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Small Annual Return Differences

It should be emphasized that this article was written at a specific date based on the information relevant at the time of writing around 2022-01. It is more than likely that the content will quickly become outdated and this content will not necessarily be updated to remain relevant. This is applicable to the laws around tax, pertinence of Regulation 28, performance of the mentioned funds, and so on. Other sources should always be consulted for confirmation of the validity of the claims put forward.

A small improvement or deterioration in annual return can make a significant difference over long time periods. As a realistic example, this concept can be applied to retirement accounts in South Africa. Despite the almost universal recommendation from the majority of financial advisors and media personalities, a retirement account may not be the most effective option for investments in South Africa. Unfortunately and disappointingly, it seems that these financial advisors and media personalities often make generalized statements based on their anecdotal opinions and without evidence to back up their statements (although this is not unexpected from the disreputable behaviour of the majority of the financial industry seeking to enrich themselves rather than their clients, while a very small minority continue to try their best to maintain a fiduciary duty). With consideration of the evidence for whether retirement accounts are rational in South Africa, it becomes apparent that, in most circumstance, a retirement account should not be recommended for the majority of people, especially for young people with a long time horizon who are uncertain of their future goals.

General Retirement Account Characteristics

There are multiple structures which countries use to apply tax to retirement and other tax-advantaged accounts. In many cases, a country will often offer more than one of these tax-advantaged accounts to its citizens. For example and apart from taxable accounts, in the United States, the general available accounts include an Individual Retirement Account (IRA) or 401(k) and Roth Individual Retirement Account (Roth IRA); in the United Kingdom, the general available accounts include a Self-Invested Personal Pension (SIPP) and Individual Savings Accounts (ISA); in Canada, the available accounts include a Registered Retirement Savings Plan (RRSP) and Tax-Free Savings Account (TFSA); and, in South Africa, the general available accounts include a Retirement Annuity or Preservation Provident Fund or Preservation Pension Fund (collectively referred to as a retirement account for simplification) and Tax-Free Savings Account (TFSA). There may also be other more specialized structures, such as the Lifetime Individual Savings Accounts (LISA) in the United Kingdom with the government partially matching contributions up to a certain amount.

The structures are usually concerned with the taxation of contributions, returns, and withdrawals. A traditional taxable account can be seen as the least favourable structure with taxation on contributions, taxation on returns, and exemption on withdrawals (taxed-taxed-exempt) - most accounts will tax either contributions or withdrawals and almost no account taxes both contributions and withdrawals. Obviously, the most favourable structure would have an exemption on contributions, exemption on returns, and exemption on withdrawals (exempt-exempt-exempt), but most countries do not offer an account of this type unfortunately. The most common tax-advantaged accounts include a structure with either exemption on contributions, exemption on returns, and taxation on withdrawals (exempt-exempt-taxed) or taxation on contributions, exemption on returns, and exemption on withdrawals (taxed-exempt-exempt). In most countries, the primary tax-advantaged option includes an exempt-exempt-taxed structure, while the secondary tax-advantaged option includes a taxed-exempt-exempt structure.

Deciding which option is optimal under specific circumstances requires considerations of the advantages and disadvantages of each structure. An exempt-exempt-taxed structure has the advantages of deferring taxes until retirement, such that it may be possible to decrease the effective tax rate, as it is usually expected for income in retirement to be lower than income during accumulation. However, this has the disadvantage of not knowing what the tax rates will actually be during retirement and, if the tax rates are increased, it could have detrimental consequences (conversely, if the tax rates are decreased, it could have beneficial consequences). A taxed-exempt-exempt structure has the advantage of knowing what the tax rate will be during accumulation without the uncertainty of having to wait until retirement. However, as mentioned, it is usually expected for income during accumulation to be higher than income in retirement which may result in a higher effective tax rate. In addition, an account with a taxed-exempt-exempt structure is usually freely accessible for withdrawal before retirement, while an account with an exempt-exempt-taxed structure usually has requirements which are locked for withdrawals until a specific retirement age is reached.

