2015 Ec Banking MEF2 Lecture01

Lecture 1

Christos Koulovatianos

University of Luxembourg

February 2015

(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 1 / 40

Observations2030

40

50

60

70

80

90

100

110

90 92 94 96 98 00 02 04 06 08 10

Price-Dividend Ratio

8

12

16

20

24

28

32

36

90 92 94 96 98 00 02 04 06 08 10

Price-Earnings Ratio

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

90 92 94 96 98 00 02 04 06 08 10

Log Dividend

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

90 92 94 96 98 00 02 04 06 08 10

Log Earnings

5.2

5.6

6.0

6.4

6.8

7.2

7.6

90 92 94 96 98 00 02 04 06 08 10

Log Price

15

20

25

30

35

40

45

50

55

90 92 94 96 98 00 02 04 06 08 10

Crash Confidence Index


Observations

20

30

40

50

60

70

80

90

100

110

90 92 94 96 98 00 02 04 06 08 10

Price-Dividend Ratio

8

12

16

20

24

28

32

36

90 92 94 96 98 00 02 04 06 08 10

Price-Earnings Ratio

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

90 92 94 96 98 00 02 04 06 08 10

Log Dividend

2.75

3.00

3.25

3.50

3.75

4.00

4.25

4.50

90 92 94 96 98 00 02 04 06 08 10

Log Earnings

5.2

5.6

6.0

6.4

6.8

7.2

7.6

90 92 94 96 98 00 02 04 06 08 10

Log Price

15

20

25

30

35

40

45

50

55

90 92 94 96 98 00 02 04 06 08 10

Crash Confidence Index


Key Question

Why do P-D ratios Jump (#) during disasters?

Overreaction?


Are Banks Undervalued?

US data

0

10

20

30

40

50

1975 1980 1985 1990 1995 2000 2005 2010

BanksAgg. Market

-80

-40

0

40

80

120

160

1975 1980 1985 1990 1995 2000 2005 2010

% Deviation of Bank Variable from Agg. Market

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

1975 1980 1985 1990 1995 2000 2005 2010-80

-40

0

40

80

120

160

1975 1980 1985 1990 1995 2000 2005 2010

3.6

4.0

4.4

4.8

5.2

5.6

6.0

6.4

6.8

7.2

7.6

1975 1980 1985 1990 1995 2000 2005 2010-60

-40

-20

0

20

40

60

80

1975 1980 1985 1990 1995 2000 2005 2010

Log Price Index

Log Earnings

PE Ratio


Are Banks Undervalued?

UK data

Log Price Index

Log Earnings

PE Ratio

0

5

10

15

20

25

30

1975 1980 1985 1990 1995 2000 2005 2010

BanksAgg. Market

-80

-40

0

40

80

120

1975 1980 1985 1990 1995 2000 2005 2010

% Deviation of Bank Variable from Agg. Market

1

2

3

4

5

6

1975 1980 1985 1990 1995 2000 2005 2010-80

-40

0

40

80

120

160

1975 1980 1985 1990 1995 2000 2005 2010

3

4

5

6

7

8

1975 1980 1985 1990 1995 2000 2005 2010-60

-40

-20

0

20

40

60

80

100

1975 1980 1985 1990 1995 2000 2005 2010


Are banks more exposed to disaster risks?

if yes, then WHY?


Balance Sheet of a Bank

Assets Liabilities

Investments(generatingearnings)

1. Deposits

2. Equity

Is equity valuation of a bank an exercise of putting a price on a gambler?


Investment concepts: present value

Present Value (PV): Transforms values earned or spent in future timespots in time into values of the present moment.

Examples: What is the PV of $100 earned after ve years fromnow if: the annual interest rate is r = 5%, for all ve years. Answer:

PV =$100

(1+ 0.05)5= $78.35

the annual interest rate changes; it is r1 = 5% for the rst two years,and r2 = 3% for the remaining three years. Answer:

PV =$100

(1+ 0.05)2 (1+ 0.03)3= $83


Investment concepts: present value

The intuition behind PV: If you invest the PV that was calculatedusing a particular stream of given interest rates, you will obtain thesame amount at the specic future time spot.

When we calculate the PV of an investment such that we earn or paymoney in many dierent future time spots, we must add up the PVsof every particular future time spot. In this way we evaluate a futurestream of events in terms of values of the present.


Present value examples: Perpetuity

Perpetuity: It pays a constant amount, A, every period, forever. Ifthe interest rate, r , is constant, then the following formula holds:

PV =A

1+ r+

A

(1+ r)2+ ... =

Ar

(1)



Proof of Formula (1):

PV =A

1+ r+

A

(1+ r)2+

A

(1+ r)3+ ...

so,

PV =A

1+ r+

11+ r

"A

1+ r+

A

(1+ r)2+ ...

#(2)



Proof of Formula (1) contd:Since

PV =A

1+ r+

A

(1+ r)2+ ...

we can substitute this last equation into (2) to get

PV =A

1+ r+

11+ r

PV . (3)



Proof of Formula (1) contd:Now, all we need to do is to solve (3) for PV .

PV =A

1+ r+

11+ r

PV )

)1 1

1+ r

PV =

A1+ r

)

) r1+ r

PV =A

1+ r)

) PV = Ar

which proves formula (1).



Key Result to Remember: Sum of Geometric series

If 0 < < 1, then

1+ + 2 + ... =1

1 (4)To see that (4) is true, set

X = 1+ + 2 + ... (5)



Notice that

X = 1+ + 2 + ...

= 1+ 1+ + 2 + ...

[use equation (5)]

= 1+ X

In brief,X = 1+ X ,

which gives (after solving for X ),



X =1

1 ,and using (5), it is,

1+ + 2 + ... =1

1 ,

which is the same as (4).

This formula gives us another way of proving formula (1). With equation(4) at hand, notice that

PV =A

1+ r+

A

(1+ r)2+

A

(1+ r)3+ ...)

) PV = A1+ r

"1+

11+ r

+1

(1+ r)2+ ...

#(6)



From equation (6) we can calculate the term

1+1

1+ r+

1

(1+ r)2+ ...

using the formula (4) after we set

=1

1+ r.

Notice that for r > 0, it is

0 g , it is

0 0, and with Ct denoting consumption in periodt 2 f0, 1, ...g, while 2 (0, 1) and u has standard properties, u0 > 0and u00 < 0 (other technical conditions we will mention along theway). The investor chooses the optimal consumption path and howmany stocks to hold in each period.


Why an innitely-lived agent

The making of a dynasty from overlapping generations



The making of a dynasty from overlapping generations (Contd)



Utility of any person at any point in time can be seen as:

u (ct ) + u (ct+1) + 2u (ct+2) + ... =

s=t

stu (cs )

which is the utility of the whole innitely-lived dynasty starting fromany person at any point in time.

By default, if we call todays time period 0", then the utility of adynasty is

U (c0, c1, ...) = u (c0) + u (c1) + 2u (c2) + ... =

t=0

tu (ct )


Lecture 1

2015 Ec Banking MEF2 Lecture01

Documents

Transcript of 2015 Ec Banking MEF2 Lecture01