Monetary Theory and
Business Cycles
• From the very beginning of the option theory, it was
considered as a part of much larger foundation.
• I like the beauty and symmetry in Mr. Treynor’s
equilibrium models so much that I started designing
them myself. I worked on models in several areas:
•
•
Monetary theory
•
Business cycles
•
Options and warrants
•
• For 20 years, I have been struggling to show people the
beauty in these models to pass on knowledge I received
from Mr. Treynor.
• In monetary theory --- the theory of how
money is related to economic activity --- I
am still struggling. In business cycle theory
--- the theory of fluctuation in the economy
--- I am still struggling. In options and
warrants, though, people see the beauty.
(p. 93)
•
• Fischer Black may not realize that his
breakthrough in options is much more
fundamental. It extended CAPM from one
period to continuous time. With such a
continuous time framework slightly
modified, the problem of business cycles
can be understood very easily.
• So is the monetary theory.
• By applying the production theory.
• We will use some examples to illustrate
the applications to monetary theory and
business cycles.
Discount rate and economic
structure
Suppose in three different markets in countries
A, B and C, annual sales capacity is 1 million
dollars. Uncertainty is 50% per annum.
Decision makers will attempt to maximize the
net present value of investment project. If
discount rates are 5%, 10% and 15% per
annum in country A, B, C respectively, how
much will be the desired fixed costs and how
long will be the expected project durations?
What are NPV of three projects? What
conclusion we can draw from the calculations?
Solving the problem
S
1
K
1.590832
R
0.15
T
6.591449
sigma
0.5
d1
1.050402
d2
-0.23329
c
0.611885
NPV
0.967405
• In Excel, Click Tools. Select solver,
maximize NPV, by changing fixed cost and
duration.
Solution
Discount rate fixed investment duration
NPV
15%
1.6
6.6
0.97
10%
2
9.2
1.66
5%
2.6
13.8
2.94
Pattern
• Lower the discount rate, higher fixed
investment, longer duration, higher NPV.
• Calculation also shows that marginal profit
stays roughly constant. Variable costs are
around 60% for all three projects.
Discussion
• In other classes, we have discussed how
the level of interest rate affect investment
decisions.
• The advantage of this theory is that the
parameters here, such as the fixed cost,
duration, NPV and profit margins are
determined endogenously. They are not
set up in an ad hoc manner.
Unexpected change
• Continued from the last problem. Suppose
after five years, market conditions change
unexpectedly and as a result, all three
projects have to close down. What are the
realized value of three projects? Realized
values are defined as (S-C)T – K, where T
is the number of years a project actually
operates. What conclusion you can draw?
Solution
realized value 1
0.349741
realized value 2
-0.00256
realized value 3
-0.56495
percentage change from realized value
over expected value
project 1
-0.64
project 2
-1.00
project 3
-1.19
Discussion
• When unexpected changes are few or
unexpected changes are mostly in the
positive direction, production systems do
better in low discount rate environments.
• In the past, with the increasing
consumption of fossil fuels, economy
grows most of the time. Low discount rate
policy benefit economy most of the time.
Discuss (Continued)
• When negative unexpected changes
occur, the production systems in higher
discount rate environment perform better.
• Production systems in high discount rate
environments are less volatile.
• In the future, higher discount rate policy
may serve economy better.
How high discount rate should go?
• Reduce the effort from the central banks
so financial institutions will be more
sensitive to market risks. This will increase
the prevailing discount rates in the market.
• Gradually increase the weight of market
discount rate and reduce the weight of
government power.
Critiques of current monetary
theory
• Policy makers try to maneuver discount
rate to adjust level of economic activities.
• From our theory, the level of discount rate
affect not only current economic activities,
but also future economic activities.
• Low discount rate policy have especially
long term impacts on future economic
activities.
• Low discount rate policy induce individuals and
firms to borrow to consume or to invest, which
stimulate economy. At the same time, policy
makers warn against “excessive” borrowing.
• Policy makers take credit for short term
economic stimulus, but blame the long term
negative impacts to the public. This is the heart
of problem in many different areas.
Stability is destabilizing
• Hyman Minsky: “Stability is destabilizing”
• What does it mean?