Primary tax-advantaged options and mechanisms in different countries:

South African Retirement Accounts

Firstly and most importantly, a retirement account in South Africa is governed by the Pensions Funds Act and Regulation 28 which limits the allocation to certain asset classes. The purpose of Regulation 28 is idealistic with the aim of protecting investors against poorly diversified portfolios and ensuring investments are sensible without excessive exposure to risky assets (unfortunately, it does not protect investors from predatory fees). As a result, this leads to a more conservative portfolio (usually with predatory fees). However, as academic research has repeatedly shown, this is not ideal and it is unfair to use universal criteria when each investor is unique based on their personal requirements and goals - a young investor should be taking on as much risk as they can tolerate, not as much risk as is arbitrarily allowed by Regulation 28. Currently, the primary restrictions of Regulation 28 include equity exposure limited to 75%, local or international property exposure limited to 25%, and foreign investment exposure limited to 30%. When academic research recommends an equity exposure of 200% for young investors, these limitations are completely unfair, while the limitation to have at least 70% of assets invested in South Africa is simply irrational and illogical. Thus, a retirement account will almost certainly underperform a more aggressive portfolio over the long-term.

A retirement account in South Africa follows an exempt-exempt-taxed structure, so the primary advantage of a retirement account is the deferral of tax until retirement. The other advantages of a retirement account include the tax-free lump sum at withdrawal which is currently only up to R500,000 and exemptions from taxes on capital gains, dividends, and interest to reduce the effective tax rate. However, for young people, a large part of these advantages may become irrelevant as the rules around retirement accounts could easily change in the future based on the decisions of the government. For emphasis, these changes may be beneficial for the investor, but it is ultimately a gamble, as it is just as likely for these changes to be detrimental depending on the state of the country in the future - it is not useful to defer taxes until retirement if the tax rates in the future will be higher. Moreover, there are the additional disadvantages that it is not possible to withdraw from the account without tax penalties until the age of 55, there is forced annuitization upon retirement with only a fractional amount accessible as an initial lump sum, and there is a waiting period of 3 years if someone emigrates before they are able to access their account (although, just to mention, financial emigration is usually unnecessary and simply used as something for financial advisors to sell to clients).

As another caveat of retirement accounts, it should also be noted that the fees are excessive and most funds are actively managed. Consequently, this almost always leads to underperformance and uncompensated risk from an incompetent fund manager. For reference, out of almost 181 funds, the CS BCI Aggressive Prudential Fund of Funds was the 90th best performing fund in the category of South African Multi Asset High Equity with compliance with Regulation 28. This arbitrary fund had an expense ratio of 2.85%, 5-year cumulative return of 45.92%, and volatility of 11.73%. This is the median result and would be expected for most investors, while the mean result was a similar 5-year cumulative return of only 45.68%. To consider the best case scenario in which someone was lucky enough to invest in the best option, the Long Beach Managed Prescient Fund was the best performing funds in the category of South African Multi Asset High Equity with compliance with Regulation 28. This arbitrary fund had an expense ratio of 1.64%, 5-year cumulative return of 91.19%, and volatility of 15.1%. The strange thing is that the Long Beach Managed Prescient Fund was ranked 237th out of 248 funds for its 1-year performance, so it is not too radical to allege that its early performance was based on luck more than skill. Regardless, the Morningstar Global Target Market Exposure Gross Return (which is an index comparable to a globally-diversified portfolio of equities based on market capitalization, such as the Vanguard Total World Stock Index ETF with an expense ratio of only 0.08%) had a 5-year annualized return of 17.41% which corresponds with a 5-year cumulative return of 137.2%. This is an increase of 198.3% over the expected result and 50.24% over the best result. However, it should be kept in mind that a single period of 5 years is very short and global equities, especially in the United States, were strong over this particular period, but it is still unlikely for the result to change if the timescale was expanded.

As of 2021-12-31, the following expense ratios are listed for several common funds with their longest available cumulative performance (interestingly, the best performing funds are the 10X High Equity Index Fund and Sygnia Skeleton Balanced 70 Fund which both have similar passive strategies). As a result of these high fees, a globally-diversified portfolio is already beginning with an advantage, as it is required for these funds to make up this fee before they even match a globally-diversified portfolio which usually has a negligible fee. In other words, if a fund has a fee of 1.5% and the expected return from a globally-diversified portfolio is 10%, then the fund needs to have a return of 11.5% before fees just for equivalent performance after fees - this is an increased return of 15% every year in an increasingly competitive market with an incredibly shrinking alpha.

