Corporate Finance and Behavior (ECB2FIN)
2023–24
Lecture 1: Introduction, CAPM, Risk and the Cost of Capital (Ch. 8,9)
Textbook: ”Principles of Corporate Finance”, 14th Edition
– Brealy Meyers Allen Edmans –
Drs George Alexandrou
Date : 4 September 2023
Place : Kinepolis Jaarbeurs (Zaal 12)
Planning:
8 weeks (04/09 – 24/10)
Exam: 31/10
Tuesdays: Lectures
Thursdays: Tutorials
Questions:
during / after Lectures / Tutorials /Office hours or via Mail.
E-mail address:
George Alexandrou: g.alexandrou@uu.nl
Your Tutorial-Group Lecturer: ecb2fin22@uu.nl
Note:
No recordings of Lectures & Microphones muted
Office Hours (for this week):
Mon 4-Sep., 15:30-16:00pm & 17:00 – 18:00pm (ICU – SPINOZA 009)
04/09/2023
2
Assessments:
Course grade:
85% Final exam
15% weekly quizzes:
7 weekly quizzes
NO retake of quizzes
Weekly quiz structure:
60 minutes
Can be taken from 07:00 – 21:00
on Fridays
Consisting of:
Several algorithmic exercises (highest score of 3 attempts will be taken into consideration)
The build-up of your Connect© grade looks as follows:
(submitted quizzes)
Bonus in tutorials:
0 Connect quizzes above 50%:
1 Connect quiz above 50%:
2 Connect quizzes above 50%:
3 Connect quizzes above 50%:
4 or more Connect quizzes above 50%:
Connect grade = 1
Connect grade = 3
Connect grade = 5
Connect grade = 7
Connect grade = 9
Attending 5 out of 7 Tutorials will give you 1 extra point for your Connect grade and will
allow you to do a retake exam if necessary.
At least 1 submission to the Quizzes is mandatory to obtain a grade for ECB2FIN.
For Effort requirement => see Course Manual.
04/09/2023
3
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For more information see Blackboard.
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to purchase the hard copy of the textbook, at a heavily discounted price, is you so wish.
Note (from the publisher):
In the link, you will buy a 360-day access to Connect© at a heavily discounted price. This is the only way to
purchase access to Connect. They do not work with booksellers and retailers.
04/09/2023
4
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Corporate Finance and Behaviour
Utrecht University School of Economics
2023-2024
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Course Name
Corporate Finance and Behaviour
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ECB2FIN
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George Alexandrou
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Principles of Corporate Finance, 14e (Connect)
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7
Today’s Lecture:
• What we will discuss today:
- The Capital Asset Pricing Model (CAPM) – Ch. 8
- Risk and the Cost of Capital – Ch. 9
• What do we already know:
- How firms are organized and managed and how we make financial decisions.
- Time value of money, financial arithmetic tools.
- Valuing stocks and bonds.
- Investment decisions.
- Risk, Diversification and Portfolio theory.
04/09/2023
8
Chapters to be studied:
Chapters: 8 and 9
Introduction, CAPM, Risk and the Cost of Capital
• Homework Tutorial 1
8.6, 8.8, 8.12, 8.13
9.2, 9.4, 9.5, 9.7 and 9.13
• Practice Questions
see Connect©
Note:
No recordings of Lectures
04/09/2023
9
Chapter 8:
The Capital Asset Pricing Model (CAPM)
Topics:
• Risk and returns, portfolio diversification
• Market Risk Is Measured by Beta.
• The Relationship Between Risk and Return.
• Does the CAPM Hold in the Real World?
• Some Alternative Theories.
04/09/2023
10
Figure 7.1 How $1 invested at the End of 1899 would have grown by the end of 2020
• How an investment of $1 at the start of 1900 would have grown by the end of 2020, assuming
reinvestment of all dividend and interest payments.
• Source: E. Dimson, P. R. Marsh, and M. Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns
(Princeton, N J: Princeton University Press, 2002), with updates provided by the authors.
