By Cliff M.
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6 Conditioning Information The difference between a conditional and unconditional model is the information set used. If payoffs and discount factors (and therefore, prices) are 30 CHAPTER 2. ASSET PRICING iid, then conditional and unconditional models are the same. t. t. Et [Rp∗ ] = Et [Rp ] By iterated expectations, this gives UMV ⊆ CMV. If a portfolio is UMV it must be CMV, but the converse need not be true. We can also consider the set of minimum variance portfolios conditional on Z, CMVZ . Then CMV includes CMVZ , which in turn includes UMV.
Both the excess return on the tangent portfolio and the SR depend on Rf . Rewriting as σm = E[m]SR, the H-J bound is a function of E[m]. As we change E[m], we get a new Rf , a new tangency portfolio, and a new Sharpe ratio. Plotting σm as a function of E[m] gives us the locus of points comprising the H-J bound. Note that if we know Rf , the the bound is just a point. These results are based on the law of one price (LOP), and do not use the no arbitrage (NA) restricition that m > 0. 21). The NA bound is very similar to the LOP bound for moderate values of E[m], but as E[m] becomes more extreme (higher SR), the NA bound is much stricter (higher).
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. Instead of a binary reject/fail to reject result, the HJ bounds offer some insights as to why the model may be rejected. The model is most useful for testing models like the consumption model where m is explicitly specified.
Finance notes by Cliff M.