Examples of expense ratios and performance of several common funds as of 2021-12-31:
  • 10X High Equity Index Fund (Backtest): 0.62%, 5Y: 58.87%
  • Absa Managed Fund: 2.11%, 5Y: 35.88%
  • Allan Gray Balanced Fund: 0.96%, 5Y: 40.62%
  • Ashburton Balanced Fund: 1.32%, 5Y: 34.66%
  • BCI Prudential Fund of Funds: 2.16%, 5Y: 48.16%
  • Coronation Balanced Plus Fund: 1.64%, 5Y: 55.50%
  • Discovery Balanced Fund: 1.98%, 5Y: 49.89%
  • Fairtree Invest Strategic Factor Prescient Fund: 1.20%, 1Y: 19.22%
  • FNB Multi Manager Balanced Fund: 1.64%, 6M: 7.41%
  • Hollard Prime Strategic Assertive Fund of Funds: 1.65%, 5Y: 51.83%
  • Investec BCI Diversified Growth: 2.27%, 1Y: 22.24%
  • Marriott Balanced Fund: 2.12%, 5Y: 31.24%
  • Momentum Focus 7 Fund: 1.62%, 5Y: 36.36%
  • Nedgroup Investments Balanced Fund: 1.60%, 5Y: 55.45%
  • Ninety One Opportunity Fund: 1.83%, 5Y: 52.64%
  • Old Mutual Balanced Fund: 1.63%, 5Y: 48.91%
  • PPS Balanced Fund: 1.80%, 5Y: 49.66%
  • PSG Balanced Fund: 1.77%, 5Y: 39.12%
  • Sanlam Investment Management Balanced Fund: 1.57%, 5Y: 35.05%
  • STANLIB Balanced Fund: 1.34%, 5Y: 46.09%
  • Sygnia CPI + 6% Fund: 1.64%, 5Y: 52.74%
  • Sygnia Skeleton Balanced 70 Fund: 0.42%, 5Y: 58.16%
  • Furthermore, there is a common misunderstanding with regard to the refund or rebate received at the end of the tax year for contributions to a retirement account. Basically, although this is not applicable when contributions are accounted for in advance by an employer, someone pays their normal tax during the year and then claims a refund when they submit their tax return. When the government gives this person their refund, the person often interprets this as a windfall of sorts. Instead, they should have interpreted it as them giving the government an interest-free loan, as they ultimately overpaid their taxes and got their money back without interest. In addition, they incurred an opportunity cost by missing out on the possible performance during which this refund was not invested. If someone does contribute to a retirement account, they should ensure the tax consequences from the contributions are accounted for in advance (either through their employer or by only contributing towards the end of the tax year).

    In South Africa, a tax-free savings account is also offered and follows a taxed-exempt-exempt structure. This means that tax is applied before contributions, but then the capital gains, dividends, interest, and withdrawals are sheltered from tax. Most notably, the primary advantage of a tax-free savings account is that it is not governed by Regulation 28 and it is free to invest in a globally-diversified portfolio (although local ETFs or unit trusts need to be used). For this reason alone, a tax-free savings account is often more preferable to a retirement account under almost all circumstances, although the contributions are currently limited to only R36,000 per year and only R500,000 over its lifetime. An additional advantage of tax-free savings accounts is the certainty of the tax rate compared to a retirement account which has the risk of tax rates increasing in the future and mitigating any potential advantages from deferring tax.

    In this regard, another misconception about retirement accounts should be pointed out. There is often a belief along the lines of those that returns from a retirement account must be naturally enhanced directly due to the deferral of tax. This is even a common interpretation among financial advisors and media personalities, but it is mostly incorrect and misguiding. Someone does not earn an additional return on the amount they would have paid in tax, as they still have to pay tax on this amount when they withdraw. Assuming the same investment, if someone is taxed at the same rate while they are accumulating as they are during retirement, then there is no difference between a retirement account and tax-free savings account (there will only be a slight difference for a taxable account due to taxes on capital gains, dividends, and interest). Since the tax is a percentage, it does not matter if it is paid from a smaller initial amount or larger final amount. If someone is taxed at a higher rate in retirement, then a tax-free savings account is better than a retirement account. If someone is taxed at a lower rate in retirement, then a retirement account is better than a tax-free savings account (although, as mentioned, it is not usually possible to access an equivalently rational and low-cost investment due to Regulation 28 irrationally prohibiting access to a globally-diversified portfolio).

