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Applied Finance Lectures
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
• 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors
What is Finance?
Equity
Debt
Investors
Dividends
Companies
Interests
Operating cash flow
Capital expenditures
Portfolio management
Asset pricing models
Time
Uncertainty
Discounted cash flow method
Capital Asset Pricing Model
MarkowitzSharpe Lintner
Option Pricing Models
Black ScholesCox Ross Rubinstein
State Prices
Arrow-Debreu
Stochastic discount factors
Outline
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
• 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors
Discounted cash flow method
nn
n
r
C
r
C
r
CPV
)1(...
)1(1 22
2
1
1
Cash flows
Required rates of return
PV = C1 v1 + C2 v2 + …+Cn vn
Penetration rate of discount cash flow
Diffusion Curve for DCF Techniques
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Per
cen
t A
do
pti
ng
Callahan, C. and S. Haka, A Model and Test of Interfirm Innovation Diffusion: the Case of Discounted Cash Flow
Techniques, Manuscript January 2002
Outline
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
• 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors
Markowitz (1952) Portfolio selection
• Return of portfolio: normal distribution
• Characteristics of a portfolio:
1. Expected return
2. Risk: Variance/Standard deviation
Calculation of optimal portfolio
iX
X
RRX
XXVarianceMin
i
ii
iPii
i jijji
0
1
:subject to
Markowitz: the birth of modern portfolio theory
A
B
Riskless rate
Optimal risky portfolio
Optimal asset allocation
0.00
5.00
10.00
15.00
20.00
25.00
30.00
0.00 10.00 20.00 30.00 40.00 50.00 60.00
Risk (standard deviation)
Expec
ted r
eturn
Outline
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
Capital Asset Pricing Model
Stock A
Stock B
Stock D
Market portfolioStock C
0.00%
2.00%
4.00%
6.00%
8.00%
10.00%
12.00%
14.00%
16.00%
18.00%
20.00%
0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% 45.00% 50.00%
Standard deviation
Exp
ecte
d r
etu
rn
Capital Asset Pricing Model
Expected return
Beta
Risk free interest rate
r
rM
1β
)( FMF rrrr
Net Present Value Calculation with CAPM
tFMF
tt
rrr
CECPV
])(1[
)()(
Outline
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
• 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors
Jensen 1968 - Distribution of “t” values for excess return115 mutual funds 1955-1964
0
5
10
15
20
25
30
35
-5 -4 -3 -2 -1 0 1 2 3 4
Not significantly different from 0
US Equity Mutual Funds 1982-1991(Malkiel, Journal of Finance June 1995)
• Average Annual Return
• Capital appreciation funds 16.32%
• Growth funds 15.81%
• Small company growth funds 13.46%
• Growth and income funds 15.97%
• Equity income funds 15.66%
• S&P 500 Index 17.52%
• Average deviation from benchmark -3.20%
(risk adjusted)
The Efficient Market Hypothesis
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
03-J
an-0
0
16-F
eb-0
0
31-M
ar-0
0
16-M
ay-0
0
29-J
un-0
0
14-A
ug-0
0
27-S
ep-0
0
09-N
ov-0
0
26-D
ec-0
0
09-F
eb-0
1
27-M
ar-0
1
10-M
ay-0
1
25-J
un-0
1
08-A
ug-0
1
28-S
ep-0
1
14-N
ov-0
1
31-D
ec-0
1
14-F
eb-0
2
03-A
pr-0
2
16-M
ay-0
2
01-J
ul-0
2
14-A
ug-0
2
27-S
ep-0
2
11-N
ov-0
2
26-D
ec-0
2
13-F
eb-0
3
31-M
ar-0
3
14-M
ay-0
3
27-J
un-0
3
12-A
ug-0
3
25-S
ep-0
3
07-N
ov-0
3
23-D
ec-0
3
09-F
eb-0
4
24-M
ar-0
4
07-M
ay-0
4
23-J
un-0
4
06-A
ug-0
4
21-S
ep-0
4
03-N
ov-0
4
S&
P 5
00 In
dex
S&P 500 2000-2004
The Efficient Market Hypothesis
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
03/0
1/20
00
03/0
3/20
00
03/0
5/20
00
03/0
7/20
00
03/0
9/20
00
03/1
1/20
00
03/0
1/20
01
03/0
3/20
01
03/0
5/20
01
03/0
7/20
01
03/0
9/20
01
03/1
1/20
01
03/0
1/20
02
03/0
3/20
02
03/0
5/20
02
03/0
7/20
02
03/0
9/20
02
03/1
1/20
02
03/0
1/20
03
03/0
3/20
03
03/0
5/20
03
03/0
7/20
03
03/0
9/20
03
03/1
1/20
03
03/0
1/20
04
03/0
3/20
04
03/0
5/20
04
03/0
7/20
04
03/0
9/20
04
03/1
1/20
04
Dai
ly R
etu
rns
S&P 500 2000-2004
The Random Walk Model
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
8.00%
-8.00% -6.00% -4.00% -2.00% 0.00% 2.00% 4.00% 6.00% 8.00%
Return day t
Ret
urn
day
t+
1
Outline
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
• 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors
Does the capital structure matters?
