The Pension Model

In 2017, Aaslid revealed a study showing how pension from Norwegian contribution profiles differs. This study was based on historical data, covering the Norwegian market since 1872. It revealed that there are significantly large alterations between the best and the worst profile. Therefore, the thesis aims to construct a pension model that shows the differences in the contribution profiles, and how this affects the pension holding at

page 111

retirement. The thesis displays this pension in three different ways. The first is through descriptive statistics, the second is expected utility and lastly through certainty equivalents.

This model provides robust results as it displays the findings through the three different evaluation measurements. The descriptive statistics illustrate the distribution of the results, and the behavioural finance theories incorporate the investors’ perspective towards risk and return. To demonstrate the risk and uncertainty concerning the different profiles, it is chosen to use the percentiles of 1 and 99. Another way to incorporate the risk and return is using Value-at-Risk or expected shortfall, at a 95% confidence interval. However, we want this model to be realistic towards the fluctuations in the market and therefore choose to use the 1^st percentile as a measurement of a bad state, and the 99^th percentile as a measurement of a good state. Those percentiles are selected because they reflect the uncertainty of the different contribution profiles. This model does not aim to find the one optimal contribution profile, but rather to illustrate the optimal contribution profile for different types of investors. In other words, the model can be used as a tool to compare and find the optimal pension profile given the investor’s preferences. Nonetheless, the purpose of the thesis is not to uncover the potential risks related to selecting between the different contribution profiles. Therefore, an extension of the model could be to include risk management in contribution profiles.

The asset allocation of the pension model follows the theoretical frameworks of Markowitz’s static mean-variance theory. The simulations of the real return of equities and bonds follow a geometric Brownian motion, based on estimates for expected return and standard deviation. Thus, it is difficult to provide correct predictions of future price changes.

The model uses the nominal returns on equities and bonds of 6,5% and 3%, which is in line with the predicted estimates from the central bank of Norway, Mork and the Department of Finance. The measurement of volatility in the market, i.e., the standard deviation, is derived from historical data. However, Campbell and Shiller (1988) and Fama and French (1988) argue that it is possible to predict the expected risk premium without the use of simulations.

Further, Bodie et al. (1992) find that one can predict that an investor’s decisions if uncertainty diminishes. However, these findings do not affect the essence of the results. On the contrary, these findings validate the findings and support that aggressive contribution profiles are better than conservative profiles. If investors can predict the future, they will have high equity exposure in times with high returns and low exposure in times with low returns.

page 112

Several pension models incorporate personal adaptions in the investment strategy. The model does not include personal adaptions and solely focus on the differences of life cycle strategies and management fees. Aaslid (2017) finds that 93,6% of the uncertainty in pension plans can be explained by studying the asset allocation. Therefore, there is no reason to believe that the findings would change if including personal adaptions in the asset allocations of the different contribution profiles. Thus, the results might have differed if the model included stochastic simulations for some of the constant parameters. It is chosen to keep the inflation rate as a constant parameter throughout the holding period. One of the main arguments for Duvi’s aggressive profile, with 80% in equities and 20% in bonds, is that inflation can mitigate the return of bonds. And, historically, it has. The dataset from Dimson, Marsh and Staunton illustrates that the historical inflation exceeds the nominal bond return, which gives a real bond return of -0,26%. However, the historical inflation rate of 3,14% is not a robust parameter to use in the future. Therefore, the model uses the predicted inflation rate of 2%. Nonetheless, the inflation might differ from 2% in the future.

The compiled sensitivity analysis examines how the results might vary in a scenario with deflation or if the inflation rate increases. The findings from the sensitivity analysis support Duvi’s claim. They also illustrate that the model is fairly sensitive to fluctuations in annual income and the contribution rates. An extension of the model could be to include a stochastic simulation of the two parameters. Munk and Ranvid (2017) advise using a stochastic simulation where assets and income correlates, to mitigate some of the uncertainty in the estimations. The correlation will require an empirical study, and will probably vary with the investor’s education, industry, age and income level (Munk & Ranvid, 2017).

The model assumes that an investor has the same contribution profile until retirement. In reality, the investor can change the profile dynamically until retirement, to adjust to changes in lifestyle and preferences. Clark and Strauss (2008) find that men are less risk averse than women. Bucher-Koenen and Kluth (2013) and Chen and Volpe (2002) argue that men are less risk averse because they have higher confidence and greater financial literacy. By following these arguments, one might believe that men would prefer more aggressive contribution profiles than women. Further, Bertaut (1998) finds that people with a higher education-level are more likely to possess stocks. The constant relative risk aversion of 3,8 does however not include any of these preferences. An evolvement of this model could be to add personal differences, and the option to change contribution profile up until

page 113

retirement. As Aaslid (2017) illustrates, longer holding-periods result in smaller differences between the Norwegian contribution profiles. The results indicate that the pension differs even though the contribution pension has a long holding-period of 43 years. Therefore, it is decided to disregard the option to change the profile dynamically and to include personal differences but would encourage including this in future research.