# Optimising a Tax-Free Investment Strategy using Data Science

Jul 5, 2018 · 15 minute read · CommentsExploratory Data AnalysisInvestmentSimulation

In a few months time, I’m going to become a dad for the first time and with that, all the usual concerns about long-term financial security have come to the forefront of my mind. For some time, I’ve heard about the option of tax-free investments but thus far have been slow to look into them and the savings potential they offer my family.

This project aims to use the power of data science to: generate millions of combinations of investments that abide by the tax-free savings rules and then: analyse those investments to understand how one can optimise them for specific savings goals, such as a child’s future education or wedding, retirement plan or just saving for a rainy day.

There are numerous online calculators where one can play around with individual lump sum amounts, monthly contributions and risk tolerances, however using these tools is cumbersome as you can’t simulate every possible combination. This means that don’t know if you are missing out on the “best” combination that would maximise your investment. It’s also useful to have a general appreciation for how these parameters affect your investment, which these tools don’t offer.

With this post, I’d like to provide a general understanding of how these parameters affect your investment and then bring it all together by showing different options for savings specific goal amounts, namely R250K, R500K, R1M, R2M, R5M and R10M. I chose these amounts because they represent goals that range from medium-term expenses such as paying for a wedding, all the way to retirement and even financial freedom.

We’ll look at what can and can’t be achieved with tax-free investments and at the end of the analysis I’ll provide a free pdf report (no email signup) containing all the graphs in the article. You can use this as an input to your investment decision when comparing products from different financial institutions. Knowing what’s possible will make the comparisons more precise.

If you would like to reproduce or extend the analysis, you can access the project source code here

## What are Tax-free Investments?

From 1 March 2015, it become possible to invest in a class of products whose returns are not subject to any form of income tax, divident tax or capital gains tax. We refer to these as Tax-free investment products. They can be packaged together and provided by licensed banks, long-term insurers, mutual and co-operative banks and government.

Their primary goal is to encourage and incentivise South Africa’s to save.

There are a few rules surrounding tax-free investments:

- As of 1 March 2017, you can contribute a
**maximum of R33,000**per tax year. Any portion of unused annual limit is forfeited in that year. Each new year this limit is reset to R33,000. - There is a life time limit of
**R500,000 per person**. - If a person exceeds the limits, there is a penalty of 40% of the excess amount.

Example: Taxpayer X invests R35,000 in a year – this exceeds the annual limit by R2,000, 40% of R2,000 = R800 must be paid to SARS. This penalty is added to the normal tax payable on assessment.

- You can have more than one tax free investment, however, you are limited to the annual limits per tax year and lifetime limits. This means you can invest, for example, R11,000 in Old Mutual, R11,000 in Investec and R11,000 in Absa.
- Parents can invest on behalf of their minor child. The minor child will use his/her own annual or lifetime limits.

Example: A family of four could each have an account allowing a total of R33,000 x 4 = R132,000 to be invested in a given year or R2M over a lifetime.

- When returns on investment are added to the amount contributed, the balance can exceed both the annual and/or lifetime limit. The re-investment of these returns within the account does not affect the annual or lifetime limit.

Example: If you invest R33,000 for the year and receive a return of investment of R5,000, which you have chosen to re-invest, the total amount in the account will be R38,000. The following year, you will still be able to invest your full R33,000 for the year.

- If the returns are withdrawn and the same amount is reinvested, that amount is regarded as a new contribution and impacts on both the annual and lifetime limits. Withdrawals made cannot be replaced, be it returns or capital.
- Tax free investment accounts cannot be used as transactional accounts, for debit or stop orders or for ATM transactions.
- Only new accounts will qualify as the idea is to encourage new savings, in other words, existing accounts may not be converted.

## Assumptions & Caveats

With this type of analysis, there has to be some assumptions made and limitations in place:

- All data generated assumes that the lump sum and monthly contributions will remain the same throughout the entire life of the investment. Of course in real life, one might change their monthly contribution or add additional lump-sum payments when they have the funds. The fund you invest in might also increase your monthly contribution automatically each year to keep up with inflation. In this first version of the analysis, I won’t consider these cases but in a future version I will.
- We are going to look at investment options that cover 5 risk categories namely low, low-medium, medium, medium-high and high. What represents these different risk categories is the expected return one can receive for the type of investment. I will be using values which I’ve borrowed from https://savetaxfree.co.za. I’ve also used their tax-free investment calculator to ensure the investments I generate are 100% accurate.
- The
caveat here is that these are idealised investments, i.e. if a high risk investment gives you an expected return of 18% per year, then you’d get this every year without fail. Of course this is completely unrealistic because real markets fluctuate and you may get more or less than this return in any given time period. As the risk goes up, so does the risk of not getting that return, so while this analysis will be accurate in the potential idealised value one*BIG*earn, it will be slightly inaccurate in the value one*could*earn. In a future version, I would like to inject random noise that represents real market fluctuations.*will* - The returns generated are not inflation adjusted. This will be done in a future version. For now they represent the idealised, mathematical future value one could earn.
- We’ll assume interest is compunded monthly at the end of each month.
- We’ll assume returns are reinvested into the fund without withdrawal, until the maturity date.

