If you’ve spent any time in the financial independence community, then no doubt you’ve come across the 4% rule. The rule states that you can withdraw 4% of your retirement portfolio (adjusted for inflation) without running out of money. As such, 4% is known as the safe withdrawal rate.

If you play through the mathematics, the implication of the 4% rule is that you need 25x your annual expenses to retire. So many would-be early retirees structure their entire retirement plan around that 25x expenses number.

More recent studies have questioned the robustness of the 4% rule for U.S. markets. Amongst other things, they have found that 4% very quickly turns into 3.5% or below when you change equity/bond portfolio mix, retirement length and other factors.

But all of this work was done for Americans using U.S. markets data. The question for us Aussies is: Does any of this apply to us? If so, which parts?

In this article we begin to clarify some of the important — but still unanswered — questions about the 4% rule for Australians. We test whether the basic 4% rule applies to Australians and whether it needs to be adjusted for different portfolio mixes.

In future articles in this series we will elaborate on these findings and test follow-on questions, such as ‘what is the effect of retirement length of safe withdrawal rates?’, ‘can we improve safe withdrawal rates by mixing Australian and international investments?’, and more!

## How did we calculate SWRs?

We chose to use the analytical approach to safe withdrawal rate calculations that have been used by Suarez et al., Morningstar and Big ERN. This means that we select the final portfolio value that we are targeting and calculate the exact safe withdrawal rate required to achieve it.

We start by calculating the cumulative return of one dollar invested over our total retirement length (C_T). This tells us how much it would ‘cost’ us to withdraw that money and miss out on any compound interest. And then we calculate the total return of the retirement portfolio if we never took any money out (C_1).

Now we can calculate the final value (FV) of a retirement portfolio by taking the total value of the portfolio if we didn’t withdraw any money and then subtracting the opportunity cost of those withdrawals.

From there we can calculate the withdrawal rate (WR), which is the difference between the total value of the portfolio if we withdrew money and the total value of the portfolio if we didn’t withdraw money, divided by cumulative returns.

## How did we make it more applicable to Australians?

We adjusted the calculations in two ways to make the results more applicable for Australians.

Firstly, we sourced Australian equity and bond returns from 1871 to 2018. This allows us to calculate safe withdrawal rates for Australians who invest in Australia (e.g. the ASX200). And when we combine this data with our U.S. data, we can calculate safe withdrawal rates for Australians that invest in a mix of Aussie and U.S. markets. Let’s be honest, most of us do!

Secondly, we adjusted the expense ratio to reflect the reality of Australian portfolios. It’s sad but true to say that it costs us more to invest our money than in the U.S. Aussies in the FIRE community are pretty savvy when it comes to minimising fees, so we have assumed that the fees that most Australian’s pay on their portfolios is broadly in line with common ETFs.

With this in mind, we have included the following fees in our calculations:

• Australian equities: 0.14% (fees charged by Vanguard VAS)
• Australian bonds: 0.20% (fees charged by Vanguard VAF)
• U.S. equities:  0.18% (fees charged by Vanguard VGS)
• U.S. bonds: 0.20% (fees charged by Vanguard VIF)

## The results

Using the approach outlined above, we calculated over 700,000 safe withdrawal rates. Each withdrawal rate is unique combination of equity/bond split, target balance at end of retirement, retirement horizon, domestic/international split, and month (from February 1871 to July 2018). In this article will will use a subset of the 700,000 safe withdrawal rate data set, and focus on a 30 year retirement horizon only.

### Safe withdrawal rates over time

We start by calculating the safe withdrawal rate over time for a 100% equities portfolio and a 100% bonds portfolio for a 30 year retirement length. In the charts below we compare the output for the U.S. and for Australia.

The average safe withdrawal rate for both portfolios is broadly the same between the U.S. and Australia. However, U.S. safe withdrawal rates drop below 4% slightly more frequently than Australian safe withdrawal rates for both 100% equities and 100% bonds portfolios.  It remains to be seen what this means for portfolio success rates.

We find that there is low correlation between U.S. and Australian safe withdrawal rates for a 100% equities portfolio (r² = 0.07), yet there is a high correlation between the countries in a 100% bonds portfolio (r² = 0.76). This isn’t surprising, as it is well known that Australian bond yields are typically affected by changes in U.S. bond yields.

### Portfolio success rates

To understand what safe withdrawal rates mean in practical terms, we convert them into success rates. It works like this: if a withdrawal rate of 4.00% has a success rate of 95%, this means that we would have run out of money in only 88 of 1770 monthly starting points.

