How do I decompose portfolio exposures when assets may have exposure to a few of my risk factors?

For instance I have some sector and state specific risk factors. If I have a bond with exposure to two of these factors (ex- Tobacco and NJ are two of the factors so in this example I have a NJ Tobacco security) how do I split the bond's exposures across these factors?

• you'd typically use a risk model for this (eg, Barra, Axioma, etc) – Chris Jun 27 '19 at 18:52
• There is no splitting. If you add a bond worth USD 1000 to a portfolio it will contribute 1000 to the NJ exposure total (and zero to other U.S. states) and also contribute 1000 to the Tobacco exposure total. Both totals can be subject to an upper limit at the portfolio level. – Alex C Jun 27 '19 at 21:19
• @AlexC thank you that is very helpful. How does the math work in that scenario? Are you not double counting that securities exposure in the portfolio? In your example I've now allocated $2000 of risk with$1000 of true exposure to that security? – Ryan Wilkinson Jun 27 '19 at 22:30
• It might be useful to look at a manual for risk models such as Barra, Axioma, Northfield to see how they handle things. Or to mention more about the context for your question. Otherwise the whole discussion is at too high and vague level. – Alex C Jun 27 '19 at 23:21
• @AlexC sorry, was trying to simplify for question purpose. I have read Axioma's and believe they have a regression based loading scheme. My question is primarily around how I would do this if I am mapping my exposures otherwise. In your example, wouldn't my exposure matrix be x2 counting the weight of one CUSIP? Say it was 2% of the weight, I'd be reflecting a 2% exposure to NJ and a 2% exposure to Tobacco? – Ryan Wilkinson Jun 28 '19 at 0:04