Risk | Rate | Description |
---|---|---|

Low | 7.21% | Interest-bearing money market funds |

Low-medium | 9.93% | Multi-asset low equity funds |

Medium | 12.18% | Multi-asset options using average of medium equity and high equity funds |

Medium-high | 16.59% | Top 40 equity funds |

High | 18% | Small and mid-cap equity funds |

## Data Generation Process

Most data science projects use existing data, however it’s entirely possible to generate your own if it accurately represents the underlying situation. In the case of investments like these, with well known future value calculation parameteres, the data can be generated.

To do so, I first created investment combinations using:

- Time-horizon’s that span 1 to 50 years into the future.
- Lump sum’s from R0 to R30,000 in R250 increments.
- Monthly contributions from R0 to R5,000 in R50 increments.
- Risks using the 5 mentioned previously.

Then each possible combination of these options was used to generate a future value calculation of the investment.

This gave us **3,055,250** possible investments, however not all of them are valid as they exceed either the R33,000 per year limit or the R500,000 lifetime limit.

After writing an algorithm to weed out the invalid options, we are left with **744,425** investments, plenty for us to analyse.

## How Time Affects Our Investment

For this example, let’s assume we do not have enough money to contribute a lump sum, but we can afford to pay R500 per month into a medium-risk investment account. What effect does the number of years we stay invested make on our eventual outcome?

This graph clearly shows us the value of compound interest, specifically, the value of compound interest over time.

Even with no lump sum, if we are patient and keep all our money in the fund, over the course of a lifetime, we can make a substantial amount of money. As we mentioned up front, the big caveat here is these values are idealised and in real-life, they would be subject to market fluctuations. This means we wouldn’t get a perfect 12.18% return each year and due to inflation the value of the money in 50 years time is not the same as it is today, however, it still paints a very clear picture that starting to invest as early as possible ** really** does matter.

When I look at this graph, it makes me sad that I didn’t start saving much earlier in life. We’re going to unpack this in much more detail as we move through the analysis.

## How Time and Risk Affects Our Investment

Let’s build on this by comparing how risk category affects the outcome. We’ll stick with the same example of zero lump sum and R500 per month contributions. We’ll also zoom in on the 0 - 30 year period.

Clearly, the rate of return given by the risk of the investment matters.

Does this mean you should just go straight for a high risk investment? **Of course not**. By it’s very nature, it is ** high** risk and however inviting these numbers might look, you probably won’t get them. In fact, one must remember that even a low-risk option still carries risk. Another global recession can wipe out a hefty chunk of your investment so as the saying goes, don’t put all your eggs in one basket. Of course, this is the idea with the lower risk investments; they aim to be more balanced, less speculative, more diversified and hence more immune to large scale financial crises that can affect whole segements of the market.

## How Monthly Contribution and Lump Sum Affects Our Investment

This time we’re going to assume a few different combinations, specifically time horizon’s of 2, 5, 10 and 20 years; monthly contributions of R250, R500, and R1000 per month and lump sums of R0, R1,000, R5,000, R10,000 and R20,000. Initially let’s stick with the medium risk category.

While it’s clear that monthly contribution and time horizon matter, whether or not someone should wait till they have a sizeable lump sum is less clear. On the one hand, starting the fund off with something rather than nothing does increase the investment value, but if it takes you 1-2 years to save the lump sum in the first place, **wouldn’t it be better to be earn compound interest sooner rather than later?** Then a follow up question: If your funds are limited, should you start with no lump sum and a bigger monthly contribution or would a large lump sum and smaller monthly contributions suffice?

Let’s study this by comparing an investment of R250 per month and lump sum in the region of R25K - R30K with an investment of R500 per month and a lump sum in the region of R0 - R5K. We’ll use a medium risk and time horizon of 30 years.

Extra Cash on Hand is the difference between the R500 per month and R250 per month contributions summed over 30 years, less the lump sum paid. It represents the money we save by putting less into the fund each month, even though we’ve used a bigger lump sum upfront, in the case of the first option.

