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bombolles especulatives. Jaume Ventura CREI, UPF & Barcelona GSE Bojos per l’economia ! Març 2014 . An Economic Model of Asset Prices. Assumptions Time is a sequence of dates t=0,1,2,…,∞. - PowerPoint PPT Presentation
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BOMBOLLES ESPECULATIVES
Jaume VenturaCREI, UPF & Barcelona GSE
Bojos per l’economia! Març 2014
AN ECONOMIC MODEL OF ASSET PRICES
Assumptions1. Time is a sequence of dates t=0,1,2,…,∞.2. There is a market with traders willing to borrow
and lend at the expected return of 1+r per period.
Question1. What is the price of an asset that delivers pay-
offs dt in date t?
2. Assume this asset is traded only in date 0.
...,, 321 ddd
What future payments does the asset promise?
What is the expected value of these future payments?
How much are traders willing to pay today for these future payments?
,...,...,, 21 nddd
,...,...,, 02010 ndEdEdE
,...)1(
,...,)1(
,1
022010
nn
rdE
rdE
rdE
MARKET EQUILIBRIUM!!!
Let xn be today’s value of payment at time n. Then,
.
.
.
101 )1( dErx rdEx
1
101
202 )1)(1( dErrx 2)1(20
2r
dEx
nn dErrrx 0)1)...(1)(1( nr
dEx nn
)1(0
How much are traders willing to pay today for these future payments?
How much are traders willing to pay today for the asset?
Thus, the price of the asset is
,...)1(
,...,)1(
,1
022010
nn
rdE
rdE
rdE
...)1(
...)1(1
022010
nn
rdE
rdE
rdE
1
00 )1(t
tt
rdEp
o Asset prices are high when expected payments are high and interest rates are low.
1
00 )1(t
tt
rdEp
MODIFYING OUR ECONOMIC MODEL OF ASSET PRICES
We have assumed so far that the asset is traded at time 0 only.
Assume from now on that the asset is traded in all periods.
Can the ability to resell the asset modify its value?
NEW MARKET EQUILIBRIUM!!!
Let pn be the price of the asset in date n. Then:
.
.
.
.
.Iterating forever…
1010)1( pEdErpo rpE
rdEp
111010
0
202010 )1( pEdErpE 220
22010
0 )1()1(1 rpE
rdE
rdEp
10100 )1( nnn pEdErpE nn
nn
rpE
rdE
rdE
rdEp
)1()1(...
)1(100
22010
0
1
000 )1(
lim)1(t
nn
ntt
rpE
rdEp
Asset prices have a fundamental and a bubble component.
The bubble component is a pyramid scheme.
Self-fulfilling expectations play a crucial role in asset price fluctuations.
1
000 )1(
lim)1(t
nn
ntt
rpE
rdEp
Fundamental Bubble
CALCULATING FUNDAMENTAL AND BUBBLE COMPONENTS
1. Measure the cash-flows that US productive assets generate as capital income, net of taxes and investment.
2. Compute the expected present discounted value of these cash-flows by assuming –
a. The interest rate is constant for all time horizons (equal to the 1950-2010 period average); and
b. Out-of-sample cash-flows grow at a constant rate (equal to the 1950-2010 period average), and resort to perfect foresight for within-sample cash-flows.
Household Savings
Firm Savings
Investment Growth
Household Savings
Firm Savings
Investment Growth
Credit!!!
Household Savings
Firm Savings
Investment Growth
Credit!!!
BACK TO THEORY (WITHOUT EQUATIONS!!) Two effects of bubbles on investments
1. An increase in the size of bubbles today absorbs credit and lowers investment – CROWDING-OUT EFFECT.
2. An increase in the size of bubbles tomorrow provides collateral and raises investment – CROWDING-IN EFFECT.
What effects dominates?1. If bubbles are not too large, the crowding-in effect
dominates and bubbles raise investment and growth.2. If bubbles become too large, the crowding-out effect
dominates and bubbles lower investment and growth.
SIMULATED ECONOMY WITHOUT PRODUCTIVITY SHOCKS AND POLICY
SIMULATED ECONOMY WITH PRODUCTIVITY SHOCKS AND WITHOUT POLICY
POLICY IMPLICATIONS FOR CENTRAL BANKS
The behavior of the economy depends on self-fulfilling expectations and the bubble is sometimes too small and sometimes too large.
Central Banks can manage bubbles by taxing credit when the bubble is too large and subsidizing credit when the bubble is too low.
This policy raises welfare and has no fiscal cost.
SIMULATED ECONOMY WITHOUT PRODUCTIVITY SHOCKS AND WITH POLICY
SIMULATED ECONOMY WITH PRODUCTIVITY SHOCKS AND POLICY
BOMBOLLES ESPECULATIVES
Jaume VenturaCREI, UPF & Barcelona GSE
Bojos per l’economia! Març 2014