50 years of finance andré farber université libre de bruxelles inaugurale rede, francqui leerstoel...

50 years of Finance

André FarberUniversité Libre de Bruxelles

Inaugurale rede, Francqui LeerstoelVUB 2 December 2004

Francqui Leerstoel - Inaugurale Rede 2 december 2004 |2

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

• 9. Outline of following lectures


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











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











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











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



Expected return

Beta

Risk free interest rate

r

rM

1β

)( FMF rrrr


Net Present Value Calculation with CAPM

tFMF

tt

rrr

CECPV

])(1[

)()(


Outline











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











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











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











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


Outline











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


Outline of next lectures

• 1. Valuing option: inside Black-Merton-Scholes

• 2. Option and portfolio management: portfolio insurance, hedge funds

• 3. Options and capital budgeting: beyond NPV, real options

• 4. Options and risky debt: Modigliani Miller revisited

• 5. Options and capital structure: how much debt is optimal?

• 6. Options and credit risk: when rating agencies fail

All documents for these lectures will be available on my website:

www.ulb.ac.be/cours/solvay/farber/vub.htm

50 years of finance andré farber université libre de bruxelles inaugurale rede, francqui leerstoel...

Documents

francqui leerstoel vub

bruxelles inaugurale

black merton scholes

stock prices

c n v n slide

expected returns

efficient market hypothesis

following lectures