In Part 3 of our Safe Withdrawal Rate series we determined the best mix of Australian equities and bonds to maximise the chance of a retirement portfolio lasting 30 years. We discovered that a mix of 75% Australian equities and 25% Australian bond was optimal.

But in reality, most of us Aussies invest in a mix of Australian and U.S. markets (and possibly some ‘whole of world’ markets).

So in this article, we are going to extend our previous analysis to look at an internationally diversified portfolio. We are going to determine how we should allocate our retirement portfolio across Australian equities, Australian bonds, U.S. equities and U.S. bonds.

## More detail on Australian asset allocation and failure rates

In part 3 of this safe withdrawal rate series, we looked at how much Aussies could withdraw from a retirement portfolio containing Australian equities and bonds without running out of money.

We discovered that a retirement portfolio of 75% equities would result in the highest chance of the portfolio lasting the length of a 30 year retirement. Interestingly, both portfolios with 100% equities and 50% equities resulted in higher portfolio failure rates than 75% equities.

This means that the optimal mix of equities/bonds for our retirement portfolio is somewhere around 75%. But because we use 25% intervals, we don’t know if it’s actually 85%, 65% or somewhere in between.

At the request of a few loyal readers, we will kick off Part 4 of our Safe Withdrawal Rate series by calculating the *exact* Australian equities and bonds split that optimises portfolio success rate.

### What is the optimal Australian equities and bond split?

In our previous post, we showed that a 3.75% withdrawal rate results in acceptably low portfolio failure rates for any portfolio with as low as 50% equities allocation. So we are going to look at portfolio success rates at a 3.75% withdrawal rate in this analysis.

To find the optimal Australian equities and bond split, we calculated the portfolio failure rate for 50 different asset allocations, from 100%/0% equities and bonds to a 50%/50% split. We define portfolio failure to occur when the portfolio runs out of money before the end of a 30 year retirement length. The results are plotted in the chart below.

At the 3.75% withdrawal rate, there is clearly a benefit of holding some bonds in an Australian retirement portfolio. That benefit increases until an bond allocation of between 25-35% (i.e. an equity allocation of 65-75%), when the portfolio failure rate is lowest. After that, failure rates rise sharply.

This shows that there is a diversification benefit of mixing equities with bonds (up to a point). The interesting thing is that we are investing into a *lower return asset class* and it still results in higher portfolio success rates. In other words, the benefit of a lower sequence of returns risk outweighs the reduced portfolio return.

## What is the optimal mix of Aussie and U.S. equities and bonds?

As we mentioned, in part 3 of this Safe Withdrawal Rate series we examined which allocation of Australian equities and bonds would maximise the success of a 30 year retirement portfolio. We took quite a ‘blunt’ approach and simply tested different mixes of equities and bonds at 25% intervals.

That approach works well for a portfolio with two assets because it only requires testing five different asset mixes. However, now that we have a portfolio of four assets (U.S. equities, U.S. bonds, Australian equities and Australian bonds), using the same approach would require us to compare over 600 unique asset mixes!

So this time we are going to use a more analytical approach called Modern Portfolio Theory.

### What is Modern Portfolio Theory?

For any investment there is a trade-off between risk and reward. Investments with a higher return will have a higher risk (and vice versa). However, the premise behind Modern Portfolio Theory is that there are some cases in which we can minimize our risk without reducing our return. We do this through diversification.

Proper diversification isn’t just picking a random bunch of assets and claiming that we’re now diversified. True diversification requires owning assets that are not highly correlated.

For example, if you only owned a shares in Commonwealth Bank and Westpac there’d only be limited diversification benefit. No industry diversification. No geographical diversification. In fact, owning a bunch of highly correlated assets like this can be almost as risky as owning a single asset.

But if we intelligently build a portfolio with assets with low correlation, then we can minimise risk. This doesn’t mean that we can completely eliminate risk – no chance of that – but it does mean that we can get the lowest possible risk for any given return.

### Finding the optimal mix of equities and bonds, Australian and international

#### Update: Some background on these calculations

Some readers asked for more information on the assumptions and calculations behind the following analysis. For transparency, here is some background to make sure everything is clear:

- We calculate using monthly data and the data set is outlined clearly in Part 2 of this series.
- We use the analytical approach to safe withdrawal rate calculation that has been used by Suarez et al., Morningstar and Big ERN. This means that we select the final portfolio value that we are targeting (in this case it is $0) and calculate the exact safe withdrawal rate required to achieve it. I shared the formulae in Part 3 of this series.
- All calculations are reported in real dollars, which means that we have adjusted for inflation, and where applicable we have also accounted for the effect of currency movements on returns (i.e. U.S. returns are net of foreign exchange).

