Summary Macro-Finance
Lecture 0: Introduction
1. Tyler expansions
∞
1 j
f ( x )=∑
j
f (a)(x−a)
j=0 j!
2. Convergent series (savings)
∞ ∞ ∞
∑ (1+S y) j =S ∑ (1+1 y) j =S ∑ β j=S 1−β
1
j=0 j=0 j=0
1
with β=
1+ y
[ ( ) ]
N +1
1+ y 1
TS=S 1−
y 1+ y
Lecture 1: The financial system principles
and relevance
1. The financial system: 6 parts
a. Money: means of exchange (as legal tender), unit of account & store of value
b. Financial instruments:
transfer of resources from savers to investors
transfer of risk to risk-absorbers
c. Financial markets: platform for buying and selling financial instruments efficiently
d. Financial institutions: proving large scale of financial services, including access to financial
market and information collection
e. Government regulatory agencies: supervising and regulating the financial system in order
to make it safe and reliable
f. Central Banks: monetary policy, monitor and stabilize the economy (and in some case also
directly) the financial system
1
,2. The financial system: 5 core principles
a. Core principle 1: time has value and is rewarded in financial pricing through the (risk-free)
interest rate. Interest rates form the key determinant of pricing risk-free cash-flows or
projects.
b. Core principle 2: risk-taking requires compensation in the form of pecuniary payments.
And this compensation increases with the amount of risk taken and the market price of
risk. fundamental pricing equation:r i , t +1=¿ r f ,t + rpi , t +ε i ,t +1
Pi , t+ 1 D i ,t → t +1
r i , t+1 = +
Pi ,t P i ,t
c. Core principle 3: Information is a key variable underlying financial decision with the role of
information becoming more relevant as decisions increase in importance.
d. Core principle 4: financial markets “determine” financial prices and allocate resources
throughout the economy
i. Pricing fundamental assets:
Risk-free bonds
Market-wide prices of risk
ii. Financial prices = information variables
iii. Derivative financial assets prices using no-arbitrage on basis of prices of
fundamental assets
iv. Proper market functioning should be safeguarded by regulatory & supervisory
authorities
v. Digression: fundamental asset pricing
Market equilibrium
Example with simple linear demand functions
Example prediction markets
Yield curve inversion: indicator for an upcoming recession
Examples of information aggregation in financial pricing
e. Core principle 5: financial stability improves welfare
i. Financial markets: intrinsically unstable (market faillures)
ii. Maintaining financial stability requires intervention of prudential authorities
iii. Risk diversification allows to eliminate non-priced risks at individual level, but
cannot eliminate macro-financial risk
iv. Financial stability: the welfare cost of crises (persistent loss in GDP)
2
, 3. The crucial role of the financial sector
a. Reason 1: Desynchronization through time between consumption (investment) and
income streams max U ( C 1 )+ δE [ U (C2 ) ]
C 1 ,C 2
i. Graphical
ii. Case A: no financial markets implying you consume what you produce
C 1 ≤ Y 1∧C 2 ≤ Y 2
Solution: E ( U )=U ( Y 1) + δE [ U ( C2 ) ]
iii. Case B: financial markets exist that allows to save and invest (B) in period 1 and
liquidate in period 2 at a rate of r
C 1 ≤ Y 1−B∧C 2 ≤ Y 2 + ( 1+ r ) B
Solution: U ' ( Y 1−B )=δ ( 1+r ) E [ U ' (Y 2+ ( 1+ r ) B) ]
Mathematical proof of finding optimal B
−( ( 1+r ) δ)−1 / γ Y 2−Y 1
B¿ = ¿¿
b. Reason 2: Decoupling (partly) of consumption (investment) from risky income streams
(risk) max E [ U (C 2) ]= pr a U ( C 2 ,a ) +¿ pr b U ( C2 , b ) ¿
C 2 ,b ,C 2, a
i. Graphical
ii. Case A: no financial market
iii. Case B: insurance contract welfare improving
c. Reason 3: Efficient allocation of resources in an economy depends on efficient sourcing of
savings and allocation of investments in an economy
4. Why financial intermediation is not a free lunch?
a. Excessive volatility due to procyclical nature of financial sector generated by financial
accelerator and procyclical provisioning
b. Too much (too asymmetric) finance?
