Week 1:
Hirshleifer model Part 1:
Hirshleifer model: is about the allocation decision. The financial economic decision for each
individual is how much to consume, invest in the financial markets (beleggen), and invest in
the real markets (investeren).
For the investment in the financial market what is happening today (t=0) we call the financial
investments.
For the investment in the real market what is happening today we call real investments.
For investments in both financial markets and real markets, what is happening after t=0 we
call cash flows.
The Hirshleifer model has a few steps:
1. Hirshleifer model without financial market and without real market
2. Hirshleifer model with financial market but without real market
3. Hirshleifer model with financial market and real market
4. Fisher separation theorem (final outcome)
Hirshleifer model without financial market and without real market:
There are a few assumptions that we have to know at this step of the Hirshleifer model:
- A1: A certain world (no risk) is assumed: the individual knows all the decision
alternatives and the corresponding outcomes.
- A2: There is a one-period model where only two moments are important: the start of
the period (now, t=0) and the end of the period (later, t=1).
- A3: The individual has a current income of CF0 and a
future income of CF1.
At t=0 you receive CF0 and at t=1 CF1. The two things you can
do at t=0 are:
- At t=0 you can consume CF0 completely, partly or
nothing.
- If there is money left at t=0, you put this amount under
your pillow (at this step a bank still does not exist) and
you consume it including the CF1 at t=1.
Hirshleifer model with financial market but without real market:
This is the second step, so there is a financial market, so banks are introduced.
The assumption that is made here is: Assumption 14: Each participant can borrow or
lend unlimitedly against the risk-free market interest rate 𝑟𝑓.
𝐶𝐹1 1100
To calculate the Present value (Pv): 1+𝑟𝑓
= 1+10%
= 1000
This gives:
,If you know what the maximum consumption is at t=0 than you known the maximum
consumption at t=1, which is 𝐶𝐹0 · 𝑟𝑓 = 𝐶𝐹1
If we assume that the individual is able to rank his preferences consistently for the different
consumption combinations (C0,C1) and value these combinations by means of his utility
function, then we can derive indifference curves. An indifference curve in this case
contains the collection of consumption combinations to which the individual assigns an equal
utility value. At point a1, at t=0 a little is consumed. If you want to experience the same level
of utility with even less consumption at t=0, you want to be compensated with
lots of extra consumption at t=1. At points a1, a2 and a3 the same level of
utility is experienced. The slope of an indifference curve therefore is called
the marginal rate of substitution (MRS) between the present and future
consumption.
The optimal consumption combination (C0,C1) of the individual can be determined as the
point where the (highest) indifference curve is tangent to the consumption possibilities line
(blue line above).
Hirshleifer model with financial market and real market:
The existence of financial and real markets makes people “happier” → gives them higher
utility.
- Without financial markets people have to consume in the same period as they have
income.
- Without real markets profitable projects will be unused.
- The existence of both markets makes it possible for people to achieve higher
indifference curves.
Example:
- CF0 € 1000
- CF1 € 2100
- rf 5%
- Investment at t=0 € 500
- Revenue at t=1 € 630
What is the maximum consumption at t=0?
At t=0 500 is invested, so 1000 - 500 = 500 is what is left at t=0. However we can borrow
because there is a CF as t=1 and a revenue from the investment. Together this is:
2100 + 630 = 2730
The present value of this is: .05 = 2600
Together with the 500 that was left this is: 2600 + 500 = 3100
So, 3100 is the maximum consumption at t=0.
, We can also calculate the maximum consumption at t=1
At t=0 500 is invested, so 1000 - 500 = 500 is what is left at t=0. This amount can be used at
t=1. When we lend this to someone else we will receive 1.05 * 500 = 525 at t=1
This together with what we will receive in t=1 is: 525 + 630 + 2100 = 3255
Fisher separation theorem:
Theorem: The real investment decision is taken independently from the consumption
decision.
- Step 1 optimal investments: Marginal return = interest rate (opportunity cost of
capital*)
- Step 2 optimal consumption: Marginal utility of consumption now and later =
interest rate
* “The opportunity cost of capital (or more simply, the cost of capital), which is the best
available expected return offered in the market on an investment of comparable risk and
term to the cash flow being discounted.”
Meaning of the separation theorem:
- Everybody wants the same level of capital investments (until the marginal return =
interest rate).
- Managers can focus on real investment projects that add value.
- The financial market takes care of the individual choice with respect to consumption
now and later.
Concepts in Finance:
- Time:
Assume that: I offer to pay you €55 one year from now. There is no risk (can be sure
I’ll pay). The interest rate is 10%. For this generous offer, I ask you to pay me a
certain amount of money. How much would you pay for my offer?
Maximum = 55€ / 1.1 = 50€
There are some formulas that are used to calculate the value of a cash flow at
different times:
- Calculating the present value (PV) of a cash flow:
𝐶𝐹1
𝑃𝑉0 = 1 When we are dealing with a CF further in the future than t=1
(1+𝑟1)
we can use:
𝐶𝐹𝑇 55
𝑃𝑉0 = 𝑇 → 𝑃𝑉0 = 1 = 50
(1+𝑟𝑇) (1+10%)
- Calculating the future value:
𝑇 1
𝐹𝑉𝑇 = 𝐶𝐹0 × (1 + 𝑅𝑇) → 𝐹𝑉𝑇 = 50 × (1 + 10%) = 55
- Calculating the present value from a series of cash flows:
−1 −2
𝑃𝑉0 = 𝐶𝐹1 × (1 + 𝑅1) + 𝐶𝐹2 × (1 + 𝑅2) + ...
