By Alex White, Head of ALM Research, Redington
However, the second example may need a more thorough model for other risk factors, such as credit and interest rates, and for the interactions between these. Different tasks call for different tools.
In fact, the point is stronger. Excessive detail and complexity is not only unnecessary, it can be harmful. If a model is there to draw out key points, then making the model more confusing and less tractable makes it worse at its core function. It also means key assumptions can be hidden. This risk is largest when a model tries to do too many different things. In general, models should be as simple as possible.
One archetypal example of these trade-offs is in the choice between long-term and short-term models. A pension fund has a long time-horizon, and a long-term model has several advantages:
• It can more directly answer key questions, such as “what is the probability the scheme pays all pensions in full?”
• It can factor in risks which only appear through time, such as the risk of having returns that are stable but too low (which, in DC for instance, can be far bigger than the risk from short-term shocks, especially for younger members).
• It can allow for risks which may have different short and long-term behaviour.
However, none of these benefits come without any disadvantages, and there are a lot of advantages to using a shorter-term model (or, more precisely, using risk figures based on a shorter horizon):
• Better evidence. For example, 100 years of data is 100 disjoint 1-year data points, but only 5 disjoint 20-year data points. A 1-year model will therefore have 100 data points instead of 5, so will have 20 times better data behind it than a 20-year model.
• Less sensitivity to inputs. Compounding means that a small change can lead to significant differences and therefore longer term models will be more exposed to margins of error. If a difference in inputs that is within margins of error is driving a different decision, then the model is not a viable decision-making tool.
• More tractable. It’s almost always easier to understand shorter-term models, which means it’s easier to see why the outputs are what they are.
It is worth pointing out that tractability is not an idle theoretical argument- in the world of pension funds, very clever people have made very clever models for decades, but the track record of investing on the back of them has been poor. This is in large part due to mean reversion assumptions in interest rates discouraging hedging. The models that drove these decisions had theoretical merit, but hid significant risks. In a simpler model, it’s harder to hide anything.
So short and long-term models have different advantages and disadvantages- but how should schemes use them? For me, it’s a case of using different tools for different tasks. A long-term model is better suited to setting big picture goals, like how quickly to target full funding, as it can answer questions more directly. However, because of the lower sensitivity and better evidence, shorter-term risk modelling is a better fit for designing and monitoring a strategy to meet those goals.
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