*Updated with corrected simulation results on 23rd February

Do I have enough financially to retire at 40 and last me till 100?

This is a thought that came across my mind umpteen times. How much money will I need to do that? Will I end up sleeping on the roads if I miscalculated or overestimated my chances of retiring successfully?

To answer all these burning questions, I decided to take a data-science based approach and run through multiple simulations to put a quantitative sense into understanding my chances of success.

Now, before you run any simulation, you will need to first define the parameters. This is not different too and here are the parameters I assume.

Retirement sum: 500,000 SGD

Retirement age: 40 (gasp!)

Number of years to go before I meet my maker: 60 (assuming I live till 100)

Yearly expenses during retirement: 60,000 SGD

Inflation rate during my years of retirement: 3% annually

Investment methodology: Full investment of retirement sum of 500,000 SGD into STI Index*

Assumptions: No more outstanding debt (housing loan fully covered), CPF is not taken into consideration

*The STI index average annualised returns over the past 10 years is 9.2% with dividends reinvested, and had a volatility of 12.74% per annum for the past 5 years. You may refer here for the details. The FTSE Asia Monthly Report in the link provides details on the performances for various indices of interests for Asia Pacific region.

Using this historical performances of the STI index, we will assume future performance of the STI index to be similar and assume a normal distribution (as shown below- mean is 9.2%, standard deviation is 12.74%)

With these information, we could now use Monte Carlo simulations to create 1000 different scenarios of varying performance of the STI index to understand my chances of succeeding within the above mentioned parameters. For the uninitiated, Monte Carlo is a class of computation algorithms which rely on random sampling (key element here is randomness) to obtain a numerical result to a pre-defined problem. You may read up more on Monte Carlo simulations here.

What's the success criteria to determine that the retirement plan is a success?

If my overall retirement sum together with dividends returns minus off the expenses accumulated (together with inflation) over the years results in a positive amount, the retirement plan is then deemed to be successful. Similarly, if the results is a negative amount, it means that my retirement sum could not sustain my expenses and my retirement plan is then deemed to have failed. *

*(Simulation had taken into account the deduction of yearly expenses and inflation from the retirement sum every year)

So, what are my chances after 1000 simulations?

Here's the results.

Here is my possible total retirement sum after full investment of my retirement sum of 500,000 SGD into STI index across 1000 different scenarios of possible returns from STI index.

While the returns from STI index follows a normal distribution, the end results from the Monte Carlo simulations often follows more of a log-normal distribution as you can see here. At the 66th percentile, the total sum starts to turn positive. From 0th to 65th percentile, the total sum is negative. In general, you will want the percentile where the total sum turns positive to be as small as possible as it represents a higher possibility of positive outcome from a statistical point of view.

Example: if you score 55th percentile in a class exam, it means that 45% of the class did better than you. As such, if the total sum is negative till 65th percentile, it means 35% of my simulated results have a positive outcome.

Hence, my chances of successfully retiring at 40 years old with a retirement sum of 500,000 SGD to cover my 60,000 SGD annual expenses till the age of 100 is 35%!

This works out if my annualised rate of return from my investments is at least 15.1% (which is really high!)

How will my chances of success changes if I have a retirement sum of 1,000,000 SGD at age 40 when I decided to retire?

Running through 1000 simulations, here's the results.

My chances of success increases by 17 percentage points as the percentile at which a positive sum emerges (after deduction of expenses) happens at 49th percentile instead. Hence my chances of success is now 52%.

Similarly, the required annualised rate of return for my investments (with a retirement sum of 1,000,000 SGD) now drops to 9.2%.

Well, to double my retirement sum to 1,000,000 SGD when I am at age 40 seems a bit difficult. How could I increases my chances of success with the original sum of 500,000 SGD? What happens if I do not retire completely but do a semi retirement instead? This means to take up a part time job which pays me 2000 SGD a month (a total of 24,000 SGD annually) for 10 years till I am 50 years old and retire completely after that?

Running through 1000 simulations, here's the results.

My chances of success now increases by 20 percentage points to 55%! (better than the chances of success I would have with a 1,000,000 SGD at age 40). That's actually good to know since doing a semi-retirement is sure easier than doubling my retiring sum at age 40.

Will my chances actually increases if I were to invest in US indices such as S&P 500 instead since everyone seems to be saying that S&P 500 provides better returns than STI? To answer that, let's now assume that I invest my full retirement sum into S&P 500 instead and run through 1000 simulations.

Since adopting 500 stocks into the index, S&P 500 has provided an annualised returns of 9.4% with a volatility of 16.16%. In comparison to what we have used for STI in the above simulation, the S&P 500 has a higher annualised return but also a higher volatility.

Assuming all other factors such as expenses, retirement age, inflation etc all remains the same, here's the results.

This is surprising, isn't it? My chances actually drop by 1 percentage point if I were to invest in S&P 500 instead.

I'm actually expecting my chances of success to increase if I were to invest in S&P 500 since it has a higher annualised return. However, it is also more volatile than STI. This thus results in a wider spread of the normal distribution and might hence negatively affects the chances of success when put through a high number of simulations.

After all these simulations, what are the key takeaways?

1) While a higher retirement sum is always desirable, a higher annualised rate of return is even more important. If you could constantly have a high annualised rate of return, the snowball effects from compounding will ensures you always stay ahead of the inflation curve.

2) Semi-retirement instead of full retirement is an option for you if you want to increases your chances of success in retiring well financially (see above simulation). So you don't really need to wait till you are sitting on one million cash before you consider retiring.

3) Being debt free is key! All these simulations are run with the assumption you have no debt and hence there is no need to service your debt with its interest rate. The situation will be different if you have any forms of debt.

4) Investing in a fund/index which has low volatility is an important consideration apart from a high annualised rate of return. It will increase your chances of success in retiring well financially (see above comparison of STI vs S&P 500).

Wishing all the best to you in your retirement plans!

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