• Modigliani Miller 1958: NO, under some conditions
Debt
Equity
Trade-off theory
Market value
Debt ratio
Value of all-equity firm
PV(Tax Shield)
PV(Costs of financial distress)
Outline
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
• 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors
Options
• Right to:
• Buy (CALL)
• Sell (PUT)
• an asset
• at a fixed price (EXERCICE PRICE / STRIKING PRICE)
• up to or at a future date (MATURITY)
• at a future date (EUROPEAN OPTION)
• up to a future date (AMERICAN OPTION)
Buy 1 Fortis share
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40
Stock price
Val
ue
of
po
rtfo
lio
Buying a put
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40
Stock price
Val
ue
at m
atu
rity
Put
Stock
Stock + Put
Buying a call
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40
Stock price
Call
Bond
Bond + Call
How to value an option
• Standard present value calculation fails
• Value of option = f(Stock price, Time)
• Required rate of return = f(Stock price, Time)
• Black Merton Scholes
• Combine stock and option to create a riskless position
• Law of one price (no arbitrage)
f=(#shares)(Stockprice)+Bond
The fundamental partial differential equation
• Assume we are in a risk neutral world
rfSS
f
S
frS
t
f 22
2
2
2
1
Expected change of the value of derivative security
Change of the value with respect to time Change of the value
with respect to the price of the underlying asset
Change of the value with respect to volatility
And now, the Black Scholes formulas
• Closed form solutions for European options on non dividend paying stocks assuming:
• Constant volatility
• Constant risk-free interest rate
)()( 210 dNKedNSC rT Call option:
Put option: )()( 102 dNSdNKeP rT
TT
KeSd
rT
5.0)/ln( 0
1
Tdd 12
N(x) = cumulative probability distribution function for a standardized normal variable
Binomial option pricing model
Stock price S
Stock price Su
Option fu
Stock price Sd
Option fd
Time interval Δt
tr
fppff du
1
)1(
Risk neutral probability
Risk free interest rate
du
d
SS
StrSp
)1(
Outline
• 1. What is finance?
• 2. The diffusion of the discounted cash flow method
• 3. Markowitz and the birth of modern portfolio theory
• 4. CAPM: the relationship between expected returns and risk
• 5. The Efficient Market Hypothesis: do stock prices move randomly?
• 6. Modigliani-Miller: does financing matter?
• 7. Black – Merton – Scholes: how to value options
• 8. Beyond Black-Merton-Scholes: state prices, stochastic discount factors
State prices
Current price
State
Up Down
Stock S Su Sd
Risk free bond 1 1+rΔt 1+rΔt
Law of one price
(no free lunches) )1()1(1 trvtrv
SvSvS
du
dduu
tr
pvu
1
Price of a digital option
Stochastic discount factors
• Valuing a derivative:
)~~
(
)()(
1fM
vf
v
fvfvf
d
ddu
u
uu
dduu
Expectation operator
Stochastic discount factor
Random payoff of derivative
Growth of derivative industry
0
50,000
100,000
150,000
200,000
250,000
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Pri
nc
ipa
l A
mo
un
t U
SD
Bil
lio
ns
Markets OTC
Explosion of the market for options
0.0
5,000.0
10,000.0
15,000.0
20,000.0
25,000.0
30,000.0
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Pri
nci
pal
am
ou
nt
US
D b
illio
ns