portfolio optimization in practice

[gopala]

I am planning to write a code for solving a portfolio optimization consisting of 73 ETF's. I would appreciate very much if someone can answer the following questions as related to the practical implementation of portfolio optimization:

1. Is the Mean-variance QP as seen in books solved in practice to obtain the optimal portfolio?

2. How are the mean return's calculated if I am interested in monthly resturns to be atleast 5%

3. What techniques are used in practice to determine the covariance structure between the assets?

4. How is CAPM related to solving the Portfolio optimization problem?

5. How are beta's for individua assets with respect to some index calculated in practice?

5. Is it possible to use the betas for the assets in the objective to minimize the risk instead of the QP (this makes the objective linear)?

i.e., min sigma beta_i*w_i
subject to
sigma w_i = 1
sigma w_i*r_i >= 5%
w_i >= 0

Thanks very much for your help.

[jzamoras]

I strongly suggest not to use historic mean, in average is a poor estimator. You may want to check robust optimization. Also, keep in mind that you should always check how your strategy is performing against 1/n portofolio without transaction costs.

best,
jaime

[iqfront]

You could try this: Professional portfolio management and reporting tool

It uses historical daily adjusted closing prices to estimate the covariances and returns, but there is also a functionality to put emphasis on the most recent data in a controlled way. By playing around with it for a while you can assess whether or not the estimates are sufficiently robust for your needs.

[Sam Chan]

Hi there,

1. Is the Mean-variance QP as seen in books solved in practice to obtain the optimal portfolio?
I'm not an industry expert to comment on this. But from the academic papers I have read, it is better to minimize the portfolio's variance instead. Estimating returns are much harder and are subjected to larger errors.

3. What techniques are used in practice to determine the covariance structure between the assets?
You could try the follow:
i) Factor Models (Using principal component analysis...lookup for Alexendra Carol.)
ii) Multivariate Garch Models (Dynamic Conditional Correlation Models)

4. How is CAPM related to solving the Portfolio optimization problem?
CAPM postulates that investors are compensated for taking covariance risk not individual risk. As such, in a similiar vien, for portfolio optimization problems, covariance is important.

5. How are beta's for individua assets with respect to some index calculated in practice?
- Simple OLS.

5. Is it possible to use the betas for the assets in the objective to minimize the risk instead of the QP (this makes the objective linear)?
- Factor models exploit betas to reduce the parameters to estimate for covariance matrix.