3
Utility function – Risk aversion
R
C
A
5
0.60
B
3
4
0.27
0.18
2
0.15
1
0.15
0.20
0.50
3

The Historical Risk and Return in Large Portfolios
Source: CRSP, Morgan Stanley Capital International
13
Historical Volatility and Return for 500 Individual Stocks, Ranked Annually by Size
Source: CRSP
14
Figure 7.13 Southwest and Amazon
• The curved line illustrates
how expected return and
standard deviation change
as you hold different
combinations of two stocks.
• Diversification reduces risk.
28
Effect on Volatility and Expected Return of Changing the Correlation between
Intel and Coca-Cola Stock
16
Portfolios of Intel and Coca-Cola Allowing for Short Sales
17
Efficient Frontier with Ten Stocks Versus Three Stocks
18
Figure 7.12 Even Random Diversification Eliminates Specific Risk
• Risk that diversification cannot eliminate is market risk, NYSE, 2010–2019.
26
Figure 7.14 Efficient Portfolios
• Each dot shows the expected return and standard deviation of stocks. These are
efficient portfolios, denoted with A, B, and C.
30
Figure 7.16 Lending and Borrowing
• Lending or borrowing at the risk-free rate (rf) allows us to exist outside the efficient frontier.
31
The Efficient Portfolio with Borrowing and Lending
22
The Market Risk is Measured by Beta
• Market Portfolio: Portfolio of all assets in the economy. In practice, a broad stock market
index such as the S&P Composite is used to represent the market.
• The risk that a stock contributes to a well-diversified portfolio is its market risk.
• Market risk is the risk that a stock shares with the market.
• Beta: Sensitivity of a stock’s return to the return on the market portfolio, defined as:
𝛽𝑖 =
𝜎𝑖𝑀
2
𝜎𝑀
(1)
𝜎𝑖𝑀 is the covariance between the returns on stock i and the returns on the market.
2
𝜎𝑀
is the variance of the returns on the market.
Total risk = (Market risk) + (Specific risk) => 𝜎𝑖 = 𝜌𝑖𝑀 𝜎𝑖 + (1 − 𝜌𝑖𝑀 )𝜎𝑖
𝑀𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 = 𝜌𝑖𝑀 𝜎𝑖 =
𝜎𝑖𝑀
𝜎
𝜎𝑖𝜎𝑀 𝑖
=
𝜎𝑖𝑀
𝜎𝑀
=
𝜎𝑖𝑀
2 𝜎𝑀
𝜎𝑀
= 𝛽𝑖 𝜎𝑀
==>
𝑴𝒂𝒓𝒌𝒆𝒕 𝒓𝒊𝒔𝒌 = 𝜷𝒊 𝝈𝑴 (2) where: 𝛽𝑖 =
23
𝜎𝑖𝑀
2
𝜎𝑀
(1)
Figure 8.1 The Return on Amazon Stock
• The return on Amazon stock changes on average by 1.55% for each 1.00% change
in the market return. Beta is therefore 1.55.
24
Security Market Line (𝑆𝑀𝐿) 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛:
04/09/2023
𝐸 𝑟 = 𝑅𝑓 + 𝛽 ∗ (𝑅𝑚 − 𝑅𝑓 )
25
Table 8.1 Estimated Betas for Select U.S. Stocks.
Stock
Beta (β)
United States Steel
2.98
Southwest Airlines
1.58
Amazon
1.55
Wells Fargo
1.14
ExxonMobil
1.14
Johnson & Johnson
0.75
Tesla
0.50
Coca-Cola
0.46
Consolidated Edison
0.31
Newmont
0.16
26
Table 8.3 Portfolio Risk, Beta
(1)
(2)
(3)
(4)
(5)
Deviation from
Average Company
Return
(6)
(7)
Squared Deviation
from Average Market
Return (Columns 4×4)
Product of Deviations
from Average Returns
(Columns 4×5)
Month
Market
Return
Company
Return
Deviation from
Average Market
Return
1
−8%
−11%
−10
−10
100
130
2
4
8
2
6
4
12
3
12
19
10
17
100
170
4
−6
−13
−8
−15
64
120
5
2
3
0
1
0
0
6
8
6
6
4
36
24
Average
2
2
Total
304
456
• Beta is the ratio of the covariance of the returns on the stock to the returns on the market: 𝛽𝑖 =
𝜎𝑖𝑀
2
𝜎𝑀
• Calculating the covariance between the returns on the market and those of Anchovy Queen and the variance of
the market returns here:
• Covariance = 𝜎𝑖𝑀 = (456 / 6) = 76;
2
Variance = 𝜎𝑀
= (304 / 6) = 50.67;
Beta (𝛽𝑖 ) = (76 / 50.67) = 1.5
27
Why Betas Determine Portfolio Risk
We know that:
