lecture 3 - state preference theory

Question 1

how is uncertainty modeled?

Answer 1

uncertainty is modeled by assuming that a finite number of S mutually exclusive states of the world can occur in the future

Question 2

what are the assumptions of the states of nature and utility?

Answer 2

homogenous expectations ( all investors assign the same probability for a state to occur)
no transaction costs in portfolio construction
initial wealth and an investors preferences are fixed

Question 3

what does the payoff matrix show for the states of nature and utility?

Answer 3

the future payoffs of all assets can be summarised in an payoff matrix where each row describes the vector of payoffs of a particular asset and each column describes the payoff of all financial assets in particular state of the world.

Question 4

what is linear independence?

Answer 4

assets (vectors) d_A, d_B, d_C are called linearly independent if there are no numbers λ1,λ2,λ3 different from zero such that λ1d’_A +λ1d’_A +λ1d’_A = (0_1,0_2-0_3)

Question 5

what is a complete capital market?

Answer 5

a capital market is callled complete if the number of linearly independent assets is equal to the number of states of the world

Question 6

what is the simple test for linear independence of assets and completeness of a market?

Answer 6

a non zero determinant of the payoff matrix

Question 7

given a complete security market, how can investors eliminate the uncertainty about their future wealth?

Answer 7

they could eliminate the uncertainty about their future wealth by holding diversified (risk free ) portfolios

Question 8

what is arbitrage?

Answer 8

arbitrage is an investment strategy that yields a strictly positive gain today without incurring a loss in any state of the world in the future

Question 9

what is the zero arbitrage principle?

Answer 9

two portfolios with the same state contingent payoffs should be priced identically ( the law of one price in markets)

Question 10

what is a pure security?

Answer 10

a pure security is a asset which pays £1 in a given state of nature and £0 in all other

Question 11

true of false, all assets in the market can be represented using a portfolio of pure security?

Answer 11

true

Question 12

how are prices of securities determined?

Answer 12

they are determined by the supply and demand on the financial market

Question 13

on the supply side, what are the determinents of pure security prices?

Answer 13

the determinents involve the productivity of the capital in different states of the world

Question 14

on the demand side, what are the determinents of pure security prices?

Answer 14

expectations about the probability that a particular state will occur
time preferences for consumption
individuals attitudes towards risk

Question 15

what can the price of pure securities be decomposed into ?

Answer 15

the price of pure securities can be decomposed into P_s = π_s*θ_s
where π_s is the probability of state s and θ_s is the price of a pure security if state s happens with certainty ( state contingent price)
this assumes homogenous expectations such that probability is the same for all individuals

Question 16

what is the formula for the state contingent price θs

Answer 16

the state contingent price for a pure security can be calculated as the £1 payoff discounted by E(R_s) - the expected rate of return if state s happens with certainty
1/(1+E(R_s))

Question 17

what is the firms objective function?

Answer 17

firms objective function is to maximise its share price and any asset can be represented by an equivalent portfolio of pure securities
Price_j = ΣQ_js *P_s
where Q_js is end of period payoffs on firms j shares in state s and P_s is the prices of the pure securities

Question 18

what occurs when firms accept positive net present value projects?

Answer 18

the firms value will increase

Question 19

complete at a later date