Appunti Financial Markets and Economic Activity

C Y

 

t t

C Y

+ = +

0 0

t t

(1 ) (1 )

r r

+ +

1 1

t t

= =

Example 3

Consider again Example 1 with only labor income, and discover that whatever financial decision is made in year 0,

the total present value of consumable resources cannot exceed 70,000 + 70,000/(1.05) = 136,666.7.

1) Consumption plan for year 0 2) Consumption plan for year 0

Labour income €70,000 Labour incomes €70,000

Bank loan €10,000

  

Saving € €80,000

€60,000 Consumption plan for year 1

Consumption plan for year 1 Labour incomes €70,000

Labour incomes €70,000 €10,500

Debts and interests

Capital and interests €10,500 €59,500

€80,500

Geometry of intertemporal budgeting

(1

+ + ) = + (1 + )

(1 (1

ℎ ℎ = + + ) − + )

The intertemporal budgeting line identifies the set of possible options regarding

the composition of the plan.

∗ ∗

> ; <

Intercept with x-axe is the option where all consumption is done in period t;

while the intercept with the y-axe is the option where consumption is all done in

period t+1. 

The point A is always present plan where the present consumption = present income, future consumption

= future income

The interest rate is the "rate of exchange" between present and future consumption

Define in each year, then, by intertemporal budgeting

∆ = − = − = −∆

(1

+ ) = − = ∆

∆

1+ = − ∆

Therefore €1 of saving (less consumption) buys €(1+r) of future consumption;

> 0

€1 of borrowing (more consumption) costs €(1+r) of future consumption.

< 0

Note: if there is inflation, i.e., the price level of consumption goods increases from one year to the next, it is

necessary to use the real interest rate, which is (nominal rate − inflation rate)

Considerations

 Saving (borrowing) cannot change the present value of the consumption plan. which is only determined

by the present value of non-financial incomes.

 Financial wealth only matters if it exists initially, and if our household has planned a final value greater

or lower than the initial value.

 Given these results, is there any economic rationale for saving? Motivations for saving include

buying goods that exceed the value of present incomes

o taking care of future needs and events

o hoarding resources for retirement

o

These motivations share the reason we have seen at the basis of finance: people attach some well-being to

delinking their consumption path from that of incomes: saving exchanges less present consumption for more

future consumption, borrowing exchanges more present consumption for less future consumption.

Time distribution of incomes and consumption of Example 3

Saving or borrowing?

Growth of consumption and growth of incomes

Saving or borrowing result from the growth rate of consumption with respect to incomes

One synthetic way of expressing the household's desired time profile of consumption with respect to incomes

(especially in long-term plans) is to make reference to growth rates.

In the usual two-period plan (0, 1), the household's consumption plan ( , ) can be expressed as

where

= (1 + ) = ℎ

 

a constant consumption plan = 0

 

a growing consumption plan > > 0

 

a decreasing consumption plan < < 0

The consumption plan should not violate the intertemporal budget constraint.

 Saving S0 > 0, if gc > gy: consumption grows more than incomes

 Borrowing S0 < 0, if gc < gy: incomes grow more than consumption

 No saving, no borrowing, S0 = 0, if gc = gy: consumption grows like incomes

Exercise

Y = €70,000, Y = €70,000, gy = 0

0 1

In the plan with saving, we observe that

C = €60,000, C = €80,500, gc = 34.2%

0 1

Check that these data, given r = 5%, yield in fact (approx.) S = €10,000 in the previous formula

0

In the plan with borrowing, we observe that

C = €80,000, C = €59,500, gc = -25.6%

0 1

Check that these data, given r = 5%, yield in fact (approx.) S = -€10,000 in the previous formula

0

Long-term planning

Long-term planning is a key aspect of households' economic and financial management. There is a growing

intermediary industry devoted to assisting households in this activity. It consists of three basic ingredients

 Eliciting the preferred consumption profile

 Assessing the intertemporal budget constraint accurately

 Deriving the time path of the relevant variables (typically consumption, saving and wealth)

Let the preferred consumption profile be expressed in terms of year growth rate gc, i.e.

