Good deals in markets with frictions

This paper studies a portfolio choice problem such that the pricing rule may incorporate transaction costs and the risk measure is coherent and expectation bounded. We will prove the necessity of dealing with pricing rules such that there exists an essentially bounded stochastic discount factor, which must be also bounded from below by a strictly positive value. Otherwise good deals will be available to traders, i.e., depending on the selected risk measure, investors can build portfolios whose (risk, return) will be as close as desired to (−infinity, infinity) or (0, infinity). This pathologic property still holds for vector risk measures (i.e., if we minimize a vector valued function whose components are risk measures). It is worthwhile to point out that essentially bounded stochastic discount factors are not usual in financial literature. In particular, the most famous frictionless, complete and arbitrage free pricing models imply the existence of good deals for every coherent and expectation bounded (scalar or vector) measure of risk, and the incorporation of transaction costs will not guarantee the solution of this caveat.

Constructing good deals in discrete time arbitrage-free dynamic pricing models

Recent literature has proved that many classical pricing models (Black and Scholes, Heston, etc.) and risk measures (V aR, CV aR, etc.) may lead to “pathological meaningless situations”, since traders can build sequences of portfolios whose risk leveltends to −infinity and whose expected return tends to +infinity, i.e., (risk = −infinity, return = +infinity). Such a sequence of strategies may be called “good deal”. This paper focuses on the risk measures V aR and CV aR and analyzes this caveat in a discrete time complete pricing model. Under quite general conditions the explicit expression of a good deal is given, and its sensitivity with respect to some possible measurement errors is provided too. We point out that a critical property is the absence of short sales. In such a case we first construct a “shadow riskless asset” (SRA) without short sales and then the good deal is given by borrowing more and more money so as to invest in the SRA. It is also shown that the SRA is interested by itself, even if there are short selling restrictions.

Letter names and sounds: their implications for the phonetisation process

Our aim was to analyse the impact of the characteristics of words used in spelling programmes and the nature of instructional guidelines on the evolution from grapho-perceptive writing to phonetic writing in preschool children. The participants were 50 5-year-old children, divided in five equivalent groups in intelligence, phonological skills and spelling. All the children knew the vowels and the consonants B, D, P, R, T, V, F, M and C, but didn’t use them on spelling. Their spelling was evaluated in a pre and post-test with 36 words beginning with the consonants known. In-between they underwent a writing programme designed to lead them to use the letters P and T to represent the initial phonemes of words. The groups differed on the kind of words used on training (words whose initial syllable matches the name of the initial letter—Exp. G1 and Exp. G2—versus words whose initial syllable is similar to the sound of the initial letter—Exp. G3 and Exp. G4). They also differed on the instruction used in order to lead them to think about the relations between the initial phoneme of words and the initial consonant (instructions designed to make the children think about letter names—Exp. G1 and Exp. G3 —versus instructions designed to make the children think about letter sounds—Exp. G2 and Exp. G4). The 5th was a control group. All the children evolved to syllabic phonetisations spellings. There are no differences between groups at the number of total phonetisations but we found some differences between groups at the quality of the phonetisations.