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A Monte Carlo Case Study: Can I Retire Early?

2017-12-02T21:36:59+00:00February 4th, 2013|Categories: Financial Planning|Tags: |22 Comments

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.



  1. J A H February 4, 2013 at 9:30 am

    The couch is gone!

    On a more serious note, do Justin Bender’s plans come with an investment policy statement? In the example above were the client’s goals going to be on track with continued holdings of 40% equity after age 63 or was there going to be some change to that?

    Thanks for sharing the example plan. Sometimes the conclusions of these plans seem self evident but doing the work really does have a positive effect.

  2. Justin Bender February 4, 2013 at 9:52 am

    @JAH – An investment policy statement (IPS) is a document that is normally drafted between a portfolio manager and a client – it is really a guideline for what the portfolio manager can and can’t do. If a client will no longer be working with the portfolio manager (such is the case with our DIY investor service), an IPS is not relevant (i.e. a DIY investor cannot tell PWL how to manage their portfolio when we’re not managing their portfolio).

    Investors who graduate from our DIY investor service will walk away with a strategic asset allocation, along with rebalancing thresholds, that they can refer to. However, life circumstances will change, which is why we still advise DIY investors to seek professional advice when significant changes occur in their lives (such as a job loss).

    After age 63, the investor may find that they are less willing to take on risk (or perhaps interest rates will increase enough so that they may not have to take on as much risk as they have been in order to have a high probability of meeting their financial goals).

  3. Jerry February 4, 2013 at 10:13 am

    “30% short-term corporate bonds, 30% GICs”

    Why are federal/provincial/municipal bonds not an option?

  4. Justin Bender February 4, 2013 at 10:17 am

    @Jerry – Federal/provincial/municipal bonds are always an option.

  5. Oldie February 4, 2013 at 10:39 am

    @CCP: Playing with the MCSimulator from Vanguard from your last post (and acknowledging the warnings of imprecision) I discovered what first appeared to be a paradox — increasing the allocation percentage of fixed income INCREASED my chances of my portfolio lasting 30 years of retirement (with a given annual withdrawal and no further contributions); but I figured it out — although this reduced the portfolio value at 30 years in the most probable scenario, the left hand probability tail was smaller, due to less volatility, and thus did not dip across the 2% probability boundary (I had assigned a 98% chance of success as acceptable). Is this the same phenomenon as your “Surprisingly…” comment above?

    Suppose after retirement Laura persisted with this plan for a few years, the markets performed in the middle of range of expectations, and her portfolio grew in value, as predicted. If a review with a new simulation showed that she could now increase her equity allocation back to her original level of risk comfort (assuming this risk tolerability had not changed), would this choice be irrational behaviour in any way? I’m trying to sort this out, and I realize there are actually 2 different risks we have to assess our tolerance for — the risk of our portfolio losing value in a bear market, and the risk of our portfolio not lasting the years we plan to survive for. It’s only the latter risk that Laura’s portfolio has now given more wriggle room for.

  6. J A H February 4, 2013 at 10:42 am


    I appreciate that I may have used a term that in your day to day professional experience is not applicable. However, I would not draw the same conclusion that an IPS is irrelevant.

    A DIY investor both has themself as portfolio manager, and has to battle the range of emotional hurdles that sometimes interfere with successful investing. Having a personal IPS can make a big difference in resetting and reblancing a portfolio annually, especially a couch potato portfolio.

    I currently have one that I’m very happy I paid for and I’m glad it is there to pull out of my files once a year (at least).

    It’s true that at retirement most people would benefit from a check up with a planner. I’ll presume by your reply that the plan Dan shared was meant to get the client to retirement at which point she would have to renew the planning process.

  7. Canadian Couch Potato February 4, 2013 at 11:05 am

    @Oldie: Yes, the phenomenon you discovered was what I was referring to when I said “surprising.” Many people assume that taking more equity risk will improve the likelihood of success, and usually it will over very long periods. But over shorter periods it can decrease the chances of outliving your money: ask someone who retired in 2007 or 2008 with a high allocation to stocks and then started drawing down what little of the portfolio was left.