1. The market risk of a stock is measured by its beta.
2. The risk of a well-diversified portfolio is given by its market risk.
• We also know the beta of a portfolio is the weighted average of the betas of the
individual stock in the portfolio.
• Beta measures undiversifiable risk. So, there is no diversification effect when adding
a stock to a well-diversified portfolio.
• If a portfolio includes a large number of randomly selected stocks, its beta is 1.0
• Adding low-beta stocks to a portfolio lowers the overall risk, but this is NOT
“Diversification” it is “de-risking”
• Investing higher proportion of your wealth in Treasury bills is another way of de-risking.
28
The relationship between Risk and Return – CAPM
We know that the market risk of a stock is measured by its beta.
• How much extra return an investor expects for bearing market risk?
From Chapter 7:
Capital Market Line: 𝑟𝑝 = 𝑟𝑓 +
𝑟𝑀 −𝑟𝑓
𝜎𝑀
𝜎𝑝 (3)
This equation gives the expected return for an efficient portfolio that combines borrowing or lending and
the market portfolio.
• An investor is rewarded only for market risk (𝛽𝑖 ,eq.2) (we replace 𝜎𝑝 with 𝛽𝑖 ):
𝑟𝑖 = 𝑟𝑓 +
𝑟𝑀 − 𝑟𝑓
𝑟𝑀 − 𝑟𝑓
𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑖 = 𝑟𝑓 +
(𝛽𝑖 𝜎𝑀 ) = 𝑟𝑓 + 𝛽𝑖 (𝑟𝑀 − 𝑟𝑓 )=>
𝜎𝑀
𝜎𝑀
𝒓𝒊 = 𝒓𝒇 + 𝜷𝒊 (𝒓𝑴 − 𝒓𝒇 ) (4) or:
𝒓𝒊 = 𝒓𝒇 + 𝜷𝒊 (𝒓𝑴 − 𝒓𝒇 )
The risk premium of a stock depends only on its beta: 𝛽𝑖 =
(5)
CAPM
𝜎𝑖𝑀
2
𝜎𝑀
29
Risk and Return - Capital Market Line
The risk in the horizontal line is measured by the standard deviation.
04/09/2023
30
Figure 8.3 Capital Asset Pricing Model
The risk in the horizontal axis is measured by the beta (𝛽)
Security Market Line (𝑆𝑀𝐿) 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛:
𝑬 𝒓 = 𝑹𝒇 + 𝜷 ∗ (𝑹𝒎 − 𝑹𝒇 )
31
Figure 8.4 Equilibrium
What if a stock did not Lie on the security Market Line?
• In equilibrium, no stock lies below the security market line.
• Instead of buying Stock A, investors lend part of their money and put the balance in the market portfolio.
• Instead of buying Stock B, they borrow and invest in the market portfolio.
32
Capital Market Line and Security Market Line
• The Capital Market Line (CML) applies only to efficient portfolios.
• Individual stocks and inefficient portfolios carry more risk and lie below the CML.
• Investors still hold them as part of a diversified portfolio, but they get rewarded only for systematic risk.
• The Security Market Line (SML) applies to all stocks, securities and portfolios.
The expected returns in the vertical axis are drawn against…
…the total risk 𝜎𝑝 in the horizontal axis (CML),
…the market risk 𝛽𝑖 on the horizontal axis (SML).
