Dependencies and diversification - a follow up to the IFoA sessional meeting in March

Interest rate chart

The presentation of the paper was followed by a very interesting discussion on dependencies with contributions from members of the audience. Two key themes emerged from the discussion: the tools used to model dependencies; and the current state of dependencies between interest rates, inflation, and equity markets.

One member felt the paper could be a useful repository, particularly for those looking to build structural models of market risks and their interactions. While I don’t have much practical experience of such models, it does strike me that such models are worthy of further investigation as there are issues with copula techniques that struggle where risks may be connected in different directions.

A key example of this is interest rates and equity e.g. in recent times, there has been a positive correlation between falling gilt yields and equity markets, due to “flight to quality” and authorities reacting to market falls with Quantitative Easing (QE). However, in the past, during the high inflation, high yield “boom and bust” periods of the 1970s and 1980s, the correlation was in the opposite direction, with spikes in inflation leading to rising base rates and gilt yields and falling equity markets.

Copulas can struggle with this relationship in both directions. By way of follow-up to the discussion, I did some simulation of the probability of a 1-in-10 rise in gilt yields coupled with a 1-in-10 fall in equity using a Gaussian copula and assuming a positive correlation of +50% between equities and gilt yields, consistent with the Solvency 2 Standard Formula correlation between equity risk and downward interest rate risk. The joint probability simulated is ca.0.07%, effectively ascribing a near zero probability to a modest rise in gilt yields triggering an equally modest self off in equities. Actuaries involved in economic capital modelling should review their own models and see if these are giving similarly low likelihoods to scenarios where rises in gilt yields (risk-free rates) trigger equity falls, and whether this is appropriate for their firm’s risk profile.

There was a lot of discussion as to state of correlations between gilt yields and equity markets, and whether the recent paradigm of positive correlation has been replaced with the negative correlation seen in the 1980s when spikes in inflation pushed up base rates and gilt yields, triggering equity and other market falls. I must admit it is difficult to tell. The current spike in UK inflation is the severest test of the Bank of England’s inflation-targeting monetary policy since this was introduced in 1992. One would hope current high inflation is transient and that the Bank is able to bring inflation back under control but if not, we could find ourselves in the higher inflation, higher interest rate paradigm more like the 1980s with rising interest rates driving down markets as opposed to falling markets triggering rate cuts and QE.

To sum up, I intended the paper to be a starting point for actuaries when considering dependencies between risks and correlation assumptions, but I believe there is a lot more work to be done in this field, including refining approaches and also in keeping abreast of economic developments. I look to seeing more research in this area going forward.

The paper and discussion will be published and freely available in the BAJ in due course. https://www.cambridge.org/core/journals/british-actuarial-journal 

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