Optimal diversification Flashcards
Who developed mean-variance portfolio analysis?
Markowitz (1952)
What is Mean-variance analysis?
Where investors select portfolios that maximize expected returns E(R) for a given level of risk
Ways to solve it?
There are different ways to solve the mathematical problem but give identical solutions
What does the optimization do?
Gives us optimal weights to invest in the assets.
Budget constraint when investing
Whenever you invest the weights will add to one. you should invest all your budget
Global minimum Variance portfolio (GMV)
If you are completely risk averse this is the portfolio you will hold. This is when risk is minimised.
What do the optimal weights come from?
The optimality conditions of the quadratic programming problem
Efficient frontier portfolios
every portfolio on the efficient frontier is a different combination of the assets or portfolios.
What do optimal portfolios on the unbounded mean-variance frontier include?
Both positive and negative weights
Positive weights
When an investor buys an asset. This is called a long position. Predicting the asset is going to do well.
Negative weights
When an investor short sells the asset. A short position. A prediction the asset is going to do badly going forward.
Short selling
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
Process of short selling
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.
How is short selling possible?
Because index funds lend out assets and in return they receive lending fees.
Risk-free asset
An asset with a certain return. Zero variance. and zero covariance with any of the other assets
Risk free asset example
Short term government treasury bill. Zero coupon bond.
When you add non risky assets what happens to the efficient frontier?
It becomes a straight line.
With a high tolerance for risk you would?
Short sell treasury bills and invest in more risky assets
Uses of mean variance analysis
Asset allocation
Equity optimization
Tracking an index
Asset allocation
An investment decision on how an investor allocates wealth across asset classes e.g. international stock markets
Types of asset allocation
Strategic asset allocation
Tactical asset allocation
Strategic asset allocation
Pension funds - long term optimal mix of assets.
Tactical asset allocation
You can change the optimal weights if you change the inputs. Short term strategy.
Equity optimization
Stock selection.
What’s the best portfolio to hold within the stock market.
Large scale portfolio optimization. Relative to a benchmark
How to calculate residual returns
Asset returns - benchmark return
Tracking index
Can use mean-variance optimization to minimize the tracking error relative to a specific field
Criticisms of mean variance analysis
1.Variance is a poor measure of risk
2.Only consistent with expected utility maximization under restrictive assumptions
3.Only a single period model
Why is variance a poor measure of risk?
Because it treats upside and downside volatility equally, while investors are typically only concerned with downside risk
What are some alternative measures of risk to variance?
Lower partial standard deviation and Value-at-Risk (VaR).
Do alternative risk measures lead to significantly different portfolios than mean-variance strategies over short horizons?
No, they often lead to similar portfolios over short return horizons (Michaud and Michaud, 2008)
How does investment horizon affect the appropriateness of using variance as a risk measure?
For investment horizons over 1 year, variance becomes a poor measure of risk.
Under what conditions is mean-variance analysis consistent with expected utility maximization?
Only under restrictive assumptions
What is one key assumption of mean-variance analysis regarding asset returns?
That asset returns have a normal distribution.
Is the assumption of normally distributed returns valid for U.S. stock returns?
No, it can be rejected according to Kan and Zhou (2017).
How do optimal portfolios from utility maximization compare to mean-variance portfolios over short return intervals?
They are often similar
What are examples of short return intervals in portfolio analysis?
Monthly or quarterly
Is mean-variance analysis effective for long investment horizons (beyond one year)?
No, it becomes less useful for horizons beyond one year.
What is a key limitation of mean-variance analysis in terms of time horizon?
It is a single period model
Why is investment decision making considered a multiperiod problem?
Because investors typically plan over long horizons involving multiple time periods.
What did Grauer and Hakansson (1986) develop to address the multiperiod nature of investing?
A multiperiod investment rule based on a power utility function.
What is the assumption behind solving a series of single-period problems in mean-variance analysis?
That investors are myopic (short-sighted)
How can mean-variance portfolios be interpreted over short return horizons in the context of multiperiod strategies?
As an approximation of the optimal multiperiod strategy.
