Macro-Finance
Lecture 1: The financial system: principles and relevance
Slide 3
Money is divisible , durable and can be used as means of exchange -> what
makes it special? It’s legal tender (if you can pay your taxes with it) -> eg bitcoin
in Ecuador, not in Belgium.
Money is a very good financial instrument for many reasons, but not for
risk or consumption smoothing over time, because of inflation
Each financial instrument has a specific purpose, eg smooth over time -> bond
Financial markets and financial institutions regulated and supervised by ECB, EU,
NBB, European commission,…
Slide 5 - 11
First 2 core principles:
Fundamental pricing equation decided by 2 known: riskfree interest rate & risk
premium ; and 1 unknown: shock -> these 3 are going to decide how prices move
through time
Who sets the price? The marginal investor, sometimes investment firm,
sometimes speculator, not always the same ‘person’.
3rd core principle: information.
4th core principle: financial markets determine financial prices and allocate
resources throughout the economy
Price is decided by aggregated average of future variables -> see formula on
slide using taylor expansion to create linear function -> try to do it myself!
What does the formula tell us? Each agent has a different expectation
about the price, and your starting to trade in the market; then your price is
going to be a weighted average of all the expected future prices.
Who dominates the price? It’s not equally weighted, it’s weighted by
amount of demand you have in a market big players/big traders are
going to influence the price very much.
On slide 6 betting markets graph on presidential elections; economic way of
predicting, in shares per candidate. -> to infer probabilities of each candidate.
Much better because your not going to bet based on your preferences but based
on information you gathered you’re going to put money on that candidate you
estimated is going to win. We see biden stock going down long before resignment
showing anticipation of people.
Slide 12 – 16
Example of market information aggregation in financial pricing -> look for
recession indicators
,Yield curve indicator (=aggregated interest rate over period t) -> inverted yield
curve = sign that recession is coming
Financial stability -> core principle 5: financial stability improves welfare
Big disadvantage of financial markets is that they are unstable -> financial crash
after financial crash… . -> graph slide 16 shows impact of financial crash (they
are not innocent) , you enter recession that is scarring your economy (postpone
investment, lay off people,…) -> you never recover to the original growth path. -
> 10% cost of financial stability for example = on 20 trillion $ yearly is 2 trillion $
yearly => calculation net present value for the future of this yearly cost amounts
to a lot of money lost. (doing this for all the crisis -> even more money!)
Slide 18 – 21
Why financial intermediation is important: allows you to desynchronize
consumption and income (consumption smooth) and allows you to risk share
across states -> 2 dimensions time and risk
Mathematically proven why this is welfare improving: individuals derive utility
from consumption C across periods 1 and 2. -> without financial markets, people
are constrained to consume only what they earn in each period ; with financial
markets, individuals can smooth their consumption over time by saving or
borrowing
You want to maximize your expected utility over 2 periods:
max U ( C 1 )+ δE [ U (C2 )]
c 1 ,c 2
Case a) No financial markets
->You can only consume what you produce in each period: C 1 ≤ Y 1∧C 2 ≤ Y 2
or C1 = Y1 and C2 = Y2 because more consumption is better
Utility is determined directly by income in each period: E ( U )=U ( Y 1) + δE [ U (Y 2) ]
Implication: your consumption C is completely dependent on your income Y -> if
Y1 is high but Y2 is low, you cannot transfer resources to smooth your
consumption. => leads to periods of overconsumption (when Y 1 > Y2) or
underconsumption (when Y1 < Y2)
Case b) Financial markets
Financial markets allow you to:
Save = invest B in period 1, which grows at a rate r by period 2
Borrow = use future income Y2 to fund higher consumption in period 1
Under constraints:
C 1 ≤ Y 1−B (you save B in period 1).
