individual demand for risky assets Flashcards
How do investors make decisions on which asset to invest in?
decision-making is based on the different forms of dominance or
a comprehensive way is to rank assets by their expected utility
what is a simple lottery (by defn)?
one that only registers the monetary payoffs of every possible outcome,
given any combination of lotteries (compound), can i turn them into a reduced one that displays the different payoffs with their associated probabilities?
What is a rational preference? What is the rational condition necessary for?
Complete and Transitive
Complete: Within a set with n bundles, picking any two bundles there is a preference relation.
Transitive: Ranking must be consistent throughout n bundles, regardless of who is chosen to be ranked.
Rational is necessary for a preference relation to be represented by utility functions.
What does it mean for a preference relation to be continuous?
For n bundles, for two goods, the preference relation needs to be preserved under limits.
If u(X)<u(Y), can these two utility functions represent the preference relation of y strictly preferred to x?
No.
If within a set there exists X, Y, Z, and
X weakly preferred to Y, Y weakly preferred to Z, Z weakly preferred to X
Can I put these relations into a utility function?
No, not transitive means can’t even have a preference relation, so utility functions not possible.
If within a set there exists variables x,y,z, and I don’t know my preference of X relative to Z (not indifferent), can I have a utility function that relates X to Z?
No, not complete, so not rational, so cannot have pref rltn, so no function, so no util fn
If a utility function is transformed into f(u(x)), where f is a constant function, f(x)=p. Would this be representative of the original preference relation?
No. The definition of utility functions is mapping a set of preference relations where x1>x2, if and only if u(x1)>u(x2). In this case, f(u(x1))=f(u(x2)).
What does it mean to say that Asset 1 dominates Asset 2 on a mean-variance basis?
What are the ingredients necessary?
Asset 1 has a higher expected payoff than Asset 2;
Asset 1 has a lower variance than Asset 2
Mean requires, for each state: i) the payoffs, ii) the probability of the payoffs. Use i and ii to get the expected payoff = mean.
Variance can be calculated using the mean and the payoffs. (Variance refers to std dev)
How do risk-neutral investors act when making choosing among assets?
Payoff and price are the only thing that matter
More is preferred
Are always more concerned with the state that has the higher possibility of coming to fruition
A preference relation is such that L is preferred to L’ is preferred to L’’. Add å, where å takes the value in between 0, 1, and all the weights collectively sum to 1.
It will then be the case that, for åL + (1-å)L’ < åL’’ + (1-å)L’. Can these preference relations be represented with utility functions?
What about the separate case where (1-å)L + åL’ < åL’’ + (1-å)L’. Can these preference relations be represented with utility functions?
No. Contravenes preference relation rules, so cannot be represented. No independence. Preferences are independent of any lottery it’s mixed with. This is not a rational decision-maker, as their preferences are not transitive.
The second case is uncertain, as the weights are not the same. Preference relation has insufficient information to make the decision in this case.