    Whenever an investor revisits a plan after several years, the goal really should be to see whether you can decrease your equity risk, not increase it. If equity markets end up doing much better than expected and you can now reach your goal by taking less risk, then you should probably do so. This is what happened for people who retired in the early 1990s: they were likely expecting 8% or 9% returns but got more than twice that over the next several years. By the late 1990s they probably could have scaled way back on equities as a result. But what do you think most did? :)

  8. Andrew F February 4, 2013 at 11:18 am

    Do you do any sensitivity analysis on expected return on fixed income? It seems to me that 2.5% nominal/0.5% real returns on fixed income is rather conservative historically speaking. I expect the results of the simulation are rather sensitive to this assumption. While it is prudent to be conservative in return assumptions, there is the tradeoff of potentially over-saving to meet retirement goals.

    I’m also not crazy about the die-broke-at-95 assumption. Annuities seem not to have been considered in the model (other than those already provided–DB pension and CPP/OAS). No allowance for potential end-of-life medical expenses/nursing care…

    No offense intended, but MCS can easily turn into GIGO depending on the assumptions. With that in mind, I would not take them as gospel.

  9. Canadian Couch Potato February 4, 2013 at 11:53 am

    @AndrewF: I don’t think anyone takes MCS as gospel. It was never intended to predict all possible future outcomes with great precision. The enduring problem in financial planning is that there is no perfect tool, since so many factors are unknowable. So you do the best you can and you try to avoid big mistakes. In this example, the MCS helped Laura determine that retiring at age 60 was a bad idea, and that working an extra three years dramatically improved her likelihood of success. It can’t help her know where she will be at age 93.

    I’ve also seen MCS used to show investors they were taking may more risk than they needed to. One was holding over 80% stocks (and hated the volatility), but the MCS showed that at her spending rate she only needed 40% equities. You can imagine the enormous relief that brings to people.

    As for the conservative assumptions for fixed income, the DEX Universe is currently yielding 2.4% before fees. If and when interest rates rise you can change that expected return, but I would be careful.

    It’s important to understand that a simulation like this should be revisited regularly, and course corrections need to be made. But you need to have some kind of framework for the planning, even if that framework will never be perfect.

  10. Andrew F February 4, 2013 at 12:02 pm

    Sorry if that came off as harsh. My point is more that when you say:

    “MCS helped Laura determine that retiring at age 60 was a bad idea, and that working an extra three years dramatically improved her likelihood of success. ”

    I’m not convinced that the MCS estimate of probability of success is all that accurate. If you make a slightly different estimate of future interest rates, you’ll get a significantly different answer. Maybe the ‘correct’ answer is that she could have safely retired at 60.

    I hear what you’re saying about the current interest rate being below the 2.5% interest rate assumption currently, but I would suggest that a 30 year period of 2.5% rates is rather unlikely. Assuming 2.5% rates now is akin to someone assuming 6% rates 10 years ago (and concluding that they had a high probability of success that turns out to have been optimistic).

  11. Oldie February 4, 2013 at 12:49 pm

    @CC: I think I was struggling with trying to combine multiple scenarios with multiple decisions. To simplify the decisions: Laura, 5 years after retirement at 63, discovers her portfolio has grown in value, despite having 60% in fixed income, thanks to the absence of any huge downswings in the economy. Now 68 years old, she figures she might live another 27 years. She runs another MCS, and finds that hypothetically with a 50% equity allocation she can increase her annual withdrawal and still have a 97% probability of sustaining her portfolio to 27 years. Her emotional portfolio-loss risk tolerance is actually up to 60% equities, so 50% is within this envelope. (She can always drop the equity percentage slowly to zero when she has 15 years left in her “plan” if she is still alive) The simulation has given her the option to increase her withdrawals should she choose to do so.

    This has nothing to do with encouraging investors to be “greedy” which, I agree, risks sending investors the wrong message. I was just thinking that the math might give investors more options while still keeping within the parameters of their assumptions. If Laura was being particularly frugal in keeping to her allotted spending allocation, this gives her some leeway to increase her spending allocation for the rest of her life, yet still manage her portfolio within a strict, rational, responsible plan.

    I agree, it seems at odds with the general advice that “risk”, i.e. equity percentage, should drop as you get older, but in this special case, I would reason that her equity allocation would only be rising due to a previous temporary reduction in response to the other risk — of premature portfolio exhaustion — which has now been left behind. Does this make some sort of sense? Or does her previous rationale for equity percentage allocation reduction still carry forward to now, whether or not she chooses to increase her annual withdrawals? i.e. we can make a categorical rule that if life circumstances don’t change after retirement, then there is never any good reason for increasing equity percentage allocation.

