Monetary Theory and Business Cycles by pengxuebo


									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
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

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
• 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.
• In other classes, we have discussed how
  the level of interest rate affect investment
• 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?

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
• 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
• 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
• 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                            1.67641
R                                0.1
T                           8.344168
sigma                           0.55
d1                          0.994381
d2                          -0.59436

c                           0.639017
NPV                         1.335689
    Country A, uncertainty: From 15% to 55%

   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             7.48031    NPV             -1.94737
• 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
S             1
K       2.334121
R           0.03
T       14.39269
sigma       0.55
d1      0.843987
d2      -1.24259

c        0.63847
NPV     2.869267
   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
• 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.
• If low interest rate policy have so many
  potential problems, why it is still so
• 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
• When the expected economic growth rates
  are different, investment decision will be
• 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?
• 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
S                            1
K                   2.316646854
R                          0.05
T                   13.09291999
sigma                      0.55
c                   0.650024306
growth rate                0.01
total market size   13.91460306
NPV                 2.553126011
S                            1
K                   2.925933454
R                          0.05
T                   16.00274304
sigma                      0.55
c                   0.690290768
growth rate                0.03
total market size   20.16121852
NPV                 3.318182052
S                        1
K                    4.1546
R                      0.05
T                   21.5144
sigma                  0.55
c                    0.7608
growth rate            0.05
total market size   37.1354
NPV                  4.7294
• When the growth rate is higher, fixed investment
  and duration increases and NPV of the projects
• 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.
• 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.

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