    As a simple example, consider a pre-tax contribution of R10,000 with a tax rate of 30% now and in retirement, average rate of return of 8% per year, and time period of 20 years. If this contribution is given to a retirement account, an initial tax of R0 is due to give an initial amount of R10,000 which will grow to R49,268 after 20 years at 8% per year at which point a final tax of R9,854 is due upon withdrawal to give a final amount of R39,414. If this contribution is given to a tax-free saving account, an initial tax of R2,000 is due to give an initial amount of R8,000 which will grow to R39,414 after 20 years at 8% per year at which point a final tax of R0 is due upon withdrawal to give a final amount of R39,414. The final amount is identical in each case. For complement, this highlights a behavioural disadvantage of a retirement account, where the investor may think their portfolio is worth more than it actually is worth once taxes are included. If this is difficult to understand, it can be seen that the tax is applied at a single point to the total amount and it does not matter at which point it is paid - start, middle, or end will give the same results (in other words, the percentage allocated for tax is simply growing with the investment if deferred and will always remain proportional to the investment).

    Modelled Performance Considerations

    To compare the expected performance differences from small annual return differences, a model is created and, when applied to the implications of a retirement account, clearly demonstrates the inadequacy of retirement accounts even after accounting for the primary advantage offered through the deferral of tax. As mentioned, the expected underperformance of a retirement account is an objective result of the conservative restrictions of Regulation 28 with arbitrary limitations to the amount of equity exposure, introduction of uncompensated risk from Regulation 28 through concentration in a single country with a lack of exposure to a diversity of industries (and, in most cases, idiosyncratic decisions of active management relying on luck rather than skill), and comparatively high fees for the management of the funds. The primary considerations for the comparison are the differences in return and effective tax rates (unfortunately, risk cannot be fully and accurately accounted for due to a lack of the available data).

    Although some examples were given previously of several common retirement funds, the Allan Gray Balanced Fund will be considered in more detail, as it is a very popular fund with over R153,000,000,000 of assets under management as of 2021-12-31. This fund has a 10-year annualized return of 9.80%, which, according to Morningstar, is approximately equal to the ZAR/NAD Aggressive Allocation category with an average 10-year annualized return of 9.87%. The Morningstar Global Target Market Exposure Gross Return (which is an index comparable to a globally-diversified portfolio of equities based on market capitalization, such as the Vanguard Total World Stock Index ETF with an expense ratio of only 0.08%) has a 10-year annualized return of 19.94%. Although it would be useful to consider longer periods, the revision of Regulation 28 only came into full effect on 2011-12-31, so performance before this date may be inapplicable. However, it is still acknowledged that a single period of 10 years is very short. To be clear, it is not justifiably being argued that this underperformance occurred while an equivalent risk was taken, although the high fees and active management will lead to this underperformance regardless - it is being argued that Regulation 28 is irrational by restricting investors and preventing them from increasing the compensated risk of their portfolios.

    For a more complete comparison, the Morningstar Global Core Bond Gross Return (which is an index comparable to a globally-diversified portfolio of bonds based on market capitalization, such as the Vanguard Total World Bond ETF with an expense ratio of only 0.06%) has a 10-year annualized return of 8.73%. So, a globally-diversified portfolio of equities in a ratio of 75% and bonds in a ratio of 25% would have had a 10-year annualized return of approximately 17.14%. This compensated risk exposure is similar to that proposed by Regulation 28, but it does not incorporate the uncompensated risk exposure introduced by Regulation 28. Again, it is acknowledged that a single period of 10 years is very short.

    In addition, this does not account for the additional fees from the platform used to purchase the fund. If used directly, Allan Gray charge an annual platform fee of 0.50% each year (although this is likely to exclude VAT). One of the cheapest platforms, if not the cheapest platform (although Sygnia does not seem to charge platform fees for their own unit trusts), is EasyEquities which charge an annual platform fee of 0.30% each year for retirement accounts with an additional fee of 0.25% to access unit trusts (although this is likely to exclude VAT). Furthermore, the transaction costs have not been considered, where the Allan Gray Balanced Fund has an additional transaction cost of approximately 0.08%. This is in comparison to Interactive Brokers who charge a once-off fee of $0.005 per share without platform fees for a taxable account or EasyEquities who charge a once-off fee around 0.5752% per trade without platform fees for a tax-free savings account (although this is likely to exclude VAT and bid-ask spreads for ETFs on the JSE are atrocious). However, these extra fees will not be considered further to allow for a conservative assumption, but they should still be kept in mind when assessing the results and can be indirectly accounted for by adjusting the differences in return.