• An investor may hold inefficient assets as part of their portfolio because the inefficiencies
(specific risk) are wash away.
• Specific (idiosyncratic) risk is not compensated.
• An efficient portfolio is comprised of individual inefficient securities.
33
The Capital Market Line and the Security Market Line
34
Does CAPM Hold in the Real World?
• The CAPM makes several assumptions:
1. Investors choose portfolios based on expected return and risk (variance of returns).
2. All investors have the same estimates of mean returns, variances, and covariances.
3. Investors trade in perfect capital markets.
• no Taxes.
• no Transaction Costs.
• no restrictions on Short Sales.
4. Investors can borrow and Lend at the same risk-free rate.
5. Investors are price takers.
6. The supply of all assets is fixed.
Pros:
• Asset classes with more risk command a higher expected return
• The expected returns should not depend on diversifiable risk (only on market risk - beta)
• Most financial managers use it (73% in a survey by Graham, Harvey 2001)
• Questions: Unrealistic assumptions – empirical evidence.
35
Figure 8.5 CAPM (1931–2020)
• Beta Versus Average Risk Premium.
36
Figure 8.6 Relationship Between Beta and Average Return (mid-19 60s)
37
Figure 8.6 Relationship Between Beta and Average Return (19 66–2020)
• Source: F. Black, “Beta and Return,” Journal of Portfolio Management 20 (Fall 19 93), pp. 8–18. Updates courtesy of Adam Kolasinski.
38
Figure 8.7 Return Versus Book-to-Market
• http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
39
Arbitrage Pricing Theory (APT)
ATP is an Alternative to CAPM
CAPM: How investors construct efficient portfolios. Which portfolios are efficient.
ATP: Assumes that each stocks risk premium depends on pervasive macroeconomic
“factors”.
𝑹𝒆𝒕𝒖𝒓𝒏 = 𝜶 + 𝒃𝟏 𝒓𝒇𝒂𝒄𝒕𝒐𝒓 𝟏 + 𝒃𝟐 𝒓𝒇𝒂𝒄𝒕𝒐𝒓 𝟐 + 𝒃𝟑 𝒓𝒇𝒂𝒄𝒕𝒐𝒓 𝟑 + ⋯ + 𝒏𝒐𝒊𝒔𝒆
(6)
𝑛𝑜𝑖𝑠𝑒 stands for specific, diversifiable risk.
The expected risk premium on a stock depends on the expected risk premium
associated with each ‘factor’ and the sensitivity of the stock returns to each factor:
𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝑹𝒊𝒔𝒌 𝑷𝒓𝒆𝒎𝒊𝒖𝒎 = 𝒓 − 𝒓𝒇 = 𝒃𝟏 𝒓𝒇𝒂𝒄𝒕𝒐𝒓 𝟏 − 𝒓𝒇 + 𝒃𝟐 𝒓𝒇𝒂𝒄𝒕𝒐𝒓 𝟐 − 𝒓𝒇 + ⋯
(7)
40
Three-Factor Model
• Steps to Identify Factors:
1. Identify a reasonably short list of macroeconomic factors that could affect stock
returns.
