2015 ec banking mef2 lecture01
TRANSCRIPT
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Lecture 1
Christos Koulovatianos
University of Luxembourg
February 2015
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 1 / 40
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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
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 2 / 40
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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
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 3 / 40
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Key Question
Why do P-D ratios Jump (#) during disasters?
Overreaction?
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 4 / 40
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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
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 5 / 40
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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
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 6 / 40
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Are banks more exposed to disaster risks?
if yes, then WHY?
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 7 / 40
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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?
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 8 / 40
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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
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 9 / 40
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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.
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 10 / 40
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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)
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 11 / 40
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Present value examples: Perpetuity
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)
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 12 / 40
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Present value examples: Perpetuity
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)
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 13 / 40
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Present value examples: Perpetuity
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).
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 14 / 40
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Present value examples: Perpetuity
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)
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 15 / 40
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Present value examples: Perpetuity
Notice that
X = 1+ + 2 + ...
= 1+ 1+ + 2 + ...
[use equation (5)]
= 1+ X
In brief,X = 1+ X ,
which gives (after solving for X ),
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 16 / 40
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Present value examples: Perpetuity
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)
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 17 / 40
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Present value examples: Perpetuity
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.
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 37 / 40
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Why an innitely-lived agent
The making of a dynasty from overlapping generations
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 38 / 40
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Why an innitely-lived agent
The making of a dynasty from overlapping generations (Contd)
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 39 / 40
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Why an innitely-lived agent
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 )
(University of Luxembourg) MEF2 -Economics of Banking Feb. 19 40 / 40
Lecture 1