# What are the steps to perform properly a risk factor analysis on a portfolio?

I have been asked to perform a factor analysis on a given portfolio, assume it's a Swiss portfolio in CHF.

First step, I chose which factors I would like to see in my analysis.

The first factors I would add are components of the portfolio (and used the hedged performance)

• Performance of a global equity index
• Performance of a global fixed income index
• Performance of gold
• Performance of a commodity index

Then I would like to have the forex factors so I add

• EURCHF performance
• USDCHF performance

Finally, I would like to have some macro-economics indicators:

• Change in GDP of Switzerland
• Inflation Rate
• Unemployment rate.

For example.

Si I gave a large bunch of factors, my first question is, some time series have larger values in magnitude than others and I was wondering whether I should normalize them before going further?

Do you think it makes sense to split "pure" stock performance and forex components?

Second Step

I will eventually be looking to do the following:

$$Y_t = \alpha + \sum_{i=1}^k \beta_i {F_i}_t + \varepsilon_t$$

where $F_i, \quad 0<i \leq k$ is the i-th factor and $y_t$ is the return of the portfolio at time $t$.

The problem is that for this to be meaningful we need the different $F_i$ to be independent.

Is there a general accepted method in our field to use to get a set of independent factors? (I asked the question here but I could not come up with a straight answer).

Third step Once this filter is done we have $l\leq k$ independent factors. I was thinking about running the regression over the remaining $l$ factors, and then look at their p-values to see which ones are significant and hence I want to keep. Is there a better usually used in factor analysis?

• Are you really looking for a generaly accepted method? I don't think this exists for anything related to quant finance. I ask this there are probably people that know reference for this but would not post it as a "generaly accepted method". – Zarbouzou May 29 '12 at 10:25
• I was looking for something not too complicated an commonly use, but I'm of course open to any good procedure... – SRKX May 29 '12 at 11:11
• Are you iteratively subtracting-out the considered factor from your portfolio before computing the impact/beta of the next factor? I assume you're already doing that, which should have given you the linear independence you want. – chrisaycock May 29 '12 at 11:14