2. Estimate the expected risk premium on each of these factors: 𝒓𝒇𝒂𝒄𝒕𝒐𝒓 𝟏 − 𝒓𝒇 etc.
3. Measure the sensitivity of each stock to the factors (𝒃𝟏 , 𝒃𝟐 , etc.)
Factor
Measured by
Market factor
Return on market index minus risk-free interest rate
Size factor
Return on small-firm stocks less return on large-firm stocks
Book-to-market factor
Return on high book-to-market-ratio stocks less return on low
book-to-market-ratio stocks
41
Table 8.5 Estimates of Expected Equity Returns Using Three-Factor Model and CAPM
Three- Factor Model
Factor Sensitivities
a
CAPM
B market
B size
B book-to-market
Expected Return a
Expected Return b
Autos
1.12
0.26
0.31
11.9%
10.2%
Banks
1.18
0.09
0.65
13.1
10.5
Chemicals
1.19
0.26
0.41
12.8
10.7
Computers
1.30
−0.18
0.03
10.5
10.9
Construction
0.96
0.49
0.04
10.4
9.3
Food
0.67
−0.38
0.02
5.6
6.3
Oil and gas
1.17
0.49
0.90
15.3
11.0
Pharmaceuticals
0.91
0.20
−0.38
7.5
8.5
Telecoms
0.78
−0.24
0.12
7.2
7.2
Utilities
0.46
−0.36
−0.08
3.7
4.8
The expected return equals the risk-free interest rate plus the factor sensitivities multiplied by the factor risk premiums, that is:
2.0 + 𝑏𝑀𝑎𝑟𝑘𝑒𝑡 ∗ 7.0 + 𝑏𝑧𝑖𝑠𝑒 ∗ 3.1 + 𝑏𝑏𝑜𝑜𝑘−𝑡𝑜−𝑚𝑎𝑟𝑘𝑒𝑡 ∗ 4.0 .
b
Estimated as 𝑟𝑓 + 𝛽 𝑟𝑚 − 𝑟𝑓 , that is: 𝑟𝑓 + 𝛽 ∗ 7.0 Note that we use simple egression to estimate beta in the CAPM formula. This beta may,
therefore, be different from 𝑏𝑀𝑎𝑟𝑘𝑒𝑡 that we estimated from a multiple regression of stock returns on the three factors.
Source: The industry indexes are value-weighted indexes from Kenneth French’s website, mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.xhtml.
42
Chapter 9:
Risk and the Cost of Capital
Topics:
• Company and Project Costs of Capital.
• Measuring the Cost of Equity.
• Analyzing Project Risk.
• Certainty Equivalents: Another way to adjust for Risk.
04/09/2023
43
Company and Project Costs of Capital
• A firm’s value can be stated as the sum of the value of its various assets.
• “The value-additivity principle.”
• If firm is composed of assets A and B:
Firm value = PV(AV) = PV(A) + PV(B)
The value of an asset or project is estimated by discounting its expected cash
flows by the discount rate that reflects is market risk (beta).
• The true cost of capital for a project depends on the project, not on the
company.
• Projects within a firm should be evaluated using discount rates based on their
market risk (beta) not the overall cost of capital of the company.
44
Figure 9.1 Company Cost of Capital
• J&J’s company cost of capital is about 7.3%. This is the correct discount rate only
if the project beta is 0.75.
45
The Company Cost of Capital – Debt and Equity
rassets  Cost of Capital
D
E
= rE   rE 
V
V
V  DE
D  market value of debt
E  market value of equity
rD  YTM on bonds
rE  rf    rm  rf

• Important: E, D, and V are all market values of equity, debt, and total firm value
46
Estimating Beta - Figure 9.2 U.S. Steel
The SML shows the relationship between return and risk.
CAPM uses beta as a proxy for risk.
Other methods can be employed to determine the slope of the SML and thus beta.
• U.S. Steel Mar. 2010- Feb. 2015
• U.S. Steel Mar. 2015-Feb. 2020
47
Estimating Beta - Figure 9.2 ExxonMobil
• ExxonMobil Mar. 2010- Feb. 2015
• ExxonMobil Mar. 2015-Feb. 2020
48
Figure 9.2 Consolidated Edison
• Consolidated Edison
Mar. 2010- Feb. 2015
• Consolidated Edison
Mar. 2015-Feb. 2020
49
Table 9.1 Estimated Betas and Standard Errors
Beta
Standard Error
Canadian Pacific
1.07
0.18
CSX
1.18
0.24
Kansas City Southern
0.97
0.20v
Norfolk Southern
1.33
0.18
Union Pacific
1.09
0.16
Industry portfolio
1.13
0.14
50
Asset Beta
• Company cost of capital (COC) is based on the average beta of the assets.
• The average beta of the assets is based on the percentage of funds in each asset.