3
Lecture 0: Introduction
1. Tyler expansions
∞
1 j
f ( x )=∑
j
f (a)(x−a)
j=0 j!
2. Convergent series (savings)
∞ ∞ ∞
∑ (1+S y) j =S ∑ (1+1 y) j =S ∑ β j=S 1−β
1
j=0 j=0 j=0
1
with β=
1+ y
[ ( ) ]
N +1
1+ y 1
TS=S 1−
y 1+ y
Lecture 1: The financial system principles
and relevance
1. The financial system: 6 parts
a. Money: means of exchange (as legal tender), unit of account & store of value
b. Financial instruments:
transfer of resources from savers to investors
transfer of risk to risk-absorbers
c. Financial markets: platform for buying and selling financial instruments efficiently
d. Financial institutions: proving large scale of financial services, including access to financial
market and information collection
e. Government regulatory agencies: supervising and regulating the financial system in order
to make it safe and reliable
f. Central Banks: monetary policy, monitor and stabilize the economy (and in some case also
directly) the financial system
1
,2. The financial system: 5 core principles
a. Core principle 1: time has value and is rewarded in financial pricing through the (risk-free)
interest rate. Interest rates form the key determinant of pricing risk-free cash-flows or
projects.
b. Core principle 2: risk-taking requires compensation in the form of pecuniary payments.
And this compensation increases with the amount of risk taken and the market price of
risk. fundamental pricing equation:r i , t +1=¿ r f ,t + rpi , t +ε i ,t +1
Pi , t+ 1 D i ,t → t +1
r i , t+1 = +
Pi ,t P i ,t
c. Core principle 3: Information is a key variable underlying financial decision with the role of
information becoming more relevant as decisions increase in importance.
d. Core principle 4: financial markets “determine” financial prices and allocate resources
throughout the economy
i. Pricing fundamental assets:
Risk-free bonds
Market-wide prices of risk
ii. Financial prices = information variables
iii. Derivative financial assets prices using no-arbitrage on basis of prices of
fundamental assets
iv. Proper market functioning should be safeguarded by regulatory & supervisory
authorities
v. Digression: fundamental asset pricing
Market equilibrium
Example with simple linear demand functions
Example prediction markets
Yield curve inversion: indicator for an upcoming recession
Examples of information aggregation in financial pricing
e. Core principle 5: financial stability improves welfare
i. Financial markets: intrinsically unstable (market faillures)
ii. Maintaining financial stability requires intervention of prudential authorities
iii. Risk diversification allows to eliminate non-priced risks at individual level, but
cannot eliminate macro-financial risk
iv. Financial stability: the welfare cost of crises (persistent loss in GDP)
2
, 3. The crucial role of the financial sector
a. Reason 1: Desynchronization through time between consumption (investment) and
income streams max U ( C 1 )+ δE [ U (C2 ) ]
C 1 ,C 2
i. Graphical
ii. Case A: no financial markets implying you consume what you produce
C 1 ≤ Y 1∧C 2 ≤ Y 2
Solution: E ( U )=U ( Y 1) + δE [ U ( C2 ) ]
iii. Case B: financial markets exist that allows to save and invest (B) in period 1 and
liquidate in period 2 at a rate of r
C 1 ≤ Y 1−B∧C 2 ≤ Y 2 + ( 1+ r ) B
Solution: U ' ( Y 1−B )=δ ( 1+r ) E [ U ' (Y 2+ ( 1+ r ) B) ]
Mathematical proof of finding optimal B
−( ( 1+r ) δ)−1 / γ Y 2−Y 1
B¿ = ¿¿
b. Reason 2: Decoupling (partly) of consumption (investment) from risky income streams
(risk) max E [ U (C 2) ]= pr a U ( C 2 ,a ) +¿ pr b U ( C2 , b ) ¿
C 2 ,b ,C 2, a
i. Graphical
ii. Case A: no financial market
iii. Case B: insurance contract welfare improving
c. Reason 3: Efficient allocation of resources in an economy depends on efficient sourcing of
savings and allocation of investments in an economy
4. Why financial intermediation is not a free lunch?
a. Excessive volatility due to procyclical nature of financial sector generated by financial
accelerator and procyclical provisioning
b. Too much (too asymmetric) finance?
3