    Continuing with the methodology, it can be difficult to account for all the effects from different taxes, such as income tax, capital gains tax, dividends tax, and interest tax, as the taxes are applied at different times and in different proportions. However, this can be overcome by considering a single effective tax rate corresponding with the overall taxes. In other words and as mentioned, since the tax rate is a percentage, it does not matter when it is actually applied and, consequently, the effects from income tax, capital gains tax, dividends tax, and interest tax could all be combined and applied to the initial amount as a single effective tax rate. Additionally, for simplification, it can be helpful to think of the dividends tax and interest tax as a combined yield tax as the mechanisms are somewhat similar. This effective tax rate is derived below for illustration.

    Derivation of the concept of using a single effective tax rate:
    \[\begin{gather*} T_{Total} = T_{Income} + T_{Capital} + T_{Dividends} + T_{Interest} \\[6px] P_{N,\, Tax} = P_{N,\, Tax \text{\textasciitilde} Free} - T_{Total} = P_0 (1 + R_{Capital} + R_{Yield})^{N} - T_{Total} \\[5px] \text{Let }\, R_{Eff\,Tax} = 1 - \frac{P_{N,\, Tax}}{P_{N,\, Tax \text{\textasciitilde} Free}} = \frac{T_{Total}}{P_{N,\, Tax \text{\textasciitilde} Free}} \\[10px] \therefore\, P_{N,\, Tax} = P_0 (1 - R_{Eff\,Tax}) (1 + R_{Capital} + R_{Yield})^{N} \end{gather*}\]

    For South Africa, the current marginal tax rates or brackets of income tax are listed below. For capital gains tax, 40% of the capital gain is determined and then included in annual taxable income, such that the maximum effective capital gains tax rate is 18% (for someone taxed at the maximum marginal tax rate of 45%). For foreign dividends tax, the dividend is included in annual taxable income, such that the maximum effective dividends tax rate is 20%. For foreign interest tax, the interest is included in annual taxable income, such that the maximum effective interest tax rate is the marginal tax rate (notably, this makes foreign interest tax inefficient compared to dividends). These are the general conditions, but there may be certain exceptions under specific circumstances. However, it is highly likely these may change in the future, but the idea of using an effective tax rate is still valid and should simply be adjusted higher if it is expected for future taxes to be higher or lower if it is expected for future taxes to be lower.

    Income tax rates based on taxable income prescribed by the South African Revenue Service:
    Taxable Income Bracket Income Tax Rate
    R1 - R216200 18% x (Income)
    R216201 - R337800 R38916 + 26% x (Income - R216200)
    R337801 - R467500 R70532 + 31% x (Income - R337800)
    R467501 - R613600 R110739 + 36% x (Income - R467500)
    R613601 - R782200 R163335 + 39% x (Income - R613600)
    R782201 - R1656600 R229089 + 41% x (Income - R782200)
    R1656601 < R587593 + 45% x (Income - R1656600)

    For a demonstration of an effective tax rate, consider a capital return of 11% and yield return of 4% coupled with an income tax of 25%, capital gains tax of 16%, and yield tax of 16%. Over a period of 30 years, this will result in an effective tax rate of 44% based on the definition above, where the final amount would be identical given the same returns if this effective tax rate were to be applied to the initial amount without any other tax. As mentioned, considering a retirement account or tax-free savings account, there would be no taxes on capital gains, dividends, or interest, so the only concern would be the income tax at the time of withdrawal for a retirement account or contribution for a tax-free savings account and this income tax would simply be equal to the effective tax rate.

    Extra examples of the effective tax rate for sets of different taxes can be interacted for other scenarios. Interestingly, the results show that it is often preferable for capital gains rather than dividends or interest, which can be understood as the capital gains tax having a once-off effect on the final return while the tax on dividends or interest continuously affect the rate of return. It can also be useful to think of each unit quantity contributed individually rather than as a cumulative sum, such that a comparison can be made for each unit quantity individually under its specific circumstances at the particular point in time - in other words, think of it as separately contributing a specific amount for a certain period of time, as if each unit quantity was being considered individually from the particular point in time. Thus, when assessing the results, the effective tax rate should be considered to be applied to the initial amount and it is not necessary to consider any other individual forms of taxes at any other time.

