# ways to measure interest rate risk for a stock/bond portfolio

We can use effective duration to measure a bond portfolio’s sensitivity to interest rate. But what if the portfolio has stocks and bonds, what do we use?

Assuming that duration still works, how do we calculate the portfolio’s duration? I understand that portfolio duration is the weighted average of the underlying investments’ duration. However, we can’t assume stock’s duration is zero (look at the last week of May and the month of June … how bad equities got hurt when rate spiked 1% due to the tapering rumor)

Any suggestion would be helpful. Thanks.

I think this is a really interesting question. I don’t have the answer but have some points to consider which might aid in the suggestion.

From what I understand there are models that try to calculate stock ‘duration’ based off different models like the GGM - google “A Total Differential Approach to Equity Duration”. Because its derived off the GGM obviously it has the inherent weaknesses of GGM - assumption constant growth, div paying stock etc etc.

My understanding, however, is that there is not a real single standardised measure that enables you to calculate equity interest rate sensitivity per se. I think the main reasons for this are:

1. Duration or dv01 for vanilla interest rate products represent a fundamental inverse relationship: rates higher = bonds lower and vice versa. While the rate of change of dv01 may change (convexity) the inverse price-yield relationship is constant. The problem with equities is that the equity price-interest rate relationship seems to change based on different interest rate market paradigms.

2. The interest rate sensitivity relationship is not the same across stocks. Some stocks are much more sensitive to rates than other stocks (e.g. financials relative to say utilities). While you can have some interest rate products much more interest rate sensitive than others, this is a function of the fundamental characteristics of the respective interest rate product (its coupon and maturity). However for equities, the different characteristics which cause the different rate sensitivities are a multitude of factors that are not ‘built’ within the security.

3. I think equity rate sensitivity can depend on the ‘type’ of rates move. For example the recent moves off the back of tapering chatter have been a rise in real yields. I do not think nominal moves hurt interest rate stocks to the same degree as real moves owing to firm ability to pass through some of the inflation factor. I also think that the equity reaction off the back of tapering was not about the change in rates but was more the pace of the move which spooked the market.

These factors lead to me concluding there is not a standard ‘duration’ number that can be used across the equity spectrum or as part of a stock/bond portfolio. Some ways that might provide indications of the portfolio rate sensitvity may be:

• backtesting the portfolio under different interest rate regimes to analyse how the portfolio is likely to behave in current conditions

• running a multi factor model to analyse portfolio sensitivity to the main risk factors in the portfolio

• if the stocks are publically traded and have a liquid options market looking at the option rho of the options. Admittedly this is the rates sensitivity on the option (which obviously has a shorter duration) rather than the underlying but maybe this is of use?

Am in no way an expert in this area but coming from a rates / FI background am keen to learn more. Let me know your thoughts

I don’t think you will be able to find a way to just quantify interest rate risk on a random stock portfolio. You have to move over to a measure that can handle all types of risk within one measure, like we do in risk management. Better to quantify it in terms of Value at Risk for example, or Expected Shortfall depending on what type of measure you are looking for.