Transcript Risk - University of Rhode Island

Capital Market, Consumption and Investment (L1)
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Consumption and investment without capital market
Consumption and investment with capital market
Fisher separation theorem
Breaking down the separation : transaction costs
Breaking down the separation: agency problem
Application of Fisher Separation theorem: capital budgeting
and shareholder value maximization
– Materials from Chapters 1&2, CWS
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Consumption Plane
How individuals make choices among consumption bundles
C1
U
C0
Indifference curve: time preference of consumption in a consumption
The slope of the tangent line MRS
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Investment Schedule and Production Opportunity Set
C1
Marginal rate of return
A
X
B
B
ri
y0
Total Investments
I0
y1
A C0
X
Investment schedule and production opportunity set are equivalent
The slope for the tangent line of production opportunity set in B is –(1+ri) = marginal
rate of transformation (MRT)
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Equilibrium in a Robinson Crusoe World
MRS=MRT = -(1+ri)
C1
Individual 2
Individual 1
C0
Individual 1 consumes more than individual 2 in period 0
No capital market, thus there is no exchange.
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Optimal Consumption in the Presence of
Capital Market
max EU ( C 1 , C 2 )
C1 ,C 2
subject to
W0  y0 
y1
1 r
L1: Capital Market, Consumption and Investments
C 
*
0
C
*
1
1 r
5
C1
Capital Market Line
W1
B
U2
A
U1
C0
W0
With capital market, an agent can move from A to B, reaching a higher utility.
On the capital market line, one’s wealth does not change. But consumption
differs.
The slope of the capital market line is –(1+r).
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Slope of Capital Market Line
*
W0  C0 
*
C1
1 r
We have: C 1*  W 0 (1  r )  (1  r ) C 0*
And since W0(1+r)=W1. We thus have:
C 1  W 1  (1  r ) C 0
*
*
W1 is the intercept; -(1+r) is the slope of the capital market line.
Under what condition, the slope would increase?
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What Constitutes Consumptions?
GDP= C + I + G + NX
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–
–
–
C = consumption
I = investment
G = government purchases of goods and services
NX = net exports of goods and services
http://research.stlouisfed.org/fred2/categories/18
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Consumption
• Spending by domestic households on final
goods and services, accounting for about 2/2 of
GDP in the United States, including:
– Consumer durables
– Nondurable goods
– services
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Investment
• Includes both spending for new capital goods,
called fixed investment, and increases in firms’
inventory holdings, called inventory investment.
• Fixed investment includes:
– business fixed investment
– residential investment
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Joint effect of capital market and
production/investment
• See figure 1.8
• Two steps of the decision process related to
production opportunity and capital market exchange
opportunity:
– Choose the optimal production decision by taking on
projects until the marginal rate of return on investment
equals the objective market rate -- investment
– Choose the optimal consumption pattern by borrowing or
lending along the capital market line equate your subjective
time preference with the market rate of return -consumption
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Fisher Separation Theorem
• Given perfect and complete markets, the production decision is governed
solely by an objective market criterion without regard to individuals’
subjective preferences that enter into their consumption decisions.
• See figure 1.9
• In equilibrium, the marginal rate of substitution for all investors is equal to
the market rate of interest, and this in turn is equal to the marginal rate of
transformation for productive investment.
• MRSi=MRSj=-(1+r)=MRT
• That is, the marginal return on investment (MRT, marginal rate of
transformation) equals market-determined opportunity cost of capital (r)
• Irving Fisher's theory of capital and investment was introduced in his
Nature of Capital and Income (1906) and Rate of Interest (1907), although
it has its clearest and most famous exposition in his Theory of Interest
(1930).
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Fisher Separation Theorem
C1
W1
Individual 1
P1
Individual 2
C0
P0
W0
Individuals choose their respectful consumptions, where their consumptions
can be delivered by productive investments (P0, P1).
This is what we mean by separation: a separation of investment and
consumption.
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Implications
• All the consumption decisions are made along
the capital market line.
• The slope of the capital market line is –(1+r),
where r is the interest rate, not stock return.
• This is the case of consumption choices under
certainty.
• What is missing here?
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Perfect Market
• Necessary conditions
– Markets are frictionless
– Perfect competition in securities markets
– Markets are informationally efficient; that is, information is
costless, and it is received simultaneously by all individuals
– All individuals are rational expected utility maximizers
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Complete Market
• When the number of unique linearly
independent securities is equal to the total
number of alternative future states of nature.
The market is said to be complete.
– Page 77, CWS
– Details will be provided in the lectures related
Arrow-Debreu assets.
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Role of Capital Market –
Reducing Transaction Costs
• Trading is costly – thus the market is not perfect
• Having marketplaces helps to reduce transaction costs
– page 12, CWS.
• Thus financial market has its role only when
– Trading costs are non-trival
• Demsetz (1968); Kyle (1985); Glosten and Milgrom (1985);
Grossman and Miller (1988)
– Information asymmetry
• Akerlof (1970); Spence (1973); Myers and Majluf (1984)
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Breakdown of the Separation:
Transaction Costs
• See figure 1.12
• Lending rate is lower than borrowing rate
• Then the optimal consumption decision depends on
individuals’ subjective utility functions
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Breakdown of the Separation:
Agency Problem
• Given Fisher separation theorem, the investment
decision and consumption decision can be separated.
• In other words, shareholders can delegate managers
to perform the investment function
• This separation leads to separation of ownership and
control.
• Monitoring costs and compensation issue arise, which
lead to the large literature on corporate governance
and corporate finance.
– Berle and Means (1932) and Jensen and Meckling (1976)
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Value to Shareholders
• Present value of shareholders’ wealth can be
expressed as:

S0 

t 1
Div
t
(1  k s )
t
• Note: the above expression involves both capital
gains and dividends (see page 20) – all go to
shareholders
• Economic definition versus accounting definition of
profit
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Capital Budgeting Techniques
• Maximizing shareholders’ wealth is equivalent to
maximizing the discounted cash provided by
investment projects.
• Decision rules: payback period, …
• What’s the point?
– Utility function collapses to the value function
– Given the Fisher separation theorem, maximizing
shareholders’ wealth will lead to a social optimal at the
presence of the capital.
• In reality, firms have the option to undo their
decisions
– Thus the decision rule could be altered.
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Exercises
• CWS, 1.5&1.6
• What is meant by “separation” in the Fisher’s separation
theorem?
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