Applied portfolio management

Question 1

Describe problems with mean-variance optimization

Answer 1

-Highly concentrated portfolios
-Unstable portfolio weights that change drastically with input changes
-Not implementable -> extreme short selling
-Not possible to incorporate own view
-Variance is not a good risk measure if return distributino is non-normal
-Thus often poor out-of sample performance

Question 2

How can we solve MPT problems?

Answer 2

Constrain the output
-No short selling constraint
-Restrict maximum weights

Improve the inputs
-Covariance matrix (by increasing data frequency, factor models and shrinkage methods)
-Expected return (by extending data sample and black litterman approach)

Question 3

Describe Black Litterman model and the steps

Answer 3

-Approach to combine investors own subjective view with markets opinion
Steps
1. retrieve equilibrium market weights and compute covariance matrix of assets return using historical data
2. calculate benchmark - implied expected assets return through reverse optimization
3. express investor view Q and confidence level of views omega
4. compute investors adjusted ER

Question 4

Describe BL pro’s and cons

Answer 4

Pros
-Avoid extreme portfolios
-More stable weights
-Allows investors to integrate own views
-Ensure that forecasts are internally consistent
-Manager does not need to have a view on all assets

Cons
-Requires assumption about market risk aversion
-Unclera how to determine own view and its uncertainty
-Assumes that returns follow normal distribution