    To further understand the preference between taxes like capital gains compared to taxes like dividends or interest, consider the implications of having to pay taxes immediately on dividends and interest. This immediate payment will remove the possibility of future compounding on this payment, where any future compounding would have had a return component and additional tax component. For example, if a yield of 4% is received, tax is paid immediately at a rate of 20%, such that 3.2% is received and 0.8% is paid in tax and, in the following year, this yield will itself produce an additional yield of 0.128%, such that 0.1024% is received and 0.0256% is paid in tax - without further tax to be paid, a total of 3.3024% is received. Alternatively, if a yield of 4% is received, tax is delayed until later, such that 4% is received and, in the following year, this yield will itself produce an additional yield of 0.16%, such that 0.16% is received without paying tax - with the delayed tax at 20% on both yields, a total of 3.328% is received. The difference of 0.0256% occurs due to the compounding on the amount which would have been paid in tax (with the first iteration, the future compounding on the 0.8% which was paid in tax is lost, as this future compounding would have resulted in a yield of 0.032%, such that 0.0256% is received and 0.0064% is paid in tax). This impact becomes more significant over time as further compounding is realized.

    Calculation of a single effective tax rate based on parameters for an example scenario:
    Comparison between tax efficiencies based on the point at which taxes are paid as immediate or delayed:

    Another important factor to keep in mind is foreign withholdings tax. This is a tax applied by a foreign country on the dividends or interest received by a fund in that country. In some cases and in a taxable account, this can be used to reduce the liability for the overall taxes on dividends and interest, as it is possible to recover this foreign withholdings tax if there is a double taxation agreement between the respective country and South Africa. This is done through foreign tax credits when submitting a tax return, such that the overall tax, including the foreign withholdings tax, aligns with the effective tax on dividends or interest. However, since most funds available in a retirement account are domiciled in South Africa, the foreign withholdings tax will be paid internally within the fund and it is not possible to claim a foreign tax credit. Unfortunately, this problem affects a tax-free savings account in the same manner. So, in most cases, there is still some tax being paid indirectly on dividends and interest in retirement accounts and tax-free savings accounts.

    Results And Discussion

    Using effective tax rates, it is possible to compare the performance of several scenarios with an investment at a higher effective tax rate and higher return (representing a tax-free savings account or taxable account) against an investment at a lower effective tax rate and lower return (representing a retirement account). Considering a conservative example with an effective tax rate of 44% and return of 15% against an effective tax rate of 20% and return of 12%, it is seen that the investment with a lower starting principle drastically outperforms the investment with a higher starting principle over long periods of time and this outperformance exponentially increases as the period of time increases. Over shorter periods of time, the investment with a higher starting principle does tend to outperform, but this outperformance is marginal compared to underperformance and opportunity cost as the period of time increases. This effect is especially enhanced when using a tax-free savings account, as the higher effective tax rate would be dramatically decreased and mostly equivalent to the lower effective tax rate, since it is no longer necessary to account for the inclusion of taxes on capital gains, dividends, or interest (in addition to, as mentioned, allowing for greater certainty and avoiding the realistic risk of taxes increasing in the future once someone begins to withdraw from their retirement account).

    Growth for a higher effective tax rate and higher return against a lower effective tax rate and lower return:


    For extension, this can be expanded to consider the time until an investment at a higher effective tax rate and higher return becomes equal to an investment at a lower effective tax rate and lower return. Simply, if the time horizon of an investor is longer than this period, then the investment at the higher effective tax rate and higher return is preferable. Conversely, if the time horizon of an investor is shorter than this period, then the investment at the lower effective tax rate and lower return is preferable. As mentioned, it can be useful to think of each unit quantity contributed individually at this particular point in time and future points in time (rather than the cumulative sum which has already been invested).