C 2 ≤ Y 2+(1+r ) B (your savings B grow at rate r and can be consumed in
period 2)
, U '(Y 1 −B)=δ (1+ r) E[U ' (Y 2 +(1+r )B)]
The equation balances the marginal utility of consuming now with the discounted,
expected marginal utility of consuming later
Typically B* (optimal savings) is different from zero because financial
markets allow you to allocate resources across periods in a way that
maximizes overall utility
Thus, improved welfare: save during periods of high income, borrow during
periods of low income.
Graphically: individual borrows B in period 1 to increase their consumption above
their income Y1 , as a result their period 1 consumption becomes Y 1 – B. ->
borrowing B in period 1 means the individual must repay (1+r)B in period 2
period 2 consumption is reduced to Y2 + (1+r)B.
Utility gain from borrowing B in period 1 ; utility loss from repaying (1+r)B
in period 2. Overall welfare increased because utility of consumption when
income is low is higher than utility of consumption when income is high.
Optimal borrowing B* is chosen where the marginal gain in period 1 utility
= discounted marginal loss in period 2 utility (B* is negative, you borrow in
period 1)
As seen on slide 20; using a specific utility function -> the CRRA ; we solve for B*.
Borrowing if B*< 0 and saving if B*>0
Slide 21 shows research into how much consumption smoothing there is and the
income shocks people have by US state -> 60% of income shock is smoothed
away. One way to consumption smooth is through capital channel (investing
across states) -> absorbing local shocks ; 2nd channel is fiscal policy ; 3rd channel
is financial markets (borrowing and saving)
As we can see the euro area is counterproductive: not as integrated as
USA, national crisis, …
Slide 22 – 23
Don’t need to find solutions to exercise yourself! Too difficult, wont be asked on
exam.
You can also use financial markets to smooth over risk (over states). -> you’re
risk averse so you have a concave function.
Again we aim to maximize expected utility:
max E [U (C 2 )]= pa U (C 2 ,a )+ p b U (C2 , b)
C 2 ,a ,C 2 ,b
With pa and pb probabilities of risky states a and b; pa+pb = 1
Case a) no financial markets
Under constraints: C2,a = Y2,a and C2,b = Y2,b
Solution: E(U )=p a U (Y 2 ,a )+ p b U (Y 2 ,b )
, Implications : consumption is entirely dependent on income Y 2 ; if state a is good
and state b is bad, the individual experiences significant consumption variability,
reducing overall welfare -> the individual has no means to transfer resources
from one state to another
Case b) financial markets with insurance
Insurance enables individuals to shift resources between states -> paying a
premium C in period 1 to receive an insurance claim I in the bad state
New constraints: C2,a = Y2,a – C and C2,b = Y2,b – C + I
Solution: E(U )=p a U (Y 2 ,a −C)+ p b U (Y 2 ,b −C+ I )
Implications: 1) Risk reduction by transferring resources from the good state to
the bad state reducing variability ; optimal I* is typically not zero, as individuals
value the reduction in uncertainty. 2) Improved welfare -> higher utility is
achieved
Graphically:
Gain from having insurance in a bad state provides more utility then loss from
paying for insurance in good state costs utility. -> leading to welfare
improvement
Conclusion
Why is financial intermediation good? It allows you to consumption smooth and
diversify risk over time. Both, using concave utility functions, are highly welfare
improving.
Slide 24
Economic growth depends on a number of factors: technology changes, labor
growth, capital growth. -> in Europe aging population so growth has to come
from technology and capital growth
Financial system is going to determine how much of your wealth youre going to
save and consume. -> savings ratio (S/Y) determined by the efficiency of your
system -> this will determine how much your economy is going to save
How much of this saving is going to financial system and to real
investment? FS/S ratio determines this
This is followed by the regulators (reserve requirements, report requirements,…
Then we have the borrowing ratio: BOR/FS fraction of borrowing by financial
sector to the economy
How much of this goes to investment, how much to consumption? I/BOR
Financial system allocates investment ratio to different institutions (eg.
Banks, private equity funds, venture capital startups,…) their projects
Structure of financial system will determine to what extent economy is going to
save, is able to keep savings in home economy/ to keep in financial system, and
distribute to all the different locations.
