By Cliff M.
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Combining these two equations, ˆ =ˆ ˆ =ˆ Dθ c−ˆ e. The attainable set Dθ c ignores the initial endowment. I will abuse notation and consistency by letting Q and π ∗ refer to the EMM. The later is more appropriate for discrete settings. Also, dividend (payoff) vectors and matrices are indicated by d and D. Definition 1 The market is complete iff every consumption process is attainable (M = X), or iff rank(D) = k. Definition 2 An arbitrage strategy has non-negative, non-zero consumption ˆ ≥+ 0 with e(0) = (0); Dθ Definition 3 An Equivalent Martingale Measure Q (or π ∗ ) satisfies p = D π ∗ /Rf .
A bond has: 1. fixed, known maturity 2. fixed, known terminal (face) value 3. fixed, known periodic cash flows 4. more thinly traded (at least “older” issues) Term structure models can be viewed as time series models of the stochastic discount factor. 4 Forward Rates Forward rates had been viewed simply as forecasts of expected future spot rates (PEH). ) shows that the forward rates also contain expectations of the premium above one month T-bills. • Holding period return is the change in log price on a particular bond from one period to the next.
The market) will be mean-variance efficient. In other words, the content of a model comes from m = f (·), not p = E[mx]. Also, given any multi-factor or multi-beta representation, we can always find a single beta representation. The relationship between the ICAPM and CCAPM is an example of this. m as a Portfolio The portfolio that maximizes squared correlation with m is a minimum variance portfolio. m∗ , the projection, also prices assets and can replace m. 6 Hansen-Jagannathan Bounds The Hansen and Jagannathan (1991) bounds are an important addition to asset pricing.