# Using Monte Carlo Simulations In Your Retirement Planning

Wouldn’t it be nice for our retirement planning purposes if stocks consistently gave us eight to 10 percent returns each year? After all, that’s what stock markets have delivered on average over the very long term.

Indeed, between 1935 and 2016 U.S. stocks returned 11.4 percent annually, Canadian stocks returned 9.6 percent annually, and international stocks averaged annual returns of 8.3 percent.

I have an eight percent target in mind when projecting investment returns for my own retirement plan.

The trouble is that stock returns are anything but predictable and so while they may average eight to 10 percent over a 25-or-50-year period, each single year could deliver panic inducing losses, euphoric gains, or something in-between.

Since 1988, the S&P 500 had single-year returns as low as negative 37 percent (2008) and also gained as much as 37.58 percent in a single year (1995). Only in three of those 29 years did the S&P 500 deliver annual returns between eight and 11 percent. The rest of the years are all over the place.

Why does this matter to your retirement planning? Because it’s not enough to just plug “eight percent” into your retirement projections and call it a day.

What happens if stocks plunge by 35 or 40 percent in year one of retirement, as they did to those unlucky enough to retire in 2008?

### Enter the Monte Carlo Simulation

A Monte Carlo Simulation can reveal a wide variety of potential outcomes by taking into account fluctuating market returns. So instead of basing your retirement calculations on just one average rate of return, a Monte Carlo Simulation might generate 5,000 scenarios of what hypothetically might happen to your portfolio as you draw it down and markets fluctuate.

Let’s look at an example of a 60-year-old who retires with $750,000 invested in a standard balanced portfolio of 60 percent stocks and 40 percent bonds. This retiree wants to know how much is safe to withdraw from the portfolio each year and whether it can last 30, 40, or even 50 years.

We can do this with a Monte Carlo Simulation. I used Vanguard’s retirement nest egg calculator. We’ll start with a safe withdrawal rate of 4 percent per year:

- How many years should the portfolio last: 30 years
- What is your portfolio balance today: $750,000
- How much do you spend from the portfolio each year: $30,000

**The results**: There’s a 93 percent probability that this portfolio lasts 30 years.

When I re-run the simulation using a withdrawal rate of 5.3 percent (spending $40,000 per year) there’s now just a 74 percent chance the portfolio survives 30 years.

What happens if our retiree lives until 100? We’ll need to make the portfolio last for 40 years instead of 30.

Spending $40,000 each year means the portfolio has only a 62 percent chance of surviving 40 years. If we go back to our original 4 percent safe withdrawal rate ($30,000 per year) then our portfolio jumps back up to an 87 percent survival rate.

In one interesting simulation, I increased the stock allocation to 100 percent and changed the annual spending to $50,000 (or 6.7 percent of the portfolio). The $750,000 portfolio has a 50 percent chance of lasting 40 years. Not something I’d chance to a coin-flip!

How does a Monte Carlo Simulation work? According to Vanguard, they randomly select the returns from one year of the database for each year of each simulation.

Using those values, they calculate what would happen to your portfolio – subtracting your spending, adjusting for inflation, and adding your investment return.

This process is repeated one year at a time until the end of your retirement or until your portfolio runs out of money. After 5,000 independent simulations there’s a broad range of possible scenarios and clear patterns begin to emerge.

### Final thoughts

For those of you close to retirement or that have recently retired, I strongly encourage you to speak with your financial advisor about running a Monte Carlo Simulation for your own portfolio using several different inputs that match your goals and projections. DIY investors can find calculators such as Vanguard’s online to run their own simulations.

Err on the side of caution so that you’re comfortable with the outcomes. If there’s only a 50 percent chance that your portfolio lasts the length of your retirement, that’s not a plan, it’s a gamble.

Hi Robb,

As usual great advice!

With markets being “all over the place” how difficult it must be for the investment advisor as well. I just met with mine and the result on my RRSP account was reported to me as a 4% gain over 2016 and the outlook for 2017 was suggested to be very bleak.

My TFSA and non registered accounts ended where they started last year (give or take a few dollars). My advisor is suggesting moving into a program where the TFSA will change from 70% equity 30 % fixed to 25% equity 75% fixed. Now I’m sitting on the fence trying to understand how in the world any of this makes sense???

I wonder what investment advisors are thinking and what advantages they fall too? My understating is they get paid irregardless of any gains or loses investors experience.

How does one know if their best interests are being taken into consideration?

Concerned & Confused

Fire your broker and get another one as the TSX went up 17.51% last year!

