Economic Behaviour

Question 1

How can it occur where two random variables X and Y have the following properties:
Variance of X exceeds that of Y but the LSV of Y exceeds that of X

Answer 1

Left skewed distributions have a higher LSV relative to their variance so we must make sure Y is further left skewed than X

Question 2

What does first order stochastic dominance mean?

Answer 2

If B stochastically dominates A to first order then Fa>=Fb for all values . Must compare the cdfs to prove this

Question 3

What does secondorder stochastic dominance mean?

Answer 3

If B stochastically dominates A to second order then Integrated Fa>= Integrated Fb for all values . Must compare the integrated cdfs to prove this

Question 4

If we know a persons wealth distribution and their utility function how do we find their expected utility?

Answer 4

Expected utility is integral of U(w) * fx(x) where X is the wealth distribution dx

Question 5

By expected utility what would a person prefer

Answer 5

More to less - higher expected utility is preferred

Question 6

How does one show there is no increasing concave utility function under which an investor prefers E to U

Answer 6

Show U has 2nd order stochastic dominance over E

Question 7

If given integral of a complex cdf - how can we proof it holds

Answer 7

Avoid integration - differentiate the right hand side and show that its equal to the cdf plus a constant

Question 8

How to verify the stationary distribution of a matrix?

Answer 8

Stationary distribution * transition matrix = stationary distribution

Question 9

how find stationary distribution

Answer 9

Solving Pi*P=pi
Write out the equations this implies and then add in the condition that elements of pi must sum to 1

Question 10

Formula for value at risk @Alpha confidence

Answer 10

Current asset value minus the 1-Alpha % quantile

Question 11

How to calculate the ith percentile

Answer 11

Mean - SD*NORMINV(100-I)

Question 12

Why might the expected shortfall produce a lower number than the value at risk with less extreme confidence interval

Answer 12

Expected shortfall takes an average of the scenarios from confidence level to 100% confidence where VAR uses a single figure at chosen confidence level. As the loss is generally convex as a function of the confidence level the average of the worst several percent is generally more sever than a single event

Question 13

How to calculate expected shortfall

Answer 13

solve to maximize Expected losses beyond some k : E(k-X,0)
K can be found as the constraint P(Losses<k)<=alpha
k= mean-SD*NORMINV(1-alpha)

The expected shortfall is:
Current value - (k-Emax(k-x,0)/alpha)

Question 14

If Z and Y have the same distribution and are independent CaN we say LSV(Y+Z)=LSV(Y)+LSV(Z)

Answer 14

Depends - not necessarily CLT there is no reason why LSV is additive for independent sums

Question 15

Explain anonaly

Answer 15

Studies show that market overreacts to certain events and under reacts to others. And takes a long time to correct.
If this is true then traders could take advantages of the correction fof markets and efficiency here would not hold
in the EMH framework things that cause an overreaction or underreaction in the market are called anomalies in the EMH framework ex: Past performance where past winners tend to be future losers, market might appear to overreact to past performance

Question 16

Explain volatility testing

Answer 16

Volatility tests arose in the 80s as observations yielded commnts that stock prices were excessively volatile and that
In the context of EMH thhere was a view the volaitlity of stokcs could nto be justified by purely news.
This was claied to b=to be evidence of market overreaction anomalies.
The volatility tests that was first carried out found apparent evidence that volailtity contradicted Emh as actual price was not in lune with subsequent fluctuations ind ivdends. However
Others have done subsequent testing to find different results

Question 17

How can we tell for an increasing utility function which of several options an investor would prefer?

Answer 17

Find options that are first order stochastically dominant over each other. If FSA<=Fb for all values then B is eliminated as an investment option

Question 18

How can we tell for a risk averse utility function which of several options an investor would prefer?

Answer 18

We need to look at second order stochastic dominance

Question 19

How to calculate the expected mean ^2 not using integrals

Answer 19

Expected value ^”+SD^2