  12. Canadian Couch Potato February 4, 2013 at 12:58 pm

    @Oldie: In general I would agree that in five years Laura should revisit her situation, run the simulation again, and see if she can make any adjustments, such as a larger annual withdrawal.

    What I don’t understand is your comment that “her emotional portfolio-loss risk tolerance is actually up to 60% equities.” Why would her tolerance for volatility have gone up?

  13. Aziz February 4, 2013 at 4:33 pm

    Thanks for sharing this real example.

    What was the advice on the rental property? Sell it?

  14. Oldie February 4, 2013 at 7:25 pm

    @CCP: Sorry, my mistake entirely: I initially misread the preamble and was somehow working with the mistaken scenario that Laura was initially invested in a higher percentage of equities (i.e was initially risk tolerant), and was persuaded by Justin to lower this equity percentage to 40%.

    Even if this was the case, though, I see now that if, at the time of initial consultation at age 57, the MCS showed that decreasing the equity portion to 40% improved the odds of the portfolio lasting the whole 32 years of projected post-retirement spending, a later review and repeat MCS 5 years post retirement might indeed reveal a possibility of safely increasing withdrawal rate, but in answer to my original query, is still not likely (is never mathematically possible?) to demonstrate improved odds of keeping the portfolio intact to age 95 by increasing equity percentage allocation (even if her short term tolerance was accepting of this). This aspect of MC simulation is a little counter-intuitive at first, but I think I’ve got it.

    I think the trick is to focus on the lower boundary line of the 90% (or 95%, or whatever) zone of likelihood of portfolio valuation (in the Vanguard MCS) and see how it crosses the zero dollar value line at age 95. The upper boundary, no matter how high the possible value could get to be 5% of the time (or even the most likely middle of the road value) is irrelevant. It’s actually like Contract Bridge — the only priority is making your contract, no matter how many extra tricks any other strategy has the possibility for.

  15. Mandy @ MoneyMasterMom February 5, 2013 at 9:37 am

    I must have a high tolerance for risk because fixed income investments really rot my socks. They generally grow at the same rate as inflation. Although I’m sure the fact that I’m only 31 greatly influences that tolerance. I have lots of time to wait for the market to come back up.

  16. February 6, 2013 at 4:17 pm

    Mandy, some diversification is important even over the long term. A combination of uncorrelated or negatively correlated investments, combined with some portfolio rebalancing can really lower the volatility and I think the risk.

    For example, if you keep 50% in equities and 50% in bonds and if they’re not correlated, then when equities crash the bonds are still fine. So you rebalance, moving money from bonds into equities to get back to 50-50. Then when equites take off like a rocket, you rebalance again moving money from equities back over to bonds.

    Two things happen then. First your investments don’t all crash at once (because they’re not correlated). And secondly, in layman’s terms, you have forced yourself to buy low and sell high. That’s why you don’t want everything all in equities.

  17. February 6, 2013 at 4:21 pm

    And Mandy, I just visited your blog and saw the renovations thread. I’m coming down to visit in the summer to go fishin’ mmmkay? :).

  18. Noel February 6, 2013 at 7:44 pm

    This has nothing to do with the current topic. I am wondering why you switched from that wonderful logo you used to have? I miss it!

  19. Smithson February 6, 2013 at 8:21 pm

    @Noel: I think the logo was changed to make the website look a bit more “professional”. I agree with you. Bring back the couch and the potato with the bags of money :)

  20. Andrew F February 6, 2013 at 8:27 pm

    I also liked the old logo. The new one is a bit generic, while the old one was approachable.

  21. Noel February 6, 2013 at 8:35 pm

    I think this logo is the one he originally had. He’s now gone ‘corporate’ :(, but we still really like him. I agree the old logo was much more friendly, fun and not-intimidating – a place for everyone.

  22. Oldie February 9, 2013 at 10:10 pm

    @Noel, Andrew F, Smithson: Haha, guys, you describe my own gut feelings exactly regarding the “feel-good” and whimsical ambience of the dearly departed old logo we had learned to love. But the switch won’t change our appreciation for the site itself and the unchanged source of insight, rationality and good old common sense which seems to be getting more and more uncommon nowadays. Besides he’s still the same old fun, if insomniac, buddy Dan:)

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