Uncertainty Flashcards
What is expected value?
- The average outcome from an uncertain gamble
- EV = P(X)X + P(Y)Y
What is true about fair gambles and expected value?
EV = 0 OR the initial income i.e. nothing earned or lost
How can we explain risk aversion?
Utility v Income - straight line under U curve between win and lose
- Despite being fair, the gamble provides less utility than when you know you will receive for sure
What are contingent commodities?
A commodity whose level depends on which state of the world occurs
What is a contingent commodity bundle?
- The point on the graph defined by (consumption if success, consumption if lose) given the bet/situation
- i.e. work out what consumption will be if success and if lose and this combination is the contingent consumption bundle
What are the characteristics of an AFBL?
- EV = P(Y)Y + P(X)X = 0
- Slope: P(X)/P(Y), P/(1-P)
- The expected value of consumption is equal at every bundle along a fair odds line
What is risk aversion?
- Prefer sure thing to a gamble with the same expected value
- MRS = P(X)/P(Y)
- Greater: more towards perfect comp. shape
- Always at endowment point - bet not taken, unless can be on higher utility curve
What is risk neutral?
Indifferent between sure thing and gamble with same expected value
What is risk loving?
Prefer a fair gamble to sure thing with the same expected value
What is the form of an AFBL?
- CL = P(X)/P(Y).Cw + b
- CL: consumption if lose
- m: odds ratio P(X)/P(Y)
- Cw: consumption if win
- Plug in endowment for y-int
What are the steps to determining whether a gamble will be taken?
- Draw certainty
- Determine AFBL
- Determine contingent commodity bundle for taking bet
- Compare to utility curve
What is implied if the contingent commodity bundle falls below the AFBL?
unfair gamble
When will a risk lover take an unfair gamble?
Dependent on the shape of their curve, NEVER more than 90 degrees
When will a risk averse person take a gamble?
- A more than fair gamble, EV > 0
- i.e. a higher utility curve than tangential
What is a risk premium?
- Extra return necessary to compensate for risk
- i.e. making the EV greater
What will different people do if the EV of a risk (B) is the same as certainty (A) i.e. both are a fair gamble?
- A risk loving individual will take B (C.C. Bundle)
- A risk natural individual will be indifferent
- A risk averse individual will take A (tangent point)
What does the risk premium =
The vertical = horizontal distance between the C.C bundle and a risk averse persons utility curve
What is the relationship between how risk averse someone is as the risk premium?
More risk averse: higher R necessary to meet indifference curve
What is actuarily fair insurance?
Premium = EV of payout, r = p(payout) (probability x $1)
EVcompenstation = AFpremium!!!
What is fully insured?
same consumption in both world states, i.e at certainty equivalent
What is true of risk aversion and fair insurance?
If you are risk averse, and offered fair insurance, you will fully insure yourself
What is unfair insurance?
For every $ pay as premium
What is the contingent commodity bundle we are interested in when considering insurance?
Y-Int (i.e. if fire, if injured) (Cfire = 0) (i.e. you get nothing)
What is important about investigating unfair insurance?
Must compare to AFBL (P/(1-P))
What is true of risk aversion and unfair insurance?
- If risk averse fully insuring would put us on a lower indifference curve
- Partially insure (i.e. not down to AFBL endowment point)
What is true of fair insurance in regards to the BC?
AFBL = AFinsurance
What are the steps to a gamble question?
- Determine contingent commodity bundle values
- Determine EV of risk - ONLY lies on AFBC if 0 or ∆0
- Draw indifference curve to suit outcome
What is true if the expected (total) value of a contingent commodity bundle is greater than endowment?
Only that the point is not on the AFBL, whether the risk is taken depends solely on the indifference curve type and then shape
What are the steps to an insurance question?
- IF FAIR: EVcompensation = AFpremium
- Commodity bundle point
- Endowment = EV of situation
- Determine AFBL
- Commodity bundle point - Endowment should = AFpremium
What is the most important thing about insurance questions?
The endowment point is an ideal where the highest U curve would be tangent to the AFBL - the expected bundle (CCB) is the actual situation
How can a risk premium be shown on the I vs U graph?
The utility derived from the expected value of the risk is higher on certainty (normal curve) than the risk line (straight line connecting high outcome and low). Where the utility of the straight line at the expected value intersects the normal curve is x. The risk premium therefore is EV - x
What is true of the bundle in insurance?
Will never be certainty
What is true of the unfair insurance line?
Must pass through the bundle
Who desires insurance?
ONLY risk averse
When will a risk averse person need a risk premium?
If fair and below indifference
If fair but not tangent
If unfair
