Chapter 20

Question 1

indifference curve

Answer 1

An indifference curve is a tool from economics that, in this application, plots combinations of risk (standard deviation) and expected returns among which an investor is indifferent

Question 2

Investor Utility Functions

Answer 2

investor’s utility functions represent their preferences regarding the trade-off between risk and return (i.e., their degrees of risk aversion).

Question 3

Formula for expected return and SD of port. and the reduction of it since asset B is risk-free:

Answer 3

Question 4

capital allocation line

Answer 4

The line representing these possible combinations of risk-free assets and the optimal risky asset portfolio is referred to as the capital allocation line.

Question 5

When correlation goes down, what happens to the Standard Deviation ?

Answer 5

Correlation goes down and risk of portfolio goes down as well.

Question 6

Step One:

Get the Mean Return

Answer 6

Question 7

Step Two, get the port variance (standard deviation)

Know Formula

Answer 7

Question 8

Step Three, get Covariance

Know Formula

Answer 8

Question 9

Step Four, get the Correlation

Know formula for COVab and Pab

Answer 9

Question 10

Formulas:

Var Port

Weight of asset 2 given W1

Correlation (2 formulas)

Variance of Portfolio with correlation instead of Cov

Var port = Sigma squared port so know the formula for this.

Answer 10

These are the steps

Question 11

Formula for when correlation = 1 and when correlation = 0

Answer 11

Focus on highlight.
If corr are perfect positive, then use formula above
If correlation is zero , then use formula above.

Question 12

The variance of returns is 0.09 for Stock A and 0.04 for Stock B. The covariance between the returns of A and B is 0.006. The correlation of returns between A and B is:

Answer 12

Question 13

A portfolio was created by investing 25% of the funds in Asset A (standard deviation = 15%) and the balance of the funds in Asset B (standard deviation = 10%). If the correlation coefficient is -0.75, what is the portfolio’s standard deviation?

Answer 13

Question 14

True or False, Expected returns are affected by correlation.

Answer 14

False, expected returns are UNAFFECTED by correlation

Question 15

True or False, Combining assets that have lower correlation coeff get the same return for lower risk.

Answer 15

True

Question 16

Global Min Variance Portfolio

Answer 16

the port that’s got the min variance OVERALL.

Question 17

Efficient Frontier

Answer 17

Set of port., among all the possible port of individual risky assets, that offers the highest expected return for each level of risk (standard deviation)

Question 18

Correlation Definition.

Interpretations:

Correlation of Zero

Correlation +1

Correlation -1

Answer 18

Correlation is LINEAR RELATIONSHIP.
We need correlation coeff to understand the RELATIVE DEGREE of covar of two assets A and B

Corr Coeff standardisze the covariance and puts boundaries (because covar doesn’t have boundaries).

We have -1 and +1, it measure strength of linera relationship .. the line between A and b.

Correlation cant be greater than +1 or -1.

Zero correlation means no movement in LINEAR relationship with X and Y. . One has no impact on another. One asset can rise, fall or do nothing and it has no impact on other asset.

Positive correlation 1 means they move together.
+1 it moves in identical method in rate and direction. So if market rise 10% then asset is expected to rise 10%

Negative correlation means it inverse so returns on X increases, return on Y decreases.
-1 they move in opposite direction at the same rate.

Perfect positive correlation (r = +1) of the returns of two assets offers no risk reduction…Corr =1 is the highest risk… if corrr equally you are not getting diversification benefit.

whereas perfect negative correlation (r = -1) offers the greatest risk reduction…. Corr lower than 1 you get some diversification benefit. Where our SD of portfolio will be less than the weighted SD of two assets together.

Question 19

When B is risk free, what is Var Formula

Answer 19

Question 20

Formula - Risk of overall portfolio that has a combo of risky +Rf

Answer 20

Question 21

Port with combo of risky + risk free expected return formula.

Formula Rewritten x 2

W(rf) formula

W(a) Formula

Answer 21

Question 22

Portfolio Standard Deviation formula if correlation = 1.0

Answer 22

W(a)O(a) + W(b)O(b)

Weight of asset A * Sigma A

Question 23

Port Standard Deviation Example:

Answer 23

Question 24

Port Returns Variance Formula.

SigmaRP Formula
Covar formula

Correlation=1 formula for SigmaRP
Correlation < 1 formula for Simga RP

Answer 24

Perfect positive correlation (r = +1) of the returns of two assets offers no risk reduction…Corr =1 is the highest risk… if corrr equally you are not getting diversification benefit.

whereas perfect negative correlation (r = -1) offers the greatest risk reduction…. Corr lower than 1 you get some diversification benefit. Where our SD of portfolio will be less than the weighted SD of two assets together.

***Correlation coeff falls, you get diversification benefit, getting hither or equal return with lower risk.

Question 25

As corr coeff fall, what happens to variance and risk?

Answer 25

As corr fall, variance adn risk fall.