Lecture 1: The financial system: principles and relevance
Slide 3
Money is divisible , durable and can be used as means of exchange -> what
makes it special? It’s legal tender (if you can pay your taxes with it) -> eg bitcoin
in Ecuador, not in Belgium.
Money is a very good financial instrument for many reasons, but not for
risk or consumption smoothing over time, because of inflation
Each financial instrument has a specific purpose, eg smooth over time -> bond
Financial markets and financial institutions regulated and supervised by ECB, EU,
NBB, European commission,…
Slide 5 - 11
First 2 core principles:
Fundamental pricing equation decided by 2 known: riskfree interest rate & risk
premium ; and 1 unknown: shock -> these 3 are going to decide how prices move
through time
Who sets the price? The marginal investor, sometimes investment firm,
sometimes speculator, not always the same ‘person’.
3rd core principle: information.
4th core principle: financial markets determine financial prices and allocate
resources throughout the economy
Price is decided by aggregated average of future variables -> see formula on
slide using taylor expansion to create linear function -> try to do it myself!
What does the formula tell us? Each agent has a different expectation
about the price, and your starting to trade in the market; then your price is
going to be a weighted average of all the expected future prices.
Who dominates the price? It’s not equally weighted, it’s weighted by
amount of demand you have in a market big players/big traders are
going to influence the price very much.
On slide 6 betting markets graph on presidential elections; economic way of
predicting, in shares per candidate. -> to infer probabilities of each candidate.
Much better because your not going to bet based on your preferences but based
on information you gathered you’re going to put money on that candidate you
estimated is going to win. We see biden stock going down long before resignment
showing anticipation of people.
Slide 12 – 16
Example of market information aggregation in financial pricing -> look for
recession indicators
,Yield curve indicator (=aggregated interest rate over period t) -> inverted yield
curve = sign that recession is coming
Financial stability -> core principle 5: financial stability improves welfare
Big disadvantage of financial markets is that they are unstable -> financial crash
after financial crash… . -> graph slide 16 shows impact of financial crash (they
are not innocent) , you enter recession that is scarring your economy (postpone
investment, lay off people,…) -> you never recover to the original growth path. -
> 10% cost of financial stability for example = on 20 trillion $ yearly is 2 trillion $
yearly => calculation net present value for the future of this yearly cost amounts
to a lot of money lost. (doing this for all the crisis -> even more money!)
Slide 18 – 21
Why financial intermediation is important: allows you to desynchronize
consumption and income (consumption smooth) and allows you to risk share
across states -> 2 dimensions time and risk
Mathematically proven why this is welfare improving: individuals derive utility
from consumption C across periods 1 and 2. -> without financial markets, people
are constrained to consume only what they earn in each period ; with financial
markets, individuals can smooth their consumption over time by saving or
borrowing
You want to maximize your expected utility over 2 periods:
max U ( C 1 )+ δE [ U (C2 )]
c 1 ,c 2
Case a) No financial markets
->You can only consume what you produce in each period: C 1 ≤ Y 1∧C 2 ≤ Y 2
or C1 = Y1 and C2 = Y2 because more consumption is better
Utility is determined directly by income in each period: E ( U )=U ( Y 1) + δE [ U (Y 2) ]
Implication: your consumption C is completely dependent on your income Y -> if
Y1 is high but Y2 is low, you cannot transfer resources to smooth your
consumption. => leads to periods of overconsumption (when Y 1 > Y2) or
underconsumption (when Y1 < Y2)
Case b) Financial markets
Financial markets allow you to:
Save = invest B in period 1, which grows at a rate r by period 2
Borrow = use future income Y2 to fund higher consumption in period 1
Under constraints:
C 1 ≤ Y 1−B (you save B in period 1).