We started by calculating success rates for a U.S. portfolio of different equity and bond allocations. The purpose of this calculation is to ensure that we replicate Big ERN’s findings with our calculations and to use as a point of reference to compare Australian success rates later.

U.S. Retirement Portfolio Success Rates, 30 Year Retirement Length
Portfolio Equity Allocation
Withdrawal Rate100%75%50%25%0%
2.50%100.0%100.0%100.0%100.0%98.5%
2.75%100.0%100.0%100.0%100.0%95.7%
3.00%99.9%100.0%100.0%100.0%90.2%
3.25%99.8%100.0%100.0%99.9%84.3%
3.50%99.6%100.0%100.0%98.0%75.2%
3.75%99.2%100.0%99.0%90.8%66.7%
4.00%97.5%98.2%95.9%83.8%60.4%
4.25%95.2%95.7%92.0%72.7%48.4%
4.50%92.8%91.4%87.9%65.8%44.3%
4.75%89.4%88.2%79.6%52.6%41.1%
5.00%86.9%85.1%71.6%47.2%37.5%

The table above shows acceptable (95%+) success rates for withdrawal rates of 4.00% or lower when portfolios contain at least 50% equities. This is effectively the main result of the Trinity Study. However, success rates drop off sharply for withdrawal rates above 4.00% or for portfolios with less than 50% equities.

These results are broadly in line with Big ERN’s. On the one hand, we’ve used higher portfolio fees in our calculations, which would result in slightly lower success rates.  On the other hand, Big ERN has forecast equity and bonds returns beyond 2018 with zero volatility, which would result in slightly higher success rates. Overall, the difference between Big ERN’s and our success rates is between 0-1%, which feels reasonable.

Australian Retirement Portfolio Success Rates, 30 Year Retirement Length
Portfolio Equity Allocation
Withdrawal Rate100%75%50%25%0%
2.50%100.0%100.0%100.0%100.0%92.4%
2.75%100.0%100.0%100.0%100.0%85.3%
3.00%100.0%100.0%100.0%98.5%79.6%
3.25%99.8%100.0%100.0%93.8%75.3%
3.50%98.9%99.4%99.4%85.6%68.1%
3.75%98.4%98.6%96.9%81.2%62.6%
4.00%97.9%98.0%91.8%78.3%56.8%
4.25%97.0%97.0%85.3%75.2%53.9%
4.50%95.8%93.4%82.0%68.7%51.2%
4.75%94.0%87.5%78.5%59.4%44.9%
5.00%90.4%84.3%74.6%55.0%36.8%

Now for the good stuff. Overall, we see very similar results for Australian safe withdrawal rates. However, there are a few things to keep in mind:

• A withdrawal rate of 4.00% results in acceptable success rates for Australian portfolios with at least 75% equities. However, if the portfolio has only 50% equities, the withdrawal rate must be reduced to 3.75% to maintain an acceptable success rate.
• Adding some bonds into the portfolio (75% Australian equities, 25% Australian bonds) results in a higher success rate than a 100% equities portfolio. This is most likely due to diversification effects.
• For those who are happy to take significant risk, Australia tends to have higher success rates than the U.S. for withdrawal rates above 4.00%. Of course, this is not recommended as it introduces a very real risk that you run out of money before the end of retirement.

The chart above illustrates the relationship between safe withdrawal rates and success rates for various equity/bond allocations over a 30 year retirement length. As you can see, success rates fall to unacceptably low level very quickly for portfolios with 50% equities or less. To maintain an acceptable success rate you need to either reduce your safe withdrawal rate or increase your equity allocation.

## This isn’t the whole story… yet

Wait! Don’t race out and rejoice that a 4.00% withdrawal rate is acceptable for Australian retirement portfolios with at least 75% equities. Remember we are talking about a 30 year retirement length, which is probably not long enough for somebody whose goal is to retire early.

In the next article we will look at the effect of longer retirement lengths on safe withdrawal rates. Our hypothesis is that longer retirement lengths require lower safe withdrawal rates or a higher equity allocation to maintain acceptable success rates.

Update: Part 4 is focused on portfolio optimisation across domestic and international equities and bonds!

As always, if you have any questions, comments or feedback, please email me. I’d love to hear your thoughts.

All the best,

1. A great series so far, I wish that I’d seen it earlier! I’ve been playing around with similar calculations and posted about it on my own blog. I haven’t gone back as far in time as you have due to not having the datasets to play with so thanks very much for sharing them.

I’m surprised that the bond SWRs have been so high so far, I’m going to guess that at the end of that 30 year period there isn’t a huge amount of capital left and it’ll be running out entirely soon but haven’t actually run the numbers on that scenario yet.

