The Third Economic Scenario Generator

I can't remember how old I was at the time but I do remember my first epiphany. It was when I discovered that the mince that went into mince pies wasn't the same as the mince that went into a chilli. One of them was made of fruit and spices and called mincemeat; the other was made of meat that had been minced. Why were there these two completely different things on the supermarket shelves, both called mince? If you were sending someone out to the shops or writing recipes, you'd better be pretty clear which sort of mince you were talking about.

Years later, in my first few weeks at PwC, I was asked to put together some training for AIMS (the life actuarial practice) on economic scenario generators. I'm going to call them ESGs for short in the rest of this article. Apologies to those to whom ESG means Environmental Social Governance but, honestly, we got there first. Anyway, I started putting together the training. One question that I was keen to answer was what was the one thing about ESGs that, if you knew it, would set you apart from the majority of actuaries (at the time) and would enable you to engage in meaningful conversations between talks at an industry conference. Quite a challenge, but one that I managed to beat with the first (well, second) slide of my presentation.

ESGs are like mince.

That was the most important thing for any actuary to know about ESGs at the time. Just as was the case with mince, there were two different things on the shelves called ESGs. ESGs aren't like apples. There are red and green apples but they're both apples and (I'm guessing) are interchangeable within recipes. No, ESGs are like mince: there are two things calling themselves ESGs and they're very different to each other.

First, there are real world ESGs. These represent the very best estimates of the probability distribution of future interest rates, spreads, returns, etc. Plug them into an actuarial system, run it millions of times and you end up with probability distributions for solvency levels, with profits payouts, etc. All of those probability distributions are just translations of the distributions within the ESG, so they're effectively the best estimates according to whoever designed and calibrated it. Which is why senior management need to have the final say on the calibration of the ESG. Anyone who thinks they shouldn't needs to watch that Star Trek episode where a computer is allowed to captain the starship Enterprise: Captain Kirk has no say in the design and the computer, unsurprisingly, ends up captaining the starship the way that a computer programmer would.

Second, there are market consistent ESGs. These aren't used to derive probability distributions, instead being used to value guarantees (or derivatives or securities with derivative-like features). These ESGs are parameterised in a way that means that they can reproduce the market prices of specially chosen securities or derivatives and their use could be interpreted as interpolating between those prices to find the value of the guarantee we're interested in. Again the ESG is run millions of times but this time a "deflated" payoff is calculated in each run and the average of these is taken to be the value of the guarantee. A load of complicated stochastic calculus tells us that the value of a guarantee is equal to its expected deflated payoff, so we're calculating the deflated payoff loads of times and taking an average. But because the probability distributions and their parameterisation within the ESG are having to be stretched and distorted so much from reality, there's absolutely no meaning to the probability distributions that that come out of them.

And that, for me, was the most important thing for actuaries to understand about ESGs at the turn of the century. To understand whether they were talking about real world ESGs or market consistent ESGs. Without understanding the difference, it would be very easy for an actuary to quickly embarrass themselves.

But all this was over twenty years ago and I've since discovered that there's a third type of ESG. I've been using it for years but have only just realised that it exists. Being more related to understanding risks than valuing guarantees, I guess it has more in common with one type of ESG than the other, although some might claim it's not an ESG at all. Going back to the parable of the mince, it all feels a bit like quorn, so I'm going to call these quorn ESGs.

So what is a quorn ESG and how is it used? It's easier to first describe how someone might use one and only afterwards to describe its features.

Let's say you're approaching retirement and considering your options. You have a choice between drawdown and buying an annuity (or maybe a combination of the two). So you build a huge spreadsheet, include on it any state pensions or preserved final salary pensions you're entitled to. You factor in all the tax considerations, including the lifetime allowance. You include all your non-pension savings and any big forthcoming outgoing cashflows like university fees or the cost of building an art studio. If you're like me, you have a page on the spreadsheet that lists all the assumptions and inputs, an under the bonnet page with all the calculations and an output page with lots of interesting graphs showing things like the growth of unit prices and the pension you receive each year. You're almost ready to go.

But this spreadsheet is full of fixed assumptions. You can tinker around with target pension, investment return and date of death but this all feels a bit unfulfilling. The biggest risk is investment return and you'd like to understand this a bit more. And this is when you build a quorn ESG into the model. What's the simplest model for the price of a unit in an equity fund? Geometric Brownian motion? So let's create an ESG for unit prices based on geometric Brownian motion with a couple of vaguely realistic parameters. And the way we use the ESG is to go to the output page of our spreadsheet, and keep manually recalculating the spreadsheet to generate new economic scenarios. Every time a scenario shows your pension reducing from its target level, you can look at the graph of unit prices and see a scenario that could hurt you. The probability of such a scenario occurring is something you have to judge for yourself as it's not something the ESG can help you with. But a skimthrough of adverse scenarios increases understanding of risks a lot more than probabilities or capital requirements ever will. And, I can't lie, keep recalculating and you'll sometimes see strange things happening that are the result of coding errors that you might not otherwise have discovered, so quorn ESGs are also a great testing tool!

There are no rules about the calibration of a quorn ESG. It's is a probability distribution over the same sample space as the real world ESG that you might otherwise use, so recalculate the spreadsheet infinitely many times and every possible run of unit prices will eventually emerge. On the other hand, it's useful to have a calibration that results in the sort of individual runs that you're interested in. Even if you start with parameters at realistic levels, you're allowed to adjust the volatility parameters within the ESG if you find it's generating too many or too few extreme scenarios. As long as you're not using the ESG to calculate values or probability distributions, who cares?

So why not try using a quorn ESG? It might just surprise you.