Risk-Averse and Optimal Portfolio Analysis

Question 1

In the Mean-Variance Approach what is the mean?

Answer 1

Expected Return

Question 2

In the Mean-Variance Approach what is the variance?

Answer 2

Risk

Question 3

Why do we not use Expected Utility Theory?

Answer 3

It is too complex to calculate for higher N

Question 4

Does Mean-Variance approach replicate EU Theory?

Answer 4

No it closely approximates, but ignores higher moments of the distribution of returns thus skewness is ignored

Question 5

In Return-Probability space, what does larger spread mean?

Answer 5

Higher risk

Question 6

Why is an investors indifference curve line convex?

Answer 6

Investors expect a higher return for a higher level of risk giving a positive slop and are risk averse meaning they wouldn’t take a fair gamble making it convex.

Question 7

How can an individual get on a higher indifference curve?

Answer 7

If for all levels of risk/return the individual can get higher/lower return/risk.

Question 8

How do you calculate the risk of a portfolio with multiple stocks in mean-variance approach?

Answer 8

Sum of individual stock risks (variance) in portfolio and the risk each stock has on each other (covariance).

Question 9

What is systematic risk?

Answer 9

Market risk, stocks inherently have unavoidable risk due to uncontrollable events.

Question 10

What is unsystematic risk?

Answer 10

Unique risk to the stock/sector they’re in.

Question 11

What is diversification?

Answer 11

The process with which by combining securities to reduce total risk without sacrificing return.

Question 12

What does an effective diversification require?

Answer 12

Negative correlation between stocks.

Question 13

What are the limits to diversification?

Answer 13

1) There is diversification value to holding zero correlation stocks
2) Unique risk falls at a diminishing rate
3) As the number of stocks increase, the number of covariance terms increases by N(N-1)/2 making risk very difficult to calculate

Question 14

What is the efficient frontier?

Answer 14

Set of portfolios that minimise variance for a given expected return

Question 15

How do we proxy ‘riskless’ assets?

Answer 15

Using T-Bills

Question 16

What is the Capital Market Line?

Answer 16

Shows all the combinations of risk/return available to an investor with the inclusion of ‘riskless’ assets.

Question 17

What does the slope show?

Answer 17

The sharpe ratio - the extra return per unit of risk (reward-to variability ratio)

Question 18

What does 1) the Intercept 2) point m 3) any point between intercept and m 4) any point past m represent?

Answer 18

1) The return when entire portfolio is in T-bills
2) The return when entire portfolio is in risky assets
3) The return for a mixed portfolio where individual lends out risky assets to obtain riskless
4) The return where the individual is borrowing at riskless rate in order to invest more into risky assets

Question 19

Where is the optimal risky portfolio?

Answer 19

At point of tangency between efficient frontier and capital market line

Question 20

What happens to portfolio equilibrium when lending/borrowing is introduced?

Answer 20

The investor can get onto the Capital market line which dominates all points on efficient frontier other than point m. This is done by investing fully into risky assets, then trading them off (lending) for riskless assets or borrowing to get more risky assets.

Question 21

What does the separation theorem state?

Answer 21

Whatever the risk preference, all investors hold portfolio m and then borrow/lend at the riskless rate. So the difference between portfolios is just the proportion of risky or riskless assets the investor chooses.