1: Portfolio Theory

Question 1

Gamble function G(A,B; α)

What does it mean?

Answer 1

A occurs with prob α

B occurs w prob 1 - α

Question 2

Utility function models

Answer 2

Utility wrt wealth

Question 3

What are the 6 utility axioms?

Answer 3

1. Complete/Comparative
2. Transitive
3. Independent
4. Measurability
5. Ranking
6. Certainty equivalent

Question 4

Principle of Non-satiation

Answer 4

Individuals prefer moer wealth to less.

So u’(w) >0

Question 5

3 types of investors

Answer 5

Risk…
Averse
Neutral
Loving

Question 6

Risk averse investors

Answer 6

Prefer expectation of risk to the risk itself
E (W) ≻ W.
U fnc concave

Question 7

Risk neutral investors

Answer 7

W ∼ E (W )

U fnc linear

Question 8

Risk loving investors

Answer 8

W ≻ E (W )
They prefer the gamble
U fnc convex

Question 9

Risk premium definition

Answer 9

Max amount a RA investor will pay to avoid uncertainty.

Question 10

Absolute risk aversion eqn

Answer 10

A(w) = -u’‘(w) / u(w)

Question 11

Decreasing absolute risk aversion eqn means

Answer 11

We take more risky investments as wealth increases

Question 12

Relative risk aversion shows

Answer 12

Change in prop of risky assets held, as wealth changes

Question 13

Relative risk aversion eqn

Answer 13

R(w) = w*A(w)

Question 14

Mean-Variance Portfolio theory helps us

Answer 14

choose the proportion of each asset in our portfolio

Question 15

What we want with a portfolio

Answer 15

Max expected returns and min variance.

Question 16

Certainty equivalent weath equation

Answer 16

c(W) = invU( E[U(W)] )

Question 17

What is an investment risk measure?

Answer 17

it puts a number of the risk of an asset

Question 18

Most important investment risk measure

Answer 18

Value at risk

Question 19

Value at risk (alpha) meaning

Answer 19

The loss value where there’s only a 1-alpha chance of a bigger loss

Question 20

What is a shortfall measure

Answer 20

int from −∞ to L

g(L−x) f(x) dx

Question 21

semi-var(X)=

Answer 21

int from −∞ to μ

(x−μ)^2 f(x) dx

Question 22

How to find the relationship between risk measures and utility functions

Answer 22

Expand out the E() and use taylor series to make it look familiar, (eg having some terms from Variance)

Question 23

For a portfolio what happens when ρ=-1

Answer 23

basically a risk free asset

Question 24

For a ptflo what happens when ρ=0

Answer 24

The risk/rtn will lie on the sideways curve

Question 25

For a ptflo what happens when ρ=1

Answer 25

risk/rtn will lie on a straight line

Question 26

What does vector Z have

Answer 26

expected rtn for each asset

Question 27

Vector W shows

Answer 27

weights of each asset

Question 28

Σ matrix is

Answer 28

symmetrical covariance matrix

Question 29

What does the two fund theorem make us realise.

Answer 29

An efficient portfolio can be found by combining two or more other efficient portfolios

Question 30

λ=

Answer 30

(C−μB) / Delta

Question 31

γ=

Answer 31

(μA−B)/Delta

Question 32

What does one fund theorum introduce

Answer 32

a risk free asset into our portfolio

Question 33

what does one fund theorem change

Answer 33

the value of mean and var, and therefore the solution to the least var portfolio eqn.

Question 34

what is the tangency portfolio

Answer 34

where the efficient frontier meets the one fund line.

Question 35

to the left of the tangency portfolio, we are still

Answer 35

having some rf asset in the P