mon_econ_weeks4-5_algebra

# mon_econ_weeks4-5_algebra - T HE EXPECTATIONS APPROACH T O...

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THE EXPECTATIONS APPROACH TO THE TERM STRUCTURE THE FORWARD INTEREST RATE [p.552): t+krn.t : the expected interest rate - where n is the term to maturity of the security, t is the point in time at which the expectations are held, and t+k is the beginning of the period at which the interest rate becomes applicable. THE 'SPOT' RATE 1p.5521: r,,, : the actual interest rate prevailing at time period t, for a security with n periods or 'years' to maturity. These latter rates are observable, known data. THE ZERO-PROFITABLE-ARBITRAGE OR EQUI- PROFITABILITY CONDITION lp.5521: (1+r2,,)(l+r2,,) = (l+rl,t)(l+t+lrl,~ [J&H equation 131 SUPPOSE INITIALLY r,,, = r,,, . THEN EQULIBRIUM REQUIRES: AND THEREFORE: That is to say, the actual one-'year' or one-period rate in period one is expected to prevail also (or to remain the same) in period two: 'short' rates are expected to remain constant, and therefore 'long' rates equal 'short' rates. SUPPOSE NOW THAT ,+,r,,, RISES ABOVE r,,, - SHORT-RATES IN PERIOD TWO ARE EXPECTED TO BE

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