Yes Doug, the TSX did go up 17.51% but if Gert’s RRSP was heavily fixed income weighted and not equity weighted then 4% may be actually what they got. There is too little information given to make the comment to “fire your broker” – especially if Gert is risk averse and didn’t want their money in the market. If that is truly the case – that is not the broker/advisors fault. If they had good equity exposure and still returned 4% – yes, that would be cause for concern.

Actually, with dividends included, the TSX was up 21.5% last year.

Gert, with the US market up 9% last year, and bonds up 1.3%, I’d ask your broker what mix of stocks and bonds he has you in, what fees he is charging you, and how your portfolio performed against benchmarks. A globally diversified of stocks and bonds in a 70/30 allocation returned 7.7% last year, so it looks like your broker has some explaining to do.

I wouldn’t think switching to a 25/75 allocation is the answer. If I were you, I’d hire a fee ownly financial planner, who’d put you on the right track with your finances and maybe help you set up one of the portfolios from Canadian Couch Potato.

This type of Monte Carlo simulation is certainly better than nothing, but it ignores the fact that the current year’s returns are correlated with past returns. By choosing randomly from past returns for each simulation year, they destroy these correlations. In real life, if stocks crash, they tend to come back, eventually. But this simulation method can produce some spectacularly bad outcomes that we’ve never seen, such as 3 years in a row of the worst annual return that has ever happened.

I use a web-based monte carlo based retirement planning software to confirm/compare my financial advisors projections. There are lots of options in the program to change portfolio allocations and various assumptions. I find it really useful though it is not a free program, small annual fee to use it. retireware.com – it is Canadian.

@Michael B – I have used Retireware for years and also recommend it. It is very powerful and flexible for someone that wants to do detailed retirement on their own or to do additional scenarios for an advisor’s plan.

You can also check their blog or sign up for email updates here: http://retireware.blogspot.ca/

Just wanted to add that I’ve also used the software for about 3 or 4 years now. It is very beneficial and accurate. As part of a retirement course we were allowed to have a quick financial plan done for free. We did this and it was pretty close to Retireware’s plan once I made sure both plans had the same assumptions.

From my experience it has everything that you need for a good plan approximation. I update mine each year. Only negative comment is that there is a bit of a learning curve involved to get everything into the program that fits your situation. Most of the obvious stuff (90% of the data entry) is pretty straight forward. The other 10%, which may not apply to everyone, needs a bit more work. Contacting the support department has been great for help with the last 10% for me. Quick and very helpful.

Highly recommend this software. I also tried RRIFmetric but found it much harder to use. Other way more expensive professional software solutions are easier to use but 10 times the cost. Yes I tried some of those too on a trial.

Hi Michael, thanks so much for sharing this excellent (and Canadian) resource!

Grand, Robert, Doug, Thanks

From what I see my mix is as follows;

Non-Reg: 70% Fixed; 30% Equity (all CAN)

TFSA: 26% Fixed; 74% Equity (all CAN)

RRSP: 2% Cash; 32% Fixed; 66% Equity (70% CAN; 30% USA)

I guess I should seek out a Fee only Planner for some advise as you suggest Grant.

Robb, I also have an 8% nominal return in mind, not unrealistic based on prior returns. But my actual plan is based on 4% return to be quite safe. If I get 8% I am laughing, but with 4% and a bit of frugal living I know I will be OK.

First of all, not everyone is OK with full pull risk. I am a balanced investor, my spouse is conservative so we are invested conservatively. The other thing to consider is that if you are retired and go through a 2008-09 event, you change your discretionary spending to adapt. Also spending requirements change from when you are 65 to 85 (health being a consideration of course). Most retirement calculators are good for estimation purposes but none are the be-all end-all, just a tool.

Cynical me says anyone who blindly follows an investment advisor’s advice is doomed to fail. If you are questioning why a drastic change is suggested, listen to your inner voice. They have no crystal ball.

Very true. This is exactly what I went thru until I took charge and put my spends and plan on the paper and prioritize (not a stone carving exercise but accept it as sketch that you can revise it). Put my expectation down, gathered a list of all assets and then found an adviser to tell me the facts and not sugar coating to get my business. It all boils down to

1. Get yourself a life expectancy of avg + 7 yrs

2. Annual after tax cash requirement (with inflation) each year

3. Multiply the point 2 with point 1 and divide by 2 to give you a rough today’s required sum total. (if point 1 is less than 15 yr than this calculation may as good as it did for me).

Hi Dee,

Maybe off topic but how did you go about finding an adviser that you could trust? I mean, based on what I’ve posted it suggests I’m not being well represented but how can I be sure?