    Time for a higher effective tax rate and higher return to equal a lower effective tax rate and lower return:
    \[\begin{gather*} P_{A,\, Tax} = P_0 (1 - R_{A,Tax}) (1 + R_{A,Inv})^{N} = P_0 (1 - R_{B,Tax}) (1 + R_{B,Inv})^{N} = P_{B,\, Tax} \\[8px] \therefore\, N = \frac{\log(1 - R_{B,Tax}) - \log(1 - R_{A,Tax})}{\log(1 + R_{A,Inv}) + \log(1 + R_{B,Inv})} = \frac{\log((1 - R_{B,Tax}) / (1 - R_{A,Tax}))}{\log((1 + R_{A,Inv}) / (1 + R_{B,Inv}))} \\[14px] \therefore\, N = \frac{\log((1 - R_{B,Tax}) / (1 - R_{A,Tax}))}{\log((1 + R_{B,Inv} + \Delta R_{Inv}) / (1 + R_{B,Inv}))} \,\text{ with }\, \Delta R_{Inv} = R_{A,Inv} - R_{B,Inv} \end{gather*}\]

    The relationship between the time until equality and return difference is interesting, as it appears as though the outcome is ultimately dependent on the return difference rather than the actual return in either case. This is because the return difference is much more significant than the actual return for this relationship due to the application of the logarithm (in a sense, this works to be converse to the application of an exponential for compounding). Given the uncertainty in the calculations around the actual effective tax rate and return compared to the predicted effective tax rate and return, this can provide a useful estimation and general guideline with less uncertainty. For example, if the return difference is over 3%, then the time until equality will almost always be less than 15 years for all reasonable returns.

    Approximation of the time until equality of different effective tax rates for different returns:
    \[\begin{gather*} \therefore\, N = \frac{\log((1 - R_{B,Tax}) / (1 - R_{A,Tax}))}{\log(1 + \Delta R_{Inv} / (1 + R_{B,Inv}))} \approx \frac{\log((1 - R_{B,Tax}) / (1 - R_{A,Tax}))}{\log(1 + \Delta R_{Inv})} \end{gather*}\]
    Time until a higher effective tax rate equals a lower effective tax rate for various returns:

    Thus, if investing over a long-term, it can be clearly seen that an investment in a tax-free savings account is almost always the most favourable option, because of the expected and unavoidable underperformance of a retirement account due to the conservative restrictions of Regulation 28, uncompensated risk from Regulation 28 through concentration and active management, and high fees for the management of the funds. Moreover, in many cases and for the same reasons, a taxable account can still be a more preferable option than a retirement account, even after accounting for the additional taxes on capital gains, dividends, and interest. Then, as mentioned, there are also the other advantages of a tax-free savings account or taxable account, such as being able to freely access them for withdrawals before retirement, avoidance of forced annuitization upon retirement, and avoidance of the waiting period of 3 years if someone emigrates.

    Based on the figures, the model can be viewed as balanced but possibly conservative and biased towards a retirement account, since it did not directly account for the possibility of using exemptions. Currently, there is an annual capital gains tax exemption of R40,000, local interest tax exemption of R23,800, foreign dividend and interest tax exemption of R3,700 - combined, these add up to R2,025,000 if maximized over a period of 30 years. However, it also did not directly account for the possibility of using the tax-free lump sum of R500,000 for a retirement account. Obviously, with some specific calculations, these effects could be included through a reduced effective tax rate in both cases. Although increasingly uncommon in South Africa, the effect of an employer match can also be incorporated in an inverse manner by using a negative income tax rate to account for the employer match. For example, an employer match of one-to-one at an income tax rate of 20% would lead to a pre-tax contribution of R100 becoming a post-tax contribution of R160 rather than R80. Thus, a single effective tax rate of -60% could be used for a retirement account - alternatively, the employer match could be incorporated in the return by finding an equivalent compound annual growth rate. It should be noted that, in situations where an attractive employer match is offered, the retirement account will usually have the most beneficial outcome, unless the fees are excessively high with active management based on speculation and gambling - although, instead, it could be even more beneficial to negotiate a higher salary and forego the employer match.

    Derivation of a single effective tax rate for an employer match:
    \[\begin{gather*} P_{N,\, Tax} = P_{0} (1 + R_{Mtch}) (1 - R_{Eff\,Tax}) (1 + R_{Capital} + R_{Yield})^{N} \\[5px] \text{Let } P_{0} (1 + R_{Mtch}) (1 - R_{Eff\,Tax}) = P_{0} (1 - R_{New\,Tax}) \\[5px] \therefore\, R_{New\,Tax} = 1 - (1 + R_{Mtch}) (1 - R_{Eff\,Tax}) \end{gather*}\]
    Calculation of a single effective tax rate for an employer match:

    External Research

    For extra scrutiny, the evidence against retirement accounts is further compounded by the findings of Burgers (2016) in their master's dissertation: "A taxing incentive? A comparison of retirement saving using discretionary investment and Regulation 28 in a life-cycle model" and, then subsequently, the publishings of Willows, Burgers, and West (2018) in their paper: "A comparison of retirement saving using discretionary investment and Regulation 28". In this master's dissertation and paper, a quantitative risk and return analysis was performed while considering two hypothetical investors who are identical in all aspects other than their choice of investments. The authors highlight many important conclusions. However, it should be noted that the authors did not consider a globally-diversified portfolio unfortunately, but the ideas around the conclusions are still sensible and somewhat applicable.

