Utility is an economic concept, intended to be a measure of the value of something to a consumer. In retirement planning, the utility is the total lifetime value of the benefits accrued from following the plan. Calculating it is made much harder by the uncertainties of projecting into the future. For every candidate strategy for a plan, we need to be able to calculate its utility as a single number. This number has to take into account the pros, cons and uncertainties of the strategy. When optimising, we choose the strategy with the highest utility. A good utility function is one that correlates well with how potential outcomes meet the consumer’s goals.

## Utility of a scenario

In order to get a handle on the problem, we first need a utility function for a single scenario representing a possible course of the plan over its lifetime. EvolveMyRetirement® illustrates a Random Scenario on its Results page. This simulates the financial progress of a plan until the last member has died. Each scenario is different due to the randomisation that takes place, such as for investment growth, inflation and longevity. But at the end of each scenario there’s a well-defined outcome, for which we can calculate the utility. There are several steps in this calculation.

The first step is to calculate the total fixed and total discretionary spending, adjusted for inflation over the plan’s lifetime. We combine these, applying a rule of diminishing returns to discretionary spending. The idea here is the principle that the richer you already are, the less marginal utility you get from additional spending.

The next step is to calculate an uplift based on any legacy left over after deducting any inheritance tax. The amount of the uplift depends on the importance attached by the user to leaving a legacy.

If the scenario resulted in insolvency, then we make a downward adjustment. This adjustment depends on how many years before the last member died that insolvency occurred. Even a short period of insolvency impacts the utility severely. A moderate period of insolvency (more than a couple of years) virtually wipes out the utility that would have accrued. The downward adjustment is even greater if the scenario also resulted in negative net worth. We’ve intentionally not made the impact of insolvency and negative net worth black-and-white.

## Utility of Monte Carlo Simulation

We can’t use the result of the calculation for a single scenario as the utility of our plan. Every time we run a scenario, we get widely differing results. In order to arrive at a utility for the plan, we need to run a very large number of scenarios. A Monte Carlo Simulation does just that, running up to 10,000 scenarios. We then combine the results.

Firstly we calculate the average (mean) of the results of each of the scenarios. But this isn’t enough, as it doesn’t take risk into account. So we make a downward adjustment based on the number of scenarios that resulted in insolvency. And we make a further downward adjustment based on the number of scenarios that resulted in negative net worth. The extent of these adjustments depends on the user’s aversion to long-term risk.

The resulting utility is representative of our plan’s strategy as a whole, taking its risk into account. It’s important to remember that there’s an inevitable margin of error whenever we use Monte Carlo Simulation. The higher the number of trials, the lower the margin of error, and the more deterministic the utility function. So we’ve struck a balance between perfection and the need to arrive at a result within a reasonably short period of time.

## Optimisation

Optimising a single strategy setting is not too hard; we can just keep varying it until we get the best utility. But with financial and retirement planning we need to juggle many different variables, and optimising them one at a time doesn’t work. That’s why we need to be able to calculate a utility. To summarise how we calculate it:

1. We run a Monte Carlo Simulation.
2. For each trial we calculate the utility for that scenario.
3. We combine the utilities from all the trials, giving an overall utility for the strategy.

When EvolveMyRetirement® looks for an optimal strategy, it generates many candidate strategies (using a Genetic Algorithm). During each iteration, the optimiser selects the strategy having the highest utility. Once again there’s a trade-off between optimising forever and presenting a result to the user within a reasonable time.

The optimisation feature of our online financial calculator, layered as it is upon Monte Carlo Simulation, is unique to EvolveMyRetirement®.

Utility In EvolveMyRetirement®
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