Pension savings funds and dollar cost averaging: a long-term study

This article, based on my master's thesis, investigates various strategies for investing the yearly fiscal limit into an individual pension savings fund. Multiple common investment approaches are evaluated. Findings suggest that lump-sum investments often yield the highest average returns but have higher volatility. Dollar-cost averaging and a 50-50 buy-and-hold strategy offer a reduction in risk at the cost of lower returns. For investors with a power utility function, preferences exist, but differences between strategies are not substantial. 

Due to increasing doubts about the adequacy and sustainability of the Belgian statutory pension scheme, more attention is given to the other pension pillars. As contributions to individual pension savings funds continue to rise, so does the need for an insight into the dynamics of different investment strategies for individual pension savings. Selecting the right strategy is essential to ensure quality of life during retirement.

Individual pension saving in pension savings funds is a part of the third pillar of the Belgian pension system, together with individual pension saving through insurance contracts. The third pillar is encouraged through fiscal advantages up to a ceiling invested amount per year. A pension saver can only receive fiscal advantages on deposits into a pension savings fund or a pension savings insurance contract. This thesis analyses the impact of different investment strategies for a pension saver who decides to invest the yearly limit in a pension savings fund.

Literature sees two main popular strategies for investing a sum into a risky investment like a pension savings fund: a lump sum investment or dollar-cost-averaging (DCA). While a lump sum investment invests the entire sum at a single point in time, DCA seeks to lower market risk by spreading the investment over time. While DCA is often advised by financial advisors and planners, traditional finance does not favour DCA, frequently finding that it does not lower volatility in returns enough to warrant its lower return. A 50-50 buy-and-hold strategy is often found to provide equal returns at a lower volatility. DCA is found to reduce other forms of risk, lowering the conditional expected shortfall and the within-horizon probability of loss.

Behavioural finance offers a framework in which the prevalence of DCA is explained, arguing that investors make choices according to prospect theory, have an aversion to regret, make cognitive errors, and have lapses in self-control. These characteristics of investors do not make DCA rational behaviour but normal behaviour.

The objective of this study is to analyse what strategy among DCA, a lump sum investment, and a 50-50 buy-and-hold strategy is the most beneficial for an average pension saver in Belgium. Monthly return data was collected for all available pension savings funds in Belgium from 1987 onward through Thomson Datastream. As alternative investment was chosen for a money market fund and a regulated savings account. Data was collected through Thomson Datastream and personal inquiries at big Belgian banks. Monthly return data for the money market fund before 1993 was proxied by the German interbank rate minus a fictitious management fee, as no return data was available before then. Savings account interest rates were aggregated on an annual basis due to their relatively low rate of change and the stable nature of savings accounts.

Historical data was used to perform a back test and to simulate future performance. The back test was performed by assuming an investment of the limit each year and performing investments in the pension savings fund according to each investment strategy. Returns on the strategy were then a combination of the historical returns on the pension savings fund and the historical returns on the money market fund or the historical interest rates on regulated savings accounts, depending on which of the two was chosen as alternative investment.

Future performance was simulated using bootstrapping of historical data. As both money market funds and interest rates on savings accounts showed high autocorrelation, bootstrapping was done using the first differences of the respective time series.  As the first differences in monthly returns of the money market fund still showed significant levels of autocorrelation after differencing, a block bootstrapping method was chosen to preserve autocorrelation. Both series of first differences were tested for correlation with pension savings fund returns. No significant correlation was found between the first differences in monthly returns of the money market fund and monthly pension savings funds returns, and bootstraps were done independently. Significant correlation was found between the first differences in yearly interest rates on savings accounts and yearly pension savings fund returns for some funds. For these funds, sequential bootstrapping was conducted. This involved sampling the first differences in interest rates along with the corresponding year, and sampling 12 monthly pension savings fund returns from each year. Bootstrapped differences were used to construct return series for the money market fund and interest rates for the savings account. 1,000 bootstrap samples were drawn to construct 1,000 unique scenarios.

Performance measures were computed for all strategies and outcomes for the back test and the bootstrap simulations. Back test measures were summary statistics on yearly returns and the probability of a yearly shortfall and conditional expected shortfall. Bootstrap measures also included summary statistics on yearly returns, probability of shortfall and conditional expected shortfall, and measures on the distribution of terminal wealth over the 1,000 bootstraps. These measures were expected terminal wealth, standard deviation in terminal wealth, probability of shortfall of invested sums and theoretical terminal wealth, extreme quantiles, and the certainty equivalent for each strategy based on an investor with a power utility function.

Findings for the back test showed that using a money market fund as alternative investment, the least risk-averse investors prefer a lump sum investment at the start of the year, and more risk-averse investors prefer DCA or a 50-50 buy-and-hold strategy. In contrast, the most risk-averse investors only invest their money in a lump sum at the end of the year, keeping it in the money market fund for the entire year. If money only becomes available throughout the year, investing as soon as possible delivers the highest return but at the highest volatility in return.

Using a savings account as alternative return, a lump sum investment at the start of the year delivers the highest return at the cost of the highest volatility. DCA at the start of the month and a 50-50 buy-and-hold strategy offer lower risk and lower return, while DCA at the end of the month has the lowest volatility. If money only becomes available throughout the year, a lump sum investment at the end of the year promises a higher return.

Findings for the simulated future performance showed that using a money market fund as alternative investment, expected terminal wealth is lowest for a lump sum at the start of the year and highest for a lump sum at the end of the year. Investors with a lower and higher risk aversion prefer both lump sum strategies over DCA and the 50-50 buy-and-hold strategy based on the certainty equivalent. If money becomes available throughout the year, DCA has lower volatility for the same expected terminal wealth as a lump sum at the end of the year and is thus the superior strategy.

Using a savings account as alternative return, a lump sum investment at the start of the year has higher expected terminal wealth and volatility in terminal wealth than other strategies and is preferred by power utility investors for different risk aversion levels. DCA at the start of the month is preferred over DCA at the end of the month. If money becomes available throughout the year, DCA is preferred over a lump sum at the end of the year.

Despite clear preferences of power utility investors for one strategy over the others, differences in certainty equivalent are not substantially large, indicating that investors will not be much worse off choosing another strategy.

In conclusion, this thesis has evaluated and compared the performance of different investment strategies for investing in Belgian pension savings funds. The analysis indicates that different strategies impact expected terminal wealth and standard deviation in terminal wealth differently and that investors should thus choose a strategy that fits their risk profile. My thesis provides insights into the risk-return tradeoff of the different strategies and, in this manner, aids pension savers in making more informed decisions for pension saving. The thesis also contributes to the ongoing dialogue surrounding the pension system in Belgium by giving more insight into the dynamics present in pension saving.