C 2 ≤ Y 2+(1+r ) B (your savings B grow at rate r and can be consumed in
period 2)
, U '(Y 1 −B)=δ (1+ r) E[U ' (Y 2 +(1+r )B)]
The equation balances the marginal utility of consuming now with the discounted,
expected marginal utility of consuming later
Typically B* (optimal savings) is different from zero because financial
markets allow you to allocate resources across periods in a way that
maximizes overall utility
Thus, improved welfare: save during periods of high income, borrow during
periods of low income.
Graphically: individual borrows B in period 1 to increase their consumption above
their income Y1 , as a result their period 1 consumption becomes Y 1 – B. ->
borrowing B in period 1 means the individual must repay (1+r)B in period 2
period 2 consumption is reduced to Y2 + (1+r)B.
Utility gain from borrowing B in period 1 ; utility loss from repaying (1+r)B
in period 2. Overall welfare increased because utility of consumption when
income is low is higher than utility of consumption when income is high.
Optimal borrowing B* is chosen where the marginal gain in period 1 utility
= discounted marginal loss in period 2 utility (B* is negative, you borrow in
period 1)
As seen on slide 20; using a specific utility function -> the CRRA ; we solve for B*.
Borrowing if B*< 0 and saving if B*>0
Slide 21 shows research into how much consumption smoothing there is and the
income shocks people have by US state -> 60% of income shock is smoothed
away. One way to consumption smooth is through capital channel (investing
across states) -> absorbing local shocks ; 2nd channel is fiscal policy ; 3rd channel
is financial markets (borrowing and saving)
As we can see the euro area is counterproductive: not as integrated as
USA, national crisis, …
Slide 22 – 23
Don’t need to find solutions to exercise yourself! Too difficult, wont be asked on
exam.
You can also use financial markets to smooth over risk (over states). -> you’re
risk averse so you have a concave function.
Again we aim to maximize expected utility:
max E [U (C 2 )]= pa U (C 2 ,a )+ p b U (C2 , b)
C 2 ,a ,C 2 ,b
With pa and pb probabilities of risky states a and b; pa+pb = 1
Case a) no financial markets
Under constraints: C2,a = Y2,a and C2,b = Y2,b
Solution: E(U )=p a U (Y 2 ,a )+ p b U (Y 2 ,b )
, Implications : consumption is entirely dependent on income Y 2 ; if state a is good
and state b is bad, the individual experiences significant consumption variability,
reducing overall welfare -> the individual has no means to transfer resources
from one state to another
Case b) financial markets with insurance
Insurance enables individuals to shift resources between states -> paying a
premium C in period 1 to receive an insurance claim I in the bad state
New constraints: C2,a = Y2,a – C and C2,b = Y2,b – C + I
Solution: E(U )=p a U (Y 2 ,a −C)+ p b U (Y 2 ,b −C+ I )
Implications: 1) Risk reduction by transferring resources from the good state to
the bad state reducing variability ; optimal I* is typically not zero, as individuals
value the reduction in uncertainty. 2) Improved welfare -> higher utility is
achieved
Graphically:
Gain from having insurance in a bad state provides more utility then loss from
paying for insurance in good state costs utility. -> leading to welfare
improvement
Conclusion
Why is financial intermediation good? It allows you to consumption smooth and
diversify risk over time. Both, using concave utility functions, are highly welfare
improving.
Slide 24
Economic growth depends on a number of factors: technology changes, labor
growth, capital growth. -> in Europe aging population so growth has to come
from technology and capital growth
Financial system is going to determine how much of your wealth youre going to
save and consume. -> savings ratio (S/Y) determined by the efficiency of your
system -> this will determine how much your economy is going to save
How much of this saving is going to financial system and to real
investment? FS/S ratio determines this
This is followed by the regulators (reserve requirements, report requirements,…
Then we have the borrowing ratio: BOR/FS fraction of borrowing by financial
sector to the economy
How much of this goes to investment, how much to consumption? I/BOR
Financial system allocates investment ratio to different institutions (eg.
Banks, private equity funds, venture capital startups,…) their projects
Structure of financial system will determine to what extent economy is going to
save, is able to keep savings in home economy/ to keep in financial system, and
distribute to all the different locations.