Now that’s done, let’s get into it…

#### The efficient frontier (may the force be with you)

The first challenge in portfolio construction is identifying assets with low correlation. For us that’s a moot point, as we already have four assets that we need to optimise: U.S. equities, U.S. bonds, Australian equities and Australian bonds.

The second challenge is choosing the best weighting/asset allocation to give us the lowest risk and highest return. As it turns out, there is no single asset allocation that is optimal for a portfolio. The asset allocation will be different depending on the level of return desired.

Calculating the different asset allocation for each level of return is a technically complex exercise that I won’t go through here. If you’re interested in how it works, you can check it out here.

Suffice to say that the chart below illustrates the efficient frontier for a portfolio of U.S. equities, U.S. bonds, Australian equities and Australian bonds.

The line on the chart illustrates the lowest risk for any desired return. In other words, there is no mix of assets in the portfolio that will have the same amount of return but a lower standard deviation. And each point on the line will have a different mix of assets.

#### Optimal portfolio asset allocations

Now we want to look at exactly what asset allocations sit along our efficient frontier. These are the asset allocations we will use in our analysis later in this article, as they give us the highest return for the lowest risk.

The table below outlines the exact asset allocations for each point on the chart above. The numbering begins from the bottom of the line, so the point on the top-right is number 13.

Portfolio Statistics | Portfolio Allocation | |||||

# | Return | Std Dev | US Bonds | US Equities | AU Bonds | AU Equities |

1 | 2.77% | 6.60% | 100% | 0% | 0% | 0% |

2 | 3.00% | 6.40% | 95% | 2% | 0% | 2% |

3 | 3.50% | 6.15% | 86% | 6% | 0% | 7% |

4 | 4.00% | 6.16% | 77% | 11% | 0% | 12% |

5 | 4.50% | 6.41% | 68% | 15% | 1% | 16% |

6 | 5.00% | 6.88% | 59% | 19% | 1% | 21% |

7 | 5.50% | 7.53% | 49% | 24% | 1% | 26% |

8 | 6.00% | 8.32% | 40% | 28% | 1% | 31% |

9 | 6.50% | 9.21% | 31% | 32% | 1% | 35% |

10 | 7.00% | 10.17% | 22% | 37% | 2% | 40% |

11 | 7.50% | 11.19% | 13% | 41% | 2% | 45% |

12 | 8.00% | 12.25% | 3% | 45% | 2% | 49% |

13 | 8.53% | 16.78% | 0% | 0% | 0% | 100% |

We can already see a number of interesting findings:

- To maximise returns and minimise risk, we do not need Australian bonds in our portfolios. We can get near-enough optimised portfolios with just Australian equities, U.S. equities, and U.S. bonds.
- If we want to increase returns, we simply reduce the proportion of U.S. bonds in our portfolio and buy (pretty much) a 50/50 split of Australian and U.S. equities in its place.

#### Calculating portfolio success rates

It’s interesting to know which asset allocation will result in the most highly optimised risk and return. But it’s even more interesting to translate the findings into something practical, such as the likelihood that a portfolio will last throughout retirement.

In the previous post in this series, we looked at how various Australian equities and bond allocations affected portfolio success rates. We defined portfolio success as the portfolio having more than $0 after a 30 year retirement.

We want this analysis to be comparable with that previous post, so let’s convert these asset allocations into portfolio success rates. To do this, we simply test the asset allocations in the table above to calculate the proportion of historical portfolios that would have more than $0 after 30 years. This is the same approach that we took in the previous post.

The table below shows portfolio allocations (left hand side, blue) and their associated portfolio success rates (right hand side, green-red).

