The Expectations Hypothesis

There are four distinct and incompatible versions of the expectations hypothesis. The unbiased version states that current forward rates are unbiased predictors of future spot rates. Let ft T,T +1) be the forward rate at time t for the period from Tto T+ 1 and tt be the one-period spot rate at time T. The unbiased expectations hypothesis states that /Rt,t + i) is the expected value of rj. This relationship is expressed in (3.36). 

The retum-to-maturity expectations hypothesis states that the return generated by holding a bond for term tto Twill equal the expected return generated by continually rolling over a bond whose term is a period evenly divisible into T— t. This relationship is expressed formally in (3.37). 

From (3.36) and (3.37), it is clear that these two versions of the expectations hypothesis are incompatible unless no correlation exists between future interest rates. Ingersoll (1987) notes that although such an economic environment would be both possible and interesting to model, it is not related to reality, since interest rates are in fact highly correlated. Given a positive correlation between rates over a period of time, bonds with terms longer than two periods will have higher prices under the unbiased version than under the return-to-maturity version. Bonds with maturities of exactly two periods will have the same price under both versions. 

The yield-to-maturity expectations hypothesis is stated in terms of yields, as expressed in equation (3.38). 

The left-hand side of (3-38) specifies the yield-to-maturity at time t of the zero-coupon bond maturing at time 77 The equation states that the expected holding-period yield generated by continually rolling over a series of one-period bonds will be equal to the yield guaranteed by holding a long-dated bond until maturity. 

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Dhillon, U., Lasser, D., 1998. Term premium estimates from zero-coupon bonds new evidence on the expectations hypothesis. J. Fixed Income 8, 52-58. 

If the null hypothesis is assumed to be true, say, in the case of a two-sided test, form 1, then the distribution of the test statistic t is known. Given a random sample, one can predict how far its sample value of t might be expected to deviate from zero (the midvalue of t) by chance alone. If the sample value oft does, in fact, deviate too far from zero, then this is defined to be sufficient evidence to refute the assumption of the null hypothesis. It is consequently rejected, and the converse or alternative hypothesis is accepted. 

Therefore, the ratio of sample variances is no larger than one might expect to observe when in fact Cj = cf. There is not sufficient evidence to reject the null hypothesis that Of = <31. 

Given that the measured content for a certain product has been within 2% of the theoretical amount over the past, say, 12 batches, the expectation of a further result conforming with previous ones constitutes the so-called null hypothesis, Hq, i.e. no deviation is said to be observed. 

Figure 1.22. The null and the alternate hypotheses Hq resp. Hi. The normal distribution probability curves show the expected spread of results. Since the alternate distribution ND(/tb, a might be shifted toward higher or lower values, two alternative hypotheses Hi and H are given. Compare with program HYPOTHESIS. Measurement B is clearly larger than A, whereas S is just inside the lower CL(A).

Read the entire laboratory activity. Form a hypothesis about the expected ratios of reacting volumes. Form a second hypothesis about how these ratios can be used to determine the cation to anion ratio in an unknown substance. Record your hypotheses in the next column. 

One-to-one random copolymers of acrylic acid with either hydroxyethyl acrylate (a hydrogel model) or methyl acrylate failed to protect insulin from release under gastric conditions (Figure 6). In the case of the hydrogel, the expected swelling due to exposure to water occurred, releasing insulin. The behavior of the ester copolymer led to the prediction that there should be no more than about four carbon atoms per carboxylic acid group in a repeat unit of the polymers. We have not been able to disprove this hypothesis thus far. 

It is difficult to prove that quaternary ammonium compounds can cross lipid bilayers using cell uptake experiments, since several mechanisms may be operative, and separating contributions from each may be very difficult [1]. It may be an advantage to use PAMPA to investigate transport properties of permanently ionized molecules. Of all the molecules whose permeabilities were measured under iso-pH conditions in 2% DOPC/dodecane, verapamil, propranolol, and especially quinine seem to partially violate the pH partition hypothesis, as shown in Figs. 7.47a-c. In Fig. 7.47c, the solid line with slope of +1 indicates the expected effective permeability if the pH partition hypothesis were strictly adhered to. As can be seen at pH 4... 

For nuclear waste disposal, in a site such as Yucca Mountain, if the maximally exposed individual receives the proposed annual limit of 0.15 mSv, present estimates (based on the linearity hypothesis) suggest a 0.00 1 % risk of an eventual fatal cancer. The maximum dose is reached only if the wastes are dissolved in a small volume of water, and therefore only a limited number of people would receive this dose. If this number were as high as 1000, the implied toll for Yucca Mountain neighbors would be one cancer fatality per century per repository site.19 This toll would not start for many centuries, when the waste canisters begin to fail, and it not unreasonable to expect that cancer prevention and treatment will be much improved by then. Ignoring this prospect, and assuming many repositories and some doses above the prescribed limit, it still appears that the expected toll would be well under a thousand deaths per century. 

Although the tailoring hypothesis does not fit the data, there is another hypothesis that works just fine. It is the idea that antidepressants are active placebos. That is, they are active drugs, complete with chemically induced side effects, but their therapeutic effects are based on the placebo effect rather than their chemical composition. Their small advantage in clinical trials derives from the production of side effects, which leads patients to realize that they have been given the active drug, thereby increasing their expectancy for improvement. 

Only measurements of adsorption isotherms and determination of the conformation of the adsorbed chains could help the interpretation. One could indeed expect large loops in the first hypothesis and more flatted conformation if hydrogen bonds are predominant. 

The observation that lutein and zeaxanthin occur in the highest concentration in the macula soon raised expectations that the macular xanthophylls may be essential in maintaining structure and function of the retina by contributing not only to risk reduction of macular diseases but also to improving visual performance of the healthy eye, which was the original hypothesis to explain the presence of the macular yellow pigment as mentioned previously. 

If the scatter in Li is due to a dispersion in the initial rotational properties, one would expect that a dispersion is observed in all old clusters, unless they had a different initial distribution of rotation the latter hypothesis is rather unlikely, due to the fact that very similar distributions of rotational properties are currently derived for young clusters. As mentioned above (see also [23]), neither the three 2 Gyr clusters, nor NGC 188 show a significant star-to-star scatter. Although in all the four clusters fewer stars than in M 67 have been observed, both [18] and [22] provide convincing arguments that the lack of a scatter in these clusters is not due to low number statistics. 

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