Risky stock holding

Question 1

Return and riskiness of on an asset

Answer 1

= sum of each possible return multiplied by probaility of occuring.

-Riskiness refers to the variation around the expected reutn, given by the standard deviation of the asset returns:

σ(X) = sqrt( π1*(X1 - E(X))^2 + … + π1(Xn - E(x))^2 )

Question 2

Sharpe raito

Answer 2

-Measures the return of an asser relative to risk.

-Shapre ratio = Expected return - Risk free rate ) / Standard deviation

Question 3

Why is second derivative of utility function not suitable measure of risk aveersion?

Answer 3

-The second derivative of the utility function should represent identical preferences as the untility function however the second does not. Therefore not an appropriate measure of an indivuals risk preference level.

Question 4

Absolute risk averion (measuring risk aversion) + what it shows

Answer 4

-Measure of Absolute risk aversion given by:
A(W) = - U’‘(W)/U’(W)

-Involves absolute levels of wealth

-A(W) is increasing in risk aversion, therefore is one persons A(w) is greater they are more risk averse.

-The coefficient of this measure displays information about an individuals preferences not numerical representations of them.

Question 5

Relative risk aversion (measure of risk aversion) + what it shows

Answer 5

-Relates to percentage changes in weath rather than absolute levels with A(W)

-Given by R(W) = -WU’‘(W) / U’(W)
Simplified to: W * A(W)

-R(W) shows how an individual responds to % change in wealth

Question 6

Decreasing, increasing and constant abolsure risk aversion + derivative

Answer 6

DARA: as individuals wealth increases individual becomes less risk averse.
A’(W) < 0

IARA: as indivdiauls wealth increases individual becomes more risk averse.
A’(w) > 0

CARA: as wealth increases the same level of risk aversion will be maintained. A’(w) = 0

Question 7

Decreasing, increasing and constant relative risk aversion + derivative

Answer 7

IRRA: as wealth increases individual becomes more risk averse proportionally. They will invest a smaller % in risky assets R’(W) > 0

DRRA: increases in wealth lead to greater risk aversion proportionally. Individual will hold higher % in risky assets. R’(W) < 0

CRRA: Individual will maintain level of risk aversion and % of holdings in risky assets. R’(W) = 0