This is a new project for work that I am stuck on and looking for help:

If i am given a factor model (e.g. barra) and a equity portfolio we're trying to hedge, how can I come up with a hedge portfolio that will 1) reduce overall risk and 2) reduce large factor exposures? Assume we have factor exposures for a universe of all stocks, and short selling is allowed.

I don't know where to start! I have taken courses on standard portfolio optimization, but I don't know how to apply it on this problem since I need to first find the list of stocks to go in hedge portfolio then optimize the weights. Since barra gives factor exposures and factor covariance matrix, it seems I have all the inputs but I don't know how to go about finding the stocks to put in hedge portfolio and then find optimal weights.

Please give me any direction on how to approach this!

  • 1
    $\begingroup$ Welcome! If you have access to the Barra Model, you can easily find the factor exposure of any stock. So as a first step what I would do in your place is look at 10 or 20 well known stocks that your firm trades and educate myself about the factor exposures that they have. Or look at each factor that Barra defines and find the stocks that have heavy exposure to that factor. $\endgroup$
    – nbbo2
    Dec 20, 2020 at 23:05
  • $\begingroup$ thank you for the comment! I do have access to all barra factor exposures, and I am able to construct the total portfolio exposures if given a portfolio of long and short positions. For either a portfolio or a single stock, I'm wondering what's the next step to build a hedge portfolio to reduce certain exposures? E.g. i want the hedge portfolio to have 50-200 stocks to diversify. Would in this case simply picking the top x stocks with heavy offsetting exposure and making a portfolio with those suffice? How can i find the most optimal one wrt risk + factor exposure reduction $\endgroup$
    – ktong
    Dec 21, 2020 at 2:25
  • $\begingroup$ @noob2 after doing some more reading, I have a rough idea on starting with a basket of stocks with the largest factor z-scores for each factor we'd like to hedge, and then run this basket through the optimizer. I'm wondering if you think it's better to 1) set constraints on this basket to be >= the factor exposures we're hedging for or 2) add our original portfolio into the basket to optimize everything together? ideally we'd want the notional of hedge basket to not be larger than our portfolio notional $\endgroup$
    – ktong
    Dec 22, 2020 at 22:02

1 Answer 1


You can start by looking at the overall factor exposure of your portfolio (or fund of funds portfolio) and compare it with the index factor exposure.

Factor exposure can be obtained using either return based or holding based analysis (my preference is to go with holding based factor analysis).

Then you would compare your portfolio factor exposure relative to the index.

By doing so, assume you find that your portfolio is overweight growth as a style compared to the index; and you want to hedge it by being overall style neutral.

Then you technically have several options, some of which are:

1- construct another portfolio that would increase other factors (value, momentum,...) and hence it would reduce your exposure to growth.

2- or; reduce growth exposure by shorting a smart beta growth ETF

You can use an optimizer to obtain the optimal solution to such problem; however, you have to define the objective first.

In my example, the objective I want to solve is to be style neutral compared to the index.

  • $\begingroup$ thank you for the breakdown! so for us there is no index we're trying to replicate factor exposures of, we just want to hedge anything that's overexposed. So if I go by 1- construct another portfolio that will increase other factors (e.g. find a portfolio with offsetting exposures), how do I go about finding each security that goes in that portfolio? $\endgroup$
    – ktong
    Dec 28, 2020 at 14:03
  • $\begingroup$ Obtain characteristics for each factor, for instance: for value: Price/Free cash flows. Then calculate such characteristic for all stocks in the universe. Then rank them. Then for each stock check in which decile/quintile they reside. Some use Z Scores for each security compare to a universe. For the case for free cash flows, the lower the z score the more value the stock is. I hope that helps. You will have to do that for every month because characteristics change. Hence there are provides such as MSCI which give you the data ready on a monthly basis for a number of factors. $\endgroup$
    – user28909
    Jan 1, 2021 at 4:16
  • $\begingroup$ How do you define overexposed? IMHO this only makes sense relative to a benchmark unless you pick some arbitrary level. But then again, this arbitrary level needs to be motivated somehow which leads back to a benchmark. $\endgroup$
    – oronimbus
    May 15, 2023 at 6:43

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