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Notes Belk College Of Business (PowerPoint) by liaoqinmei


									  Chapter 5

Yield Curve Analysis - 1

   The purpose of this chapter is to give you a very brief
    introduction to the economic theory of interest rates
    and how they relate to the larger economy.
   The main points to take from this chapter are:
       What is the business cycle, and why does it affect interest
       What is the “real” rate of interest and how does it differ from
        the “nominal” rate of interest.

                   Business Cycles
   Economic growth is a dynamic process, at times the
    economy grows very fast, at other times it barely
    grows, and occasionally it contracts.
   Frequently this dynamic process is presented as a
    “business cycle”, but that really presents an overly
    simplistic view.
       There is no cycle in the sense that economic booms have to be
        followed by “busts”.
       It is possible to have long term economic growth.
       It is the case, however, that when the economy is contracting
        (or growing too slowly), then central banks tend to reduce
        interest rates, and when the economy is growing rapidly, they
        tend to increase interest rates.

                         Business Cycles
   The important point to recognize, however, is that
    central banks cannot arbitrarily set rates at whatever
    level they want, they can only marginally adjust rates.
   Financial assets – including bonds – compete with real
    assets for funds. Ultimately, it is the opportunities in the
    real economy that determine interest rates.
   Taylor’s Rule: (NOT Taylor’s Theorem [different Taylor])
       Target rate = Real Rate + Inflation + ½[actual – target inflation rate] + ½ [output gap]

       Output gap = potential GDP – actual GDP

              Real Interest Rates
   The real interest rate is simply the discount rate that
    equates future consumption with current consumption.
   It ignores the fact that the value of money changes, i.e.
    it ignores inflation (or deflation).
   The book does a nice job of outlining the basic theory of
    real interest rates in a two period world.
   Let’s assume that you start at time 0 with an initial level
    of wealth, W0.
   You can either consumer W0 at time 0, or invest part (or
    all) of it, which will then provide you with wealth to
    consume at time 1.

              Real Interest Rates
   We will denote c0 as your consumption at time 0, I as
    your investment at time 0 (so that W0=c0+I), and you
    consumption in time 1 as a function of your time 0
    investment, i.e. c1=f(I).
   We assume that individuals always seek to maximize
    their own happiness, which we refer to as their “utility”
    (not this is not always the same as maximizing wealth).
   We describe their utility as a function of their time 0 and
    time 1 consumption, U(c0,c1).

             Real Interest Rates
   Economists generally assume that utility is increasing in
    consumption in both c0 and c1.
   We can draw isoquants of utility, which economists refer
    to as “indifference curves” or “utility curves”.

         Real Interest Rates

                        Different utility curves

     0                                c0

             Real Interest Rates
   Consumers will normally wish to be on the highest
    indifference curve that they can attain.
   So at time 0 the person can consume between 0 and W,
    and based on that consumption they will wind up being
    able to consume between 0 and f(W0) at time 1.
   Formally, this is normally set up as a relatively
    straightforward utility maximization problem, subject to
    a budget constraint and an investment opportunity set,

                 Real Interest Rates
max U(c0 ,c1 )
c0 ,c1

subject to
c0  W0  I
c1  f(I)

              U          U
assume that        0 and      0.
              c0         c1

This thus becomes a simple constrained optimization problem (like those you
are solving in the Financial Theory class). The optimal investment level I* is
given by:

        c0 dc1
f'(I)      
        U dc0
                Real Interest Rates
   In words, what this means is that you want to maximize
    your utility, you want to set your investment level to the
    point where your marginal rate of return from you
    investment is set exactly equal to your marginal rate of
    substitution between consumption in period 0 and in
    period 1.
   The graph in the book is somewhat confusing, I’ll post a
    better one later in the week. Two points to remember:
       The higher the productivity of the investment-opportunity set
        (f(I)), the higher will be the real rate of interest.
       The greater the propensity to save, the lower will be the real
        rate of interest.

           Nominal Interest Rates
   Inflation is an increase the price of a good or service without a
    corresponding increase in quality of the good or service.
   The inflation rate between two dates, t and T is defined to be:
                           ~   pT
                          t     1

   Clearly at time t, the price level at time T (T>t) is uncertain, and
    hence so is the inflation rate.

          Nominal Interest Rates
   The real rate of return of on an investment is uncertain
    as well, since the inflation rate is also unknown.
   The best that we can say, is that the expected real rate
    of return Et[Rt] is equal to the nominal return less the
    expected rate of inflation:
                        Et[Rt] = rt – Et[πt]


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