risk and decisions

Question 1

what is the discount factor?

Answer 1

1/ [(1+r)^n]

Question 2

what do we need to know to find the present value?

Answer 2

the size of the cash flow
when it arrives
the interest rate (sometimes called the cost of capital or the required rate of return)

Question 3

how do you deal with uncertainty with the annual sales?

Answer 3

if the annual sales are uncertain, we can work out an expected value of sales using probabilities. if there are three states of the world, low medium and high demand and we are told the possible sales levels and their associate probabilities. simply apply the cash flow per unit to get cash flows in each state of the world. then apply the probabilities to calculate the expected cash flow for each year and then sum up the states.

Question 4

what is the expected utility function?

Answer 4

U(x) = [ p1 x u(X1)] + [p2 x u(X2)] …. + [pn x u(Xn)]

Question 5

what is the utility of the expected payoff?

Answer 5

the utility obtained by the expected payoff ( the money itself)

Question 6

what is the expected utility of the payoff?

Answer 6

this is the expected utility of the possible payoff (this is like the utility of the gamble)

Question 7

what does it mean to be risk neutral

Answer 7

the agents only care about the expected value ie u(x)=x
U[E(x)] = E[U(x)]

Question 8

what does it mean to be a risk seeker?

Answer 8

risk seekers are more willing to take risk - U[E(x)] < E[U(x)]

Question 9

what does it mean to be risk averse?

Answer 9

agents dislike risk so the u(x) is concave - U[E(x)] > E[U(x)]

Question 10

what is a certainty equivalent?

Answer 10

it is the value of the payoff which if we know we will have it with certainty, gives us the same utility as the risky payoff. in other words if you have a gamble which could give you an expected pay off of £x, how much certain money would give you the same utility

Question 11

how do you calculate the certainty equivalent?

Answer 11

you start with a utility function, for example lets say you have a risk averse with a function of u(x) =x^0.5. imagin a pay off with 4 and 9 with 50/50 chance. so 0.5x4^0.5 + 0.5 x 9^0.5 = 2.5 = E[U(x)]. you now work backwards with in this case squaring it to find the certainty equivalent so 2.5^2 = 6.25 which is equivalent to the expect 6.5= 4x0.5 + 9x0.5

Question 12

what is the markowitz risk premium?

Answer 12

the difference betweent the expect pay off and the certainty equivalent

Question 13

what does the utility(x) against x look like for a risk neutral person?

Answer 13

the curve is a straight line for a risk neutral person

Question 14

what does the utility(x) against x look like for a risk averse person?

Answer 14

the curve is concave for a risk-averse person

Question 15

what does the utility(x) against x look like for a risk seeking person?

Answer 15

the curve is convex for a risk seeker

Question 16

what gives demand for insurance?

Answer 16

the fact that economic agents are risk averse gives demand for insurance as insurance offers payment if a bad outcome occurs

Question 17

what is complete or full insurance?

Answer 17

it is a policy that leaves the insured equally well off irrespective of the outcome

Question 18

where do we get the probabilities from?

Answer 18

we get the probabilities from past data, professional judgement or survey data

Question 19

what is called non sample information and what is the potential issue?

Answer 19

past data which has been modified to allow for current market conditions, new technology etc
it might be subjective

Question 20

how do you make better decisions?

Answer 20

you need to get better information