And looking at your outcomes as well as my own playing with the numbers I’m guessing somewhere around a 70% to 75% equity allocation is going to be optimal for making it through the 30 year and beyond with a 4% withdrawal rate.

• Thanks mate, appreciate your comment! The calculations actually give us the SWR that would result in exactly \$0 balance at the end of 30 years. It basically ‘optimises’ withdrawals such that you don’t have any left over money.

I think you’re right in saying that the optimal allocation is somewhere around 75%. In one of the next articles in the series I’ll do some more number crunching to figure out exactly what the best equity/bond allocation is 🙂

2. I am pretty glad that someone else has taken up the challenge of creating this!

For a long time I thought I’d need to do it and have been putting it off for wanting to write about other things first!

When done I can direct them here instead of Big Erns material (which I also am incredibly impressed by)

A few things that I wanted to include that you may want to work on for future releases.

– Exchange rate data. How does historical exchange rate data (Aus/US) affect the withdrawals from a US portfolio by Australians. It’s all well and good to just replicate US SWRs but we can’t use that money until we exchange it. That means we may need to withdraw more or less than a US based 4% to get to our 4% after exchange rates have moved from our starting date.

– I have not met a person that is actually interested in capital depletion as a drawdown strategy. Please also analyse the numbers assuming capital preservation.

-Final average portfolio values. It is all well and good to increase your success by 1.2% by allocating 25% to bonds (instead of 100% equities) but that is leaving out a very important part of the story, how does this affect average final portfolio value? I believe (but am not sure) that people would be paying millions in forgone returns vs a 100% equities portfolio to gain that extra 1.2% of safety.

– Being an Australian analysis, it would also be interesting to have a look at some of the LICs. In particular have their regular dividend payments indeed provided a growing living payment enough to live on. Or were there years where they dropped dividends below 4% +inflation of the initial portfolio value (I know they claim to have not dropped dividends, but much of the time the dividend is expressed as a percentage of the current share price, so it is easy to maintain a “4% dividend” on a share price that has halved! Instead of 4% on the original value.)

– Ofcourse some different mixes of Australian and international equities taking into account exchange rates.

I’ll add more as I think of it.

Again thanks for taking up the mantle 😀

We will definitely look at capital depletion vs capital preservation. I agree that most people would rather a preservation strategy, both for peace of mind/safety net and to leave something for their loved ones.

Final average portfolio values don’t quite apply here because the calculation determines the exact safe withdrawal rate that will result in the target portfolio value after 30 years (i.e. \$0). Adjusting the target value is exactly what we’d do in a capital preservation scenario.

The exchange rates point is a good one. We could either adjust the U.S. returns to correspond to a hedged index of some sort or use forex data to ‘net off’ the effect of currency fluctuation. I’ll look into this and LICs too! 🙂

3. Looks like the comment engine didn’t like my use of the less than and greater than symbols. Feel free to delete my previous comment if you would like to clean this up

Dan

I will have to disagree.

What we are calculating here is a withdrawal rate that will give a zero probability in all of the historical returns analysed that you will have less than \$0 dollars in exactly 30 years.

So in the 1770 starting months described above you are calculating the withdrawal rate that will give you an exactly zero dollar result at the end of year 30 for the worst starting month in the data set analysed. For every one of the remaining 1769 starting months unless by pure coincidence you will have a final portfolio value at year 30 of greater than \$0.

The same would apply for a capital preservation analysis , you are calculating the SWR that will give you a 0% probability of having less than the “\$initial portfolio value” at the end of year 30. This will result in calculating the SWR for the worst starting month in the dataset. The remaining 1769 months will have a final portfolio value of greater that “\$Initial portfolio value” at the end of year 30.

I think it would be interesting and beneficial to see the average, median and max of those final portfolio values, especially with regard to the equities/bonds allocation. It is my hypothesis that being slightly less volatile a 25% bond allocation results in a slightly higher SWR because the ‘worst’ month in the dataset analysed isn’t as bad as the worst month for a 100% equities portfolio. However for the vast majority of starting months, a 100% equities portfolio will result in a much larger final portfolio value.

If this is still sounding like a bunch of baloney, happy to take it offline and have a chat 🙂

You are doing great work, keep it up.

• Apologies, I misunderstood your feedback! Ah, the semantics of ‘withdrawal rate’ vs ‘SAFE withdrawal rate’ 😐

I calculate a safe withdrawal rate for every month of the 1770 total months. That withdrawal rate is the exact withdrawal rate that will result in a \$0 final balance in 30 years. And you’re right, we could assume we withdraw 3.75% per year, which might give us a portfolio success rate of 99%. Then we could look at the balance of those 99% portfolios.

I’ll look into it 🙂