𝑇
−𝑡
= ∑ 𝐶𝐹𝑡(1 + 𝑅)
𝑡=1
Hirshleifer model Part 1:
Hirshleifer model: is about the allocation decision. The financial economic decision for each
individual is how much to consume, invest in the financial markets (beleggen), and invest in
the real markets (investeren).
For the investment in the financial market what is happening today (t=0) we call the financial
investments.
For the investment in the real market what is happening today we call real investments.
For investments in both financial markets and real markets, what is happening after t=0 we
call cash flows.
The Hirshleifer model has a few steps:
1. Hirshleifer model without financial market and without real market
2. Hirshleifer model with financial market but without real market
3. Hirshleifer model with financial market and real market
4. Fisher separation theorem (final outcome)
Hirshleifer model without financial market and without real market:
There are a few assumptions that we have to know at this step of the Hirshleifer model:
- A1: A certain world (no risk) is assumed: the individual knows all the decision
alternatives and the corresponding outcomes.
- A2: There is a one-period model where only two moments are important: the start of
the period (now, t=0) and the end of the period (later, t=1).
- A3: The individual has a current income of CF0 and a
future income of CF1.
At t=0 you receive CF0 and at t=1 CF1. The two things you can
do at t=0 are:
- At t=0 you can consume CF0 completely, partly or
nothing.
- If there is money left at t=0, you put this amount under
your pillow (at this step a bank still does not exist) and
you consume it including the CF1 at t=1.
Hirshleifer model with financial market but without real market:
This is the second step, so there is a financial market, so banks are introduced.
The assumption that is made here is: Assumption 14: Each participant can borrow or
lend unlimitedly against the risk-free market interest rate 𝑟𝑓.
𝐶𝐹1 1100
To calculate the Present value (Pv): 1+𝑟𝑓
= 1+10%
= 1000
This gives:
,If you know what the maximum consumption is at t=0 than you known the maximum
consumption at t=1, which is 𝐶𝐹0 · 𝑟𝑓 = 𝐶𝐹1
If we assume that the individual is able to rank his preferences consistently for the different
consumption combinations (C0,C1) and value these combinations by means of his utility
function, then we can derive indifference curves. An indifference curve in this case
contains the collection of consumption combinations to which the individual assigns an equal
utility value. At point a1, at t=0 a little is consumed. If you want to experience the same level
of utility with even less consumption at t=0, you want to be compensated with
lots of extra consumption at t=1. At points a1, a2 and a3 the same level of
utility is experienced. The slope of an indifference curve therefore is called
the marginal rate of substitution (MRS) between the present and future
consumption.
The optimal consumption combination (C0,C1) of the individual can be determined as the
point where the (highest) indifference curve is tangent to the consumption possibilities line
(blue line above).
Hirshleifer model with financial market and real market:
The existence of financial and real markets makes people “happier” → gives them higher
utility.
- Without financial markets people have to consume in the same period as they have
income.
- Without real markets profitable projects will be unused.
- The existence of both markets makes it possible for people to achieve higher
indifference curves.
Example:
- CF0 € 1000
- CF1 € 2100
- rf 5%
- Investment at t=0 € 500
- Revenue at t=1 € 630
What is the maximum consumption at t=0?
At t=0 500 is invested, so 1000 - 500 = 500 is what is left at t=0. However we can borrow
because there is a CF as t=1 and a revenue from the investment. Together this is:
2100 + 630 = 2730
The present value of this is: .05 = 2600
Together with the 500 that was left this is: 2600 + 500 = 3100
So, 3100 is the maximum consumption at t=0.
, We can also calculate the maximum consumption at t=1
At t=0 500 is invested, so 1000 - 500 = 500 is what is left at t=0. This amount can be used at
t=1. When we lend this to someone else we will receive 1.05 * 500 = 525 at t=1
This together with what we will receive in t=1 is: 525 + 630 + 2100 = 3255
Fisher separation theorem:
Theorem: The real investment decision is taken independently from the consumption
decision.
- Step 1 optimal investments: Marginal return = interest rate (opportunity cost of
capital*)
- Step 2 optimal consumption: Marginal utility of consumption now and later =
interest rate
* “The opportunity cost of capital (or more simply, the cost of capital), which is the best
available expected return offered in the market on an investment of comparable risk and
term to the cash flow being discounted.”
Meaning of the separation theorem:
- Everybody wants the same level of capital investments (until the marginal return =
interest rate).
- Managers can focus on real investment projects that add value.
- The financial market takes care of the individual choice with respect to consumption
now and later.
Concepts in Finance:
- Time:
Assume that: I offer to pay you €55 one year from now. There is no risk (can be sure
I’ll pay). The interest rate is 10%. For this generous offer, I ask you to pay me a
certain amount of money. How much would you pay for my offer?
Maximum = 55€ / 1.1 = 50€
There are some formulas that are used to calculate the value of a cash flow at
different times:
- Calculating the present value (PV) of a cash flow:
𝐶𝐹1
𝑃𝑉0 = 1 When we are dealing with a CF further in the future than t=1
(1+𝑟1)
we can use:
𝐶𝐹𝑇 55
𝑃𝑉0 = 𝑇 → 𝑃𝑉0 = 1 = 50
(1+𝑟𝑇) (1+10%)
- Calculating the future value:
𝑇 1
𝐹𝑉𝑇 = 𝐶𝐹0 × (1 + 𝑅𝑇) → 𝐹𝑉𝑇 = 50 × (1 + 10%) = 55
- Calculating the present value from a series of cash flows:
−1 −2
𝑃𝑉0 = 𝐶𝐹1 × (1 + 𝑅1) + 𝐶𝐹2 × (1 + 𝑅2) + ...
𝑇
−𝑡
= ∑ 𝐶𝐹𝑡(1 + 𝑅)
𝑡=1