    • To date, no literature exists which indicates whether the incentives provided in South African taxation legislation coupled with regulation for retirement savings vehicles make sense from an economic and risk perspective. The limits of Regulation 28 do not encourage optimal asset allocation in a portfolio.
    • The premium which can be earned from equity exposure is clear. Considering the holding period of a retirement fund, where members join at the beginning of their working career and withdraw upon retirement, a case can be made for greater equity exposure. As the length of the investment horizon increases, so should the allocation to equities, yet retirement funds - which operate as long-term investment options for their members - are restricted from maintaining high equity exposure.
    • While the benefits of international diversification are widely accepted, most investors hold most of their wealth in domestic assets, a phenomenon known as home bias. Despite the proven benefits of diversification, both historically and more recently, Regulation 28 still imposes limits on fund exposure to foreign investments.
    • A literature review of Regulation 28 showed strong arguments to invest in retirement funds, as these funds provide tax benefits and relatively simple investment vehicles for their members to save for retirement. However, in previous studies, it has been shown that regulation does not necessarily result in increased returns and the active management required can be detrimental to the investors involved.
    • The alternative to investing in retirement funds is for an individual to make their own discretionary investment. This would result in a loss of the tax benefit, but would also not limit the underlying investments which an individual could select. The potential advantages of discretionary investments include higher returns and accessible capital.
    • A model is created with two hypothetical individuals who are identical. The first individual will save for retirement in a compliant retirement annuity fund and will be termed the regulatory investor. The second individual, termed the discretionary investor, will save in a discretionary manner in assets which do not comply with Regulation 28 and will, therefore, forego the tax deduction of contributions. The critical assumption is that investments will earn a consistent nominal annual return equal to the historic return on the selected investment vehicle In addition, the taxes to account for capital gains, dividends, and interest levied for the discretionary investor are overly prudent and prejudice the discretionary investor, as it has the effect of overstating their tax liability and understating possible real investment returns.
    • The findings of this study indicate that Regulation 28 may be effective at reducing the investment (and, indeed, behavioural) risk to which a retirement account is exposed. Judged only by the return differential between compliant and non-compliant funds (which is the only factor being assessed in this study), the limits imposed by Regulation 28 may lead to sub-optimal investment choices should individuals be motivated to reduce their current tax liability by investing in a compliant fund.
    • The results of this study offer initial evidence that discretionary investments offers higher returns, which indicates that individuals should opt for discretionary investment. However, these results have not been risk-adjusted. Accordingly, individuals should invest in order to address their investment goal, which may be solely to maximize retirement wealth, in which case discretionary investment is preferred. However, if investors seek to maximize retirement wealth while minimizing possible variability in that wealth, then a compliant fund may be the superior alternative.
    • In summary, the findings indicate that Regulation 28 is effective in reducing the investment risk of retirement savings; however, it may also force the investor to sacrifice wealth. Depending on the tax bracket of the investor, discretionary investment may be preferential to investing in a retirement fund under the mandate of Regulation 28.
    A comparison of retirement saving using discretionary investment and Regulation 28:

    Summarized Conclusions

    As with most topics in the financial industry, the advice from the majority of financial advisors and media personalities around retirement accounts should not be taken without interrogation, as it often does not align with the evidence in reality. Currently and for most people saving for retirement, the tax-free savings account is the most beneficial option and, in many cases, this is followed by a taxable account as the second most beneficial option, while a retirement account should usually be avoided, especially by young investors. In the event an employer match is offered, then a retirement account should be considered with further analysis. At the end of the day, Regulation 28 is highly fraught with irrational contradiction and investors do not need these restrictions from the government. And this did not even consider the possibility of pursuing risk factors or using leverage in a taxable account for time diversification to increase returns and decrease risk (which would only skew the result further away from considering a retirement account).