Lecture_05

# Lecture_05 - 5 The Expectations Hypothesis A Motivation The...

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1 5 The Expectations Hypothesis A Motivation The expectations hypothesis should really be called the expectations hypotheses – plural. There are in fact more than one expectations hypothesis! One expectations hypothesis relates to a simple technique for computing present values. This hypothesis is of immense practical importance. The second relates to the ability of forward rates to forecast future (realized) spot rates of interest.

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2 Figure 5.1: The Graph of an Upward Sloping Forward Rate Curve T f(t,T) r(t) | | | | | 0 1 2 3 ... τ
3 The second form of the expectations hypothesis implies that an upward sloping forward rate curve predicts that spot rates will increase. This is a commonly held belief. Unfortunately, in general, it is not true. In fact, neither of the two expectations hypotheses are empirically valid. But, then, why study the expectations hypotheses? Although the expectations hypothesis is not true in its stated form, and not used again in the text, a modification of it is! It is important, in understanding this application, to first understand the traditional form of the expectations hypothesis.

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4 B Present Value Form To characterize this hypothesis, we first define a liquidity premium (sometimes called a term premium or risk premium ), ) ( ) , ( )) , 1 ( ( ) , ( 1 t r T t P T t P t E T t L + ( 5 . 1 ) for 1 t+ 1 < T ≤ τ . The present value form of the expectations hypothesis is that ) ( ) , ( )) , 1 ( ( 0 ) , ( 1 t r T t P T t P t E ly equivalent or T t L = + = (5.2)
5 In the theory of investments, it is normally believed that traders are risk averse , and the riskier the investment (financial instrument, e.g. common stock), the higher the expected return must be (in equilibrium) to induce traders to hold it. In these equilibrium asset pricing models, the liquidity premium is the compensation that risk-averse traders require for bearing risk. The empirical literature supports the validity of this theory – riskier assets earn higher expected returns.

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6 If investors are risk-neutral , then they do not care about risk. By definition, risk neutral investors only care about expected returns. In an equilibrium economy consisting of only risk neutral investors, the excess expected return on all assets, including bonds, must be zero. This gives the first motivation for the present value form of the expectations hypothesis. It is consistent with economic equilibrium in a risk neutral economy . Unfortunately, the evidence is inconsistent with this justification and few (if any) economists believe that investors are risk neutral.
7 The second motivation for the present value form of the expectations hypothesis can be obtained by rewriting expression (5.2) in an equivalent form.

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## This note was uploaded on 12/09/2008 for the course NBA 5550 taught by Professor Jarrow,robert during the Fall '08 term at Cornell.

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Lecture_05 - 5 The Expectations Hypothesis A Motivation The...

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