Monte Carlo Retirement Planning

In the later stages of the development of our retirement planning calculator, we put its unique optimisation features through its paces. We ran a wide variety of different scenarios. We simulated individuals and couples of different ages, financial positions, and attitudes. Quite often a generated strategy would surprise us, even though we had designed the system’s rules. There appeared to be wide variations in the financial risks between different scenarios, resulting from following the generated strategies.

Before EvolveMyRetirement® generates an optimised strategy, the user must make an important setting. This is their attitude towards the risk of running out of money during their lifetime. This can range anywhere from “I’m a gambler by nature” to “I’m extremely risk-averse”. We saw that for scenarios with identical attitude settings, the generated strategies often had very different financial risks of running out of money (insolvency). This surprised us.

We decided to look for a pattern. To do this, we started by creating a simple plan consisting of:

  • Retired single male aged 70.
  • No motivation to leave a legacy.
  • No savings other than a bit of cash in the bank.
  • Average aversion to the lifetime financial risk of running out of money.
  • Balanced attitude to investment risk.
  • No state pension.
  • No other pensions.
  • Fixed expenses of £15,000 per year.
  • No properties.

We wanted to see what effect that varying the assumed initial amount of cash in the bank would have on the generated strategies.

So we generated different strategies based on different initial cash balances. We chose £250,000, £300,000, £500,000 and £1 million. After generating each strategy for the first time, we optimised it a further two times. This way we could be sure that we had converged to a stable strategy. In all scenarios, we observed that the strategy deferred buying annuities until extremely late in life. This was hardly surprising given current annuity rates. More interestingly, the starting investment risk was always generated to be “Cautious”. It was interesting because we had set the man’s attitude to investment risk to “Balanced”. The most interesting feature of the generated strategies was the wide variation in the resulting risk of insolvency. The range was from 5% up to 24%.

We decided to do a sensitivity analysis on the strategy generated in each scenario. We edited the strategy and checked the results generated by the Monte Carlo simulation. For each generated strategy, we checked the results of:

  1. Reducing the generated discretionary spending by £500 (where possible).
  2. Increasing the generated discretionary spending by £500.
  3. Increasing the generated investment risk to “Balanced”.

Analysis Results

The summarised results of all 4 scenarios are shown below.

Scenarios Financial Risks


For the scenario with £250,000 cash, the generated strategy had no discretionary spending at all. But it still had an insolvency risk of 24%. The sensitivity analysis showed that adding just £500 of discretionary spending pushed the insolvency risk up to 38%. Unsurprisingly, the optimiser had chosen zero discretionary spending. Changing the starting investment risk to “Balanced” reduced the risk of insolvency. So we wondered why the optimiser had not chosen “Balanced”.

We found the answer when we studied the Results page. This showed that when the starting investment risk was “Cautious”, for those cases where insolvency occurred there was a 95% chance that it would occur in the last year of life. On the other hand, when the starting investment risk was “Balanced”, there was only a 73% chance that insolvency would occur in the last 2 years of life; there was a 22% chance that it would occur in the last 3 or 4 years of life. So the program had judged quite sensibly that an extra 1% chance of insolvency was more than compensated for by the greater confidence than insolvency would not occur early.

For the other 3 scenarios, the generated strategy made provision for varying amounts of discretionary spending. It came as no surprise that the higher the starting cash balance, the higher the discretionary spending in the generated strategy. More surprising was the observation that the higher the starting cash balance, the lower the insolvency risk resulting from the generated strategy.

Balancing Financial Risks

Why did the system consider an 11% risk optimal for a man starting with £300,000, but only 5% for a man starting with £1 million? For the answer, consider the following implications of decreasing or increasing discretionary spending by £500:

  1. Insolvency risk. In all 3 cases, the effect on the risk is greater when the discretionary spending increases than when it decreases. This creates a downward pressure on the level of discretionary spending during optimisation.
  2. The relative value of £500. In the case of the man with £300,000, £500 represents 25% of the generated discretionary spending. For the man with £500,000 it is only 4%, and for the man with £1 million it is a mere 1%. So the less wealthy the man is to start with, the more relatively valuable each additional £500 becomes. This creates an upward pressure on the level of discretionary spending during optimisation.

These two pressures balance out at different points depending upon the man’s starting wealth. In other words, EvolveMyRetirement® is telling us that a poor person should take bigger financial risks than a rich person, even if they both have the same feelings about risk aversion. The justification is that a poor person has more to gain from taking risks than a rich person.


Interestingly, studies show that the relatively rich tend to take calculated risks to accumulate wealth. But the rich avoid taking risks with the wealth they have already accumulated. The exception is that they sometimes gamble with amounts that are very small relative to their wealth.

The relatively poor on the other hand tend to take more gambling risks with their wealth. They thus tend to lose money over the long term.

These studies therefore suggest that the levels of insolvency risk suggested by EvolveMyRetirement® are consistent with peoples’ willingness to take risks relative to their wealth. But they also suggest that financial advice is required to make sure that sensible financial risks are taken.  This is particularly so for the relatively poor.

So when deciding how much risk to take, it’s best to follow Goldilocks’s example: don’t take too much or too little risk, but take just the right amount of risk.

Taking Sensible Financial Risks

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