Looking at the R250 per month case, the graph shows that we invest less money into the fund overall, while earning a similar return when we start off with a bigger lump sum, even if we contribute less each month. Hence if you can afford to, it pays to have a sizeable lump sum.

But what if you don’t have a lump sum available, should you save for it first before investing? No, rather start investing what you have right away. As we showed earlier:

The power of compound interest over the long term is more profound than having an initial lump sum, so rather get your money making more money for you, as soon as possible.

## Combining Monthly Contribution, Lump Sum and Risk

In the previous example, we assumed a medium risk category, let’s see what happens when we change the risk.

We’ll do this two ways: first we’ll assume a lump sum of R0, then one of R10,000.

Ah that high risk curve is a thing of beauty! If only it was guaranteed.

It’s clear that risk does matter, the greater the risk, the greater the reward. Perhaps, as it’s often suggested, one can start with higher risk options in their younger years and move down the risk categories as you get older.

If we look at a few specific points, we can see that on a medium risk product, we’d need to contribute R1,000 per month over 30 years to obtain the same value as R600 per month over 25 years on a high risk product. However that difference between 25 and 30 years on the high-risk product, regardless of how much you contribute per month, is really striking due to the long term effect of compound interest.

Let’s plot the same graph but using R10,000 as a lump sum value.

A difference, yes, but not a massive one. Again, we should rather start saving now than waiting to have a lump sum; it doesn’t matter nearly as much as the years invested and how much you can contribute monthly.

If, like me, you are about to have a baby and want to start putting money into a fund that in 18 years time could be used for your child’s university education, what could you do? Let’s compare different risks, monthly contributions and lump sum amounts over an 18 year window.

Of course, the option you choose depends entirely on your personal situation, so there is no real advice that can be given here. It’s simply useful to have a visual reminder about how the numbers play out.

## Comparing Options that Max Out Investment

Now let’s think about how we can max out our investment. Two of the ways would be to contribute either R33,000 once per year (with no further monthly contributions), or R2,750 per month. Which of these options is better? In addition, does it matter whether this payment happens at the beginning or end of a period (month or year).

Let’s find out. We’ll investigate the 1 to 30 year range and the 31 to 50 year range seperately in order to show more detail on the graphs.

It looks like a monthly payment of R2,750 at the start of each month is best and a once-off R33K payment at the end of each year would be the worst option. Either way of contributing R2,750 or paying R33K once-off in the beginning of a period yields similar returns for the first 15 years but after that it becomes clearer that regular monthly payments are better, especially if they are at the beginning of the cycle.

## Putting it All Together

You’ve probably been waiting for something that pulls all this together and show’s you much time it will take to save different amounts given all risk, lump sum and monthly contribution options.

We’re going to target a specific amount of savings (within R10K - R20K) and then plot all the combinations that lead to that value. These are probably the most useful graphs of the analysis and the ones you’ll really want to hold onto, as they make it clear what is and isn’t possible to achieve in a given timeframe.

In all of the cases below, it’s useful to look across the risks to compare what time horizon, lump sum and monthly contribution is required to obtain the investment outcome of interest.

The pdf report at the end contains these and all the other graphs we’ve shown.

### Options for Saving R250K

### Options for Saving R500K

### Options for Saving R1M

### Options for Saving R2M

### Options for Saving R5M

### Options for Saving R10M

### Options for Saving R20M

## Summary & Next Steps

Tax-free investments are a wonderful initiative that we should all be taking advantage of. However they are no panacea, nor are they a get-rich-quick scheme. Their beauty, like most investment products, lies in the waiting time of compound interest but with the added and substantial benefit of not having to pay any form of tax on your returns.

It’s clear that making use of a tax-free investment product is a smart thing to do. It’s also clear that how much you contribute into the fund per month, the amount of time you leave your money compounding and the risk category you choose, makes a substantial difference to your final investment amount. If you can afford to put a lump sum down, certainly do so, but it’s the least important factor in the investment, so rather start saving as soon as possible as the time under investment is what matters most.

As mentioned in the initial assumptions, this analysis has some limitations and in future versions I’d like to do the following:

- Take any investment fees into account.
- Simulate adding additional lump sum amounts (for example, adding a 13th cheque or bonus into the fund).
- Simulate changing the monthly contribution at various points through the time horizon.
- Simulate the market going up and down, i.e. not getting the expected return on investment.
- Inflation-adjust the returns.
- Compare this with other investment options.

I hope this analysis has been useful. Please do let me know where it can be made clearer and ideas for how it can be extended.

You can download a pdf report of the visualisations here