Portfolio Allocation | Portfolio Success at Withdrawal Rate | |||||||

# | US Bonds | US Equities | AU Bonds | AU Equities | 3.50% | 3.75% | 4.00% | 4.25% |

1 | 100% | 0% | 0% | 0% | 65.1% | 55.5% | 50.7% | 46.0% |

2 | 95% | 2% | 0% | 2% | 70.8% | 59.3% | 52.6% | 48.9% |

3 | 86% | 6% | 0% | 7% | 86.3% | 73.3% | 60.9% | 53.4% |

4 | 77% | 11% | 0% | 12% | 96.4% | 88.6% | 75.5% | 64.2% |

5 | 68% | 15% | 1% | 16% | 100.0% | 98.6% | 92.1% | 77.9% |

6 | 59% | 19% | 1% | 21% | 100.0% | 100.0% | 99.3% | 93.6% |

7 | 49% | 24% | 1% | 26% | 100.0% | 100.0% | 99.8% | 98.5% |

8 | 40% | 28% | 1% | 31% | 100.0% | 100.0% | 100.0% | 99.0% |

9 | 31% | 32% | 1% | 35% | 100.0% | 100.0% | 100.0% | 99.1% |

10 | 22% | 37% | 2% | 40% | 100.0% | 100.0% | 100.0% | 99.2% |

11 | 13% | 41% | 2% | 45% | 100.0% | 100.0% | 100.0% | 99.3% |

12 | 3% | 45% | 2% | 50% | 100.0% | 100.0% | 99.8% | 99.1% |

13 | 0% | 0% | 0% | 100% | 98.9% | 98.4% | 97.9% | 97.0% |

It’s interesting to see that the portfolios with the highest success rates (#10-12) share a similar equity/bond allocation to the optimal Australian portfolio (see the section above). And it gives further support to the notion we should keep *some* bonds in our retirement portfolios.

One big caveat: these findings are for a 30 year retirement only. We hypothesise that longer retirement lengths will require a higher proportion of equities. We’ll investigate this later in this series.

### How does this compare to purely Australian portfolios?

#### Comparing against the efficient frontier

One way to compare our international portfolios against purely Australian portfolios is to plot Australian portfolios against the efficient frontier.

Portfolios that sit on the right-hand side of the efficient frontier are sub-optimal. In other words, these portfolios have higher risk for the same level of return.

In the chart above I have taken four random portfolios and plotted them against the efficient frontier. As you can see, all four portfolios are sub-optimal.

For example, in our previous post, we showed that a 75% Australian equities and 25% Australian bonds was the optimal mix for a domestic portfolio. But in the chart above, we can see that this portfolio sits to the right of the efficient frontier. Looking closely, the chart shows that rebalancing the portfolio with international assets would allow us to either increase return by 1% or reduce standard deviation (risk) by 2.5%.

In other words, an internationally diversified portfolio is better than the ‘best’ purely Australian portfolio.

#### Comparing portfolio success rates

Another way to understand how international portfolios compare with Australian portfolios is to compare portfolio success rates. The table below compares the likelihood of the retirement portfolio having more than $0 after a 30 year retirement.

Please note that the ‘international’ portfolios in the table below use the closest portfolio allocation from the table above. For example, the international 75% equities, 25% bonds portfolio in the able below is actually portfolio 10 in the table above (22% U.S. bonds, 2% Australian bonds, 37% U.S. equities, 40% Australian equities).

Portfolio Success Rate at... | |||||||

Portfolio Allocation | 3.50% Withdrawal | 3.75% Withdrawal | 4.00% Withdrawal | ||||

Equities | Bonds | Internat'l | Domestic | Internat'l | Domestic | Internat'l | Domestic |

0% | 100% | 65.1% | 68.1% | 55.5% | 62.6% | 50.7% | 56.8% |

25% | 75% | 96.4% | 85.6% | 88.6% | 81.2% | 75.5% | 78.3% |

50% | 50% | 100.0% | 99.4% | 100.0% | 96.9% | 100.0% | 91.8% |

75% | 25% | 100.0% | 99.4% | 100.0% | 98.6% | 100.0% | 98.0% |

100% | 0% | 98.9% | 98.9% | 98.4% | 98.4% | 97.9% | 97.9% |

As you can see, portfolios containing a mix of Australian and international assets perform better than purely Australian portfolios at almost every equity/bond allocation. The one exception is a 100% bonds portfolio, where we’d be better off investing in purely Australian bonds.

## Some limitations of this analysis

There’s a few things that we should keep in mind as we digest this analysis:

- All of the calculations above are calculated based on historical risk and returns. As always, we should keep in mind that past returns do not equal future returns.
- All of the portfolio success/failure rates are based on a 30 year retirement length. This is probably shorter than the retirement lengths of some early retirees. In a future post we will examine longer retirement lengths affect portfolio asset allocation and success rates.

## Wrapping it all up

This post is quite dense, so it’s probably worth summarising it with a few key findings:

**Internationally diversified portfolios perform better than purely domestic portfolios.**Analysis of the efficient frontier and a comparison of portfolio success rates shows that retirement portfolios have higher returns with lower risk, and a higher likelihood of lasting 30 years, when the portfolio includes international assets.**There is no place for Australian bonds in an internationally diversified portfolio.**Optimising portfolios to maximise returns and minimise risks resulted in a 2% Australian bond allocation*at most*. So in practical terms we can ignore Australian bonds.**We can adjust risk appetite by adjusting the proportion of U.S. bonds**, with the remaining portfolio split 50/50 Australian and U.S. equities. To increase our risk appetite we simply reduce the proportion of U.S. bonds and replace it with equities that are split 50/50 between Australia and the U.S.

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

All the best,

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