Last week’s post about Monte Carlo simulations in financial planning sparked some interesting comments, so I thought a case study would help readers see how they work. Our real-life example comes from a past client of PWL Capital’s DIY Investor Service: the details were supplied by Justin Bender with the client’s permission.

Laura is 57 years old, single, and earning about $68,000 a year with expenses of $37,500. She socks away about $14,000 annually and has accumulated $330,000 in her RRSP and TFSA, as well as a rental property worth about $250,000. She has a defined benefit pension through her employer, though it is not indexed to inflation, and she’s eligible to receive full Canada Pension Plan and Old Age Security benefits in retirement.

Her investment portfolio was not very efficient: about a quarter of it was sitting in cash, and much of the rest was in narrow sector ETFs, individual stocks and corporate bonds. Some of the ETFs were in the wrong account types, resulting in unnecessary taxes.

Before Justin could rebuild her portfolio, however, he needed to make sure it was aligned with her financial goals. Laura’s primary objective was to determine whether she could retire before age 65—perhaps as early as 60—so she needed to know whether her investments would be able to generate enough cash flow after she quit work. Let’s look at how a Monte Carlo simulation helped answer that question.

### Sim city

Before beginning the simulation, it was important to understand Laura’s comfort with risk. The Monte Carlo might indicate a high probability of success with an equity allocation of 70% or 80%, for example, but that would be irrelevant if Laura could not deal with that level of volatility. With the help of a risk-tolerance questionnaire and an honest interview, Justin determined that Laura would be best suited to a portfolio of 60% fixed income and 40% equities.

Using the Monte Carlo software, Justin input Laura’s current portfolio size, her savings rate, her projected expenses in retirement, and her other income from employer and government pensions. (The software is already programmed with the details of CPP and OAS benefits at different ages.) Then he used the following assumptions:

- the expected returns are 2.5% for fixed income and 7% for equities, which works out to 4.3% for the portfolio
- investment costs are 0.3%, reducing the portfolio’s expected return to 4%
- the portfolio has a standard deviation (volatility) of 5.75%
- inflation is 2%, and Laura’s annual expenses would increase by this amount
- Laura would live to age 95

Given all of these inputs, what is the probability that Laura will be able to retire before age 65 and not outlive her money? Here are the results of the Monte Carlo simulation:

Proposed retirement age |
Probability of success |

60 | 38% |

61 | 63% |

62 | 83% |

63 | 94% |

64 | 98% |

65 | 99% |

As you can see, the probabilities vary a lot before age 63. For every extra year Laura works, she would be adding to the portfolio rather than drawing it down, and that makes a dramatic difference: her rate of success jumps by 25 percentage points if she works until 61 rather than 60. And if she can hang on until age 63 or 64, she has an extremely high likelihood of never running out of money.

### What if she didn’t like those odds?

If Laura felt working until age 63 was unpalatable, she could have run the simulation again with different assumptions. Raising her expected returns or lowering the inflation rate is just wishful thinking, of course, so she’d need to make some tougher choices: she could try to save more, or lower her planned spending rate in retirement. She could also experiment with taking slightly more or less risk in the portfolio. Surprisingly, increasing the allocation to fixed income might increase her chances of success: even though the expected returns are lower than for equities, the volatility is also much lower, which reduces the risk of a crippling drawdown in the early years.

In the end, Laura decided she would work for six more years and plan her retirement for age 63. Only then did Justin help her build a new ETF portfolio tailored to that goal: it ended up being 30% short-term corporate bonds, 30% GICs, and the rest split evenly between Canadian, US and international equities.

The Monte Carlo simulation helped Laura make an informed decision, but it wasn’t the end of the process. In two or three years she should revisit her situation to make sure she’s still on track to meet her retirement goal, since several factors—a job loss, an inheritance, a new relationship, an increase in interest rates—could change the key assumptions and she’d have to update her plan.