C , C = C0( 1+ gc), C2 = C1(1+ gc) = C0(1+ gc)2, …, Ct = C0(1+ gc)t, …

0 1

The same for income

Y0, Y1 = Y0( 1+ gy), Y2 = Y1(1+ gy) = Y0(1+ gy)2, …, Yt = Y0(1+ gy)t, …

Therefore, the formulas of PV for a plan of T years are the following

"Life-cycle" planning with "hump-shaped" incomes

In the first model of (work) "life-cycle" planning, elaborated by Modigliani and Brumberg, there are two

empirical facts:

 labor incomes are not constant but follow a predictable "hump" shaped path .There are three typical phases:

Y0 < Y1 > Y2

youth maturity retirement

 preference for constant consumption :

Modigliani F., Brunberg R. (1954

Life-cycle planning with three income stages: youth (20 x 3y.), maturity (100 x 8y.), retirement (70 x 5y.)

(interest rate 4%, PVI =890.7, C* = 73.5)

Assumptions:

 The present value of the consumption and income in each period is discounted to the rate of return equal

to 4%

 In this case (simplified) the human knows exactly when he dies

Life-cycle planning with constant consumption implies three financial phases



Youth debt



Maturity saving



Retirement dissaving

Is this result consistent with the general rule of saving/borrowing determined by the rate of growth of

consumption with regards to incomes?

Remember:

saving S > 0, if gc > gy: consumption grows more than future incomes

0

borrowing S < 0, if gc < gy: future incomes grow more than consumption and constant consumption

0

means gc = 0

Time profile of wealth is hump-shaped, it’s negative/low during youth, highest during maturity, low during



retirement real data

Wealth effects

Wealth accumulation (decumulation) is integral part of the consumption plan. Wealth may rise or fall for

exogenous reasons like stock market booms or crashes etc. These affect the value of consumable resources,

and are particularly important when they are deemed permanent.

Unexpected (temporary) income shocks (up and down) have limited effects on the consumption path:

saving and borrowing act as buffers. Unexpected income falls by 50% in period 6.

 Negative saving in period 6

 Then saving increases and wealth decreases (last period is 0)

Given the present value of our income we have to set the value of our consumption

Over short periods of time, changes in consumption are poorly correlated with changes in income

However, they react more than expected on a theoretical basis (correlation should be in the dimension of the

interest rate but it is in the order of 50-60%)

When income is high the households tend to consume more, so the correlation is positive but the correlation

is not 0

Implications for finance of the aggregate household sector



Demography composition of population by age

Economic organization and institutions

 labor market organization (access and exit rules, time profile of careers and salaries)

 regulation and efficiency of financial markets (access to borrowing and saving)

 pension systems (age, private and public systems)



Culture and values intergenerational behavior (cultural, religious, values that affect rules and customs in

the family relationships)

What determines the preferred consumption path?

We have seen that saving or borrowing result from the desire to delink the time path of consumption from

that of income. This attitude entails an exchange between (more or less) present consumption and (less or

more) future consumption. So far, we have taken this attitude as given without investigation. Can we learn

more about it?

The reference answer in financial analysis is based on three hypotheses

 households' choices are driven by the pursuit of the maximal well-being from consumption

 in any moment in time, higher consumption generates higher well-being, but with decreasing intensity



i.e., Hamburger example the more you eat the less utility you “gain”

 the timing of consumption affects well-being; generally, sooner is better than later (so note that if savers

wish to exchange less present consumption for future consumption, this may not be "costless").

The three hypotheses in a single plot Consumption is a source of personal well-being, called utility.

The relationship between consumption and utility is conceived of

as:

-

Do we have evidence of these hypotheses? Qualitatively yes, there is broad agreement (e.g. between

economic analysis and psychologists). Much more disagreement on the "details" (e.g. the quantification of

the effects, or the competence and consistency of people about their choices over time)

Lab experiments

- Willingness to pay/accept: "State the lowest amount you'd be willing to accept today instead of $X in

one month"

- Matching tasks (Equivalence scales): "I am indifferent between () today and $X in one month"

- Choice tasks (Multiple price lists): "Which do you prefer: $X today or $Y in one month"

Real life revealed preferences (marketing practices)

- Willingness to pay: pay an extra for fast delivery (Amazon – price of time)

- Time reward: get a discount for delayed delivery

The ratio between the optimal increase in future consumption for each unit of decreased present

∗

∆

consumption is called marginal rate of substitution. = ∗

∆

The MRS reflects the household's subjective preferences regarding the

consumption path over time. The implication is that the household is ready to

∗ ∗ ∗

save < 0 only if it expects to obtain MRSx∆ 0 (MRS is always