• In countries A and B, annual outputs are 1 million dollars
each. Discount rates are 10% per annum each. Common
uncertainty is 55% per annum. However, the government
in country A, through various measures, reduce the
uncertainty level to 15%. Decision makers in A and B
will attempt to maximize the net present value of
investment project. How much will be the desired fixed
costs and how long will be the expected project
durations in A and B? What are the net present value of
the two projects? If uncertainty level in country A returns
to 55% per annum due to reasons unforeseen by policy
makers and business decision makers, what is the net
present value of the project? What conclusion we can
draw from the calculations?
Country B, uncertainty: 55%
S
1
K
R
T
sigma
1.67641
0.1
8.344168
0.55
d1
d2
0.994381
-0.59436
c
NPV
0.639017
1.335689
Country A, uncertainty: From 15% to 55%
sigma=
15%
sigma from 15% to 55%
S
1
S
1
K
6.467525
K
6.467525
R
0.1
R
0.1
T
18.0339
T
18.0339
sigma
0.15
sigma
0.55
d1
0.218962
d1
1.140678
d2
-0.41803
d2
-1.19497
c
0.226577
c
0.749353
NPV
-1.94737
NPV
7.48031
Discussion
• When uncertainty goes up, the original
project with high NPV make heavy losses.
• We will examine how different discount
rates affect the results. We set discount
rate to be 3% and recalculate all the
results.
S
1
K
R
T
sigma
2.334121
0.03
14.39269
0.55
d1
d2
0.843987
-1.24259
c
NPV
0.63847
2.869267
sigma=
15%
sigma from 15% to 55%
S
1
S
1
K
15.85935
K
15.85935
R
0.03
R
0.03
T
67.7881
T
67.7881
sigma
0.15
sigma
0.55
d1
0.026315
d1
2.102939
d2
-1.20869
d2
-2.4254
c
0.275173
c
0.966397
NPV
33.27527
NPV
-13.5815
Discussion
• In a low discount rate environment, the
effects are more dramatic.
• The fixed cost becomes higher, duration
longer and NPV larger.
• When unexpected change occurs, the
magnitude of loss is larger.
• In current economic policy making, low
interest rate is often regarded as the cure
for recession.
Question
• If low interest rate policy have so many
potential problems, why it is still so
popular?
• This is due to low interest rate policy is
good for periods of economic growth.
• In the past several hundred years,
economic output has been increasing due
to the low cost non-renewable resources.
Economic growth and investment
decisions
• When the expected economic growth rates
are different, investment decision will be
different.
Example
• Suppose in a market, current annual sales
capacity is 1 million dollars. Uncertainty is 55%
per annum. Discount rate is 5% per annum.
Decision makers will attempt to maximize the net
present value of investment project depending
on the estimation of expected growth rate. If
expected growth rates are 1%, 3% and 5% per
annum respectively, how much will be the
desired fixed costs and how long will be the
expected project durations? What conclusion we
can draw from the calculations?
Solution
• Suppose the annual growth rate is x.
Market size of the first year is normalized to
1. Then the total market size over n years
(n can be a fractional number) is
(1  x) n  1
x
S
1
K
R
T
sigma
2.316646854
0.05
13.09291999
0.55
c
growth rate
total market size
0.650024306
0.01
13.91460306
NPV
2.553126011
S
1
K
R
T
sigma
2.925933454
0.05
16.00274304
0.55
c
growth rate
total market size
0.690290768
0.03
20.16121852
NPV
3.318182052
S
1
K
R
T
sigma
4.1546
0.05
21.5144
0.55
c
growth rate
total market size
0.7608
0.05
37.1354
NPV
4.7294
Discussion
• When the growth rate is higher, fixed investment
and duration increases and NPV of the projects
increases.
• Calculations show that when discount rates are
lower and uncertainty is lower, the levels of
increase of fixed investment and duration are
more dramatic. This shows when our projections
are more optimistic, we invest more for more
distant future, which could bring more
disappointment if the projected future scenarios
are not fulfilled.
Summary
• In the future, with non-renewable
resources more expensive to process, the
earlier advantages of low interest rate
policies will no more valid while the
potential disadvantages that cause
business cycles will be more prominent.