to any
• factor. It is essentially risk-free and
  should offer a return of rf.
• So a rf.
• The expected risk premium on a portfolio that is
  exposed only
• to factor 1 (say) should vary in proportion
  to its exposure to
• that factor. If a portfolio is exposed to
  several factors then its risk will
• vary in proportion to those factors. So
• r - rf b1 (rfactor 1 - rf ) b2
  (rfactor 2 - rf ) ...

26
Arbitrage pricing theory (APT)

• Preserves distinction between diversifiableand
  non-diversifiable risk
• CAPM and APT can both hold - e.g. CAPMimplies
  one factor APT, with r r
• But APT is more general - e.g. unlike
  CAPM,market portfolio doesn't have to be
  efficient
• But usefulness of APT requires heavy-dutystatisti
  cs to
• identify factors
• measure factor returns

factor1
m