Optimal diversification

Question 1

Who developed mean-variance portfolio analysis?

Answer 1

Markowitz (1952)

Question 2

What is Mean-variance analysis?

Answer 2

Where investors select portfolios that maximize expected returns E(R) for a given level of risk

Question 3

Ways to solve it?

Answer 3

There are different ways to solve the mathematical problem but give identical solutions

Question 4

What does the optimization do?

Answer 4

Gives us optimal weights to invest in the assets.

Question 5

Budget constraint when investing

Answer 5

Whenever you invest the weights will add to one. you should invest all your budget

Question 6

Global minimum Variance portfolio (GMV)

Answer 6

If you are completely risk averse this is the portfolio you will hold. This is when risk is minimised.

Question 7

What do the optimal weights come from?

Answer 7

The optimality conditions of the quadratic programming problem

Question 8

Efficient frontier portfolios

Answer 8

every portfolio on the efficient frontier is a different combination of the assets or portfolios.

Question 9

What do optimal portfolios on the unbounded mean-variance frontier include?

Answer 9

Both positive and negative weights

Question 10

Positive weights

Answer 10

When an investor buys an asset. This is called a long position. Predicting the asset is going to do well.

Question 11

Negative weights

Answer 11

When an investor short sells the asset. A short position. A prediction the asset is going to do badly going forward.

Question 12

Short selling

Answer 12

A process that allows you to sell an asset you don’t own. It is a bet that the asset is going to perform poorly

Question 13

Process of short selling

Answer 13

Borrowing from someone else
Sell it into the market and the buy it back at a later date to then give back to the lender.

Question 14

How is short selling possible?

Answer 14

Because index funds lend out assets and in return they receive lending fees.

Question 15

Risk-free asset

Answer 15

An asset with a certain return. Zero variance. and zero covariance with any of the other assets

Question 16

Risk free asset example

Answer 16

Short term government treasury bill. Zero coupon bond.

Question 17

When you add non risky assets what happens to the efficient frontier?

Answer 17

It becomes a straight line.

Question 18

With a high tolerance for risk you would?

Answer 18

Short sell treasury bills and invest in more risky assets

Question 19

Uses of mean variance analysis

Answer 19

Asset allocation
Equity optimization
Tracking an index

Question 20

Asset allocation

Answer 20

An investment decision on how an investor allocates wealth across asset classes e.g. international stock markets

Question 21

Types of asset allocation

Answer 21

Strategic asset allocation
Tactical asset allocation

Question 22

Strategic asset allocation

Answer 22

Pension funds - long term optimal mix of assets.

Question 23

Tactical asset allocation

Answer 23

You can change the optimal weights if you change the inputs. Short term strategy.

Question 24

Equity optimization

Answer 24

Stock selection.
What’s the best portfolio to hold within the stock market.
Large scale portfolio optimization. Relative to a benchmark

Question 25

How to calculate residual returns

Answer 25

Asset returns - benchmark return

Question 26

Tracking index

Answer 26

Can use mean-variance optimization to minimize the tracking error relative to a specific field

Question 27

Criticisms of mean variance analysis

Answer 27

1.Variance is a poor measure of risk 2.Only consistent with expected utility maximization under restrictive assumptions 3.Only a single period model

Question 28

Why is variance a poor measure of risk?

Answer 28

Because it treats upside and downside volatility equally, while investors are typically only concerned with downside risk

Question 29

What are some alternative measures of risk to variance?

Answer 29

Lower partial standard deviation and Value-at-Risk (VaR).

Question 30

Do alternative risk measures lead to significantly different portfolios than mean-variance strategies over short horizons?

Answer 30

No, they often lead to similar portfolios over short return horizons (Michaud and Michaud, 2008)

Question 31

How does investment horizon affect the appropriateness of using variance as a risk measure?

Answer 31

For investment horizons over 1 year, variance becomes a poor measure of risk.

Question 32

Under what conditions is mean-variance analysis consistent with expected utility maximization?

Answer 32

Only under restrictive assumptions

Question 33

What is one key assumption of mean-variance analysis regarding asset returns?

Answer 33

That asset returns have a normal distribution.

Question 34

Is the assumption of normally distributed returns valid for U.S. stock returns?

Answer 34

No, it can be rejected according to Kan and Zhou (2017).

Question 35

How do optimal portfolios from utility maximization compare to mean-variance portfolios over short return intervals?

Answer 35

They are often similar

Question 36

What are examples of short return intervals in portfolio analysis?

Answer 36

Monthly or quarterly

Question 37

Is mean-variance analysis effective for long investment horizons (beyond one year)?

Answer 37

No, it becomes less useful for horizons beyond one year.

Question 38

What is a key limitation of mean-variance analysis in terms of time horizon?

Answer 38

It is a single period model

Question 39

Why is investment decision making considered a multiperiod problem?

Answer 39

Because investors typically plan over long horizons involving multiple time periods.

Question 40

What did Grauer and Hakansson (1986) develop to address the multiperiod nature of investing?

Answer 40

A multiperiod investment rule based on a power utility function.

Question 41

What is the assumption behind solving a series of single-period problems in mean-variance analysis?

Answer 41

That investors are myopic (short-sighted)

Question 42

How can mean-variance portfolios be interpreted over short return horizons in the context of multiperiod strategies?

Answer 42

As an approximation of the optimal multiperiod strategy.