• Assets = debt + equity
D
E
β assets  β debt     β equity   
V 
V 
51
Example 9.3 Allowing for Possible Bad Outcomes
• Example
• Project Z will produce just one cash flow, forecasted at $1 million
at year 1. It is regarded as average risk, suitable for discounting
at a 10% company cost of capital:
PV 
C1 1,000,000

 $909,100
1 r
1.1
52
…Example 9.3 Allowing for Possible Bad Outcomes
• Example
…But now you discover that the company’s engineers are behind
schedule in developing the technology required for the project.
They are confident it will work, but they admit to a small chance
that it will not. You still see the most likely outcome as $1 million,
but you also see some chance that project Z will generate zero
cash flow next year.
Possible Cash
Flow
Probability
Probability-Weighted Cash
Flow
1.2
0.25
0.3
1.0
0.50
0.5
0.8
0.25
0.2
Unbiased Forecast
1.0, or $1 million
53
…Example 9.3 Allowing for Possible Bad Outcomes
• Example continued
• This might describe the initial prospects of project Z. But if
technological uncertainty introduces a 10% chance of a zero cash
flow, the unbiased forecast could drop to $900,000.
Possible Cash
Flow
Probability
Probability-Weighted Cash
Flow
1.2
0.225
0.27
1.0
0.45
0.45
0.8
0.225
0.18
0
0.10
0.0
PV 
0.90
 $818,000
1.1
Unbiased Forecast
0.90, or $900,000
54
Example 9.4 Correcting for Optimistic Forecasts
• The CFO of EZ Corp. finds that the cash-flows forecasts are always 10% optimistic.
What is the right response? To increase the cost of capital 10% from 12% to 22% or to
reduce the expected cash flows by 10%?
1
2
3
4
5
…
10
…
15
1. Original cash flow
forecast
$1,000.00
$1,000.00
$1,000.00
$1,000.00
$1,000.00
…
$1,000.00
…
$1,000.00
2. PV at 12%
$ 892.90
$ 797.20
$ 711.80
$ 635.50
$ 567.40
…
$ 322.00
…
$ 182.70
3. Corrected cash flow
forecast
$ 900.00
$ 900.00
$ 900.00
$ 900.00
$ 900.00
…
$ 900.00
…
$ 900.00
4. PV at 12%
$ 803.60
$ 717.50
$ 640.60
$ 572.00
$ 510.70
…
$ 289.80
…
$ 164.40
5. PV correction
−10.0%
−10.0%
−10.0%
−10.0%
−10.0%
…
−10.0%
…
−10.0%
6. Original forecast
discounted at 22%
$ 819.70
$ 671.90
$ 550.70
$ 451.40
$ 370.00
…
$ 136.90
…
$ 50.70
−8.2%
−15.7%
−22.6%
−29.0%
−34.8%
…
−57.5%
…
−72.3%
Year
7. PV “correction” at 22%
discount rate
55
Valuation by Certainty Equivalents
PV 
Ct
1  r 
t

1
CEQt
1  r 
t
f
Figure 9.3 Risk, DCF and CEQ
56
Valuation by Certainty Equivalents
2
• Example
• Project A is expected to produce CF = $100 mil for each of 3
years. Given a risk-free rate of 6%, a market risk premium of 8%,
and beta of 0.75, what is the PV of the project?
r  rf     rm  rf

 0.06  0.75  0.08
 0.12, or 12%
• Project A
Year
Cash Flow
PV at 12%
1
100
89.3
2
100
79.7
3
100
71.2
Total PV
240.2
57
Valuation by Certainty Equivalents
3
• Example: Project A is expected to produce CF = $100 mil for each of 3 years. Given a
risk-free rate of 6%, a market premium risk of 8%, and beta of 0.75, what is the PV of
the project?
• Then assume that the cash flows change but are RISK FREE (CEQ). What is the new PV?
Year 1 
100
 94.6
1.054
100
 89.6
1.0542
100
Year 3 
 84.8
1.0543
Year 2 
The difference between the 100 and the certainty equivalent (94.5) is 5.4%
This % can be considered as the annual premium on a risky cash flow.
Certain Equivalent Cash Flow (CEQ) = (Risky Cash Flow) / (1.054)
58
End of Lecture
Thank you for your attention!
04/09/2023
59