Portfolio two - Maximise Return

86 Including the two allocation restrictions does not affect the outcome of the optimisation. Table 4.5.2.3 shows the exact same outcome as the prior optimised portfolio. Looking at table 4.5.2.2 (portfolio 1a) it is evident that the two allocation restrictions are already obeyed before implementing them into the theoretical optimisation. Since this is the only feature included in this portfolio, obviously the same result will emerge.

From an intuitive point of view and not with the data input taken into account, the restrictions would imply more investments in less risky assets following the 70% limit in equity if this restriction was not obeyed before imposing it. According to modern portfolio theory, higher diversification in the portfolio, following an allocation change in the total investment, would lead to lower volatility at the same level of expected return. On the other hand, if investments are re-allocated to low risk assets, only as a result of the restrictions imposed, the expected return will probably decline together with the volatility since assets with low volatility has a lower return from a theoretical point of view. The theoretical gain from diversification in such case will be reduced caused by the restrictions imposed. Therefore, both lower volatility and return is expected from such scenario.

87 contributors to highest possible extent, it is found relevant to focus on the other relevant aspect in portfolio composition; the expected return.

If the aim only is to maximise return without any concerns about the volatility, the entire investment will logically be allocated in Danish equity since this asset has the highest expected return, as seen in section 4.5.2 Portfolio One – The Minimum Variance Portfolio. This 100%

allocation in Danish equity constitutes portfolio 2a, illustrated in table 4.5.3.1. The non diversified portfolio shows a high return of 8,00% and a large standard deviation of 19,44%. The Sharpe ratio is lower than the Sharpe ratios of portfolio 1a and 1b, why the performances of these portfolios are better. In portfolio 2a the rise in expected return is proportionally lower than the rise in the standard deviation. The expected return per unit of total risk is thus higher in portfolio 1a and 1b.

Such an investment is unrealistic since it is assessed that the Danish pension fund sector would act rather conservatively in their investment strategy, even if the allocation restrictions were not enforced by law. This conservative approach to investments is caused by the fact that they are responsible for managing pension contributors’ retirement savings.

This optimised portfolio is included to strengthen the theoretical argument of diversifying portfolios and thereby improving the performance. This is seen from the low Sharpe ratio of portfolio 2a compared to portfolio 1a and 1b.

Asset Class Optimal Portfolio

Danish Equity 100,00%

Foreign Equity 0,00%

Government Bonds 0,00%

Mortgage Bonds 0,00%

Inflation-Linked Bonds 0,00%

Corporate Bonds 0,00%

Total 100,00%

Expected return 8,00%

Standard deviation 19,44%

Sharpe ratio 0,25 Portfolio 2a: Maximum return

Source: Own contribution

Table 4.5.3.1 Portfolio 2a

88 The outcome of optimising a maximised return portfolio, where the allocation restrictions are imposed, is illustrated in table 4.5.3.2.

As earlier stated, one of the allocation restrictions dictates a maximum allocation in equity of 70%. In portfolio 2b, all 70% is allocated into Danish equity due to its high expected return. The remaining 30% must be invested in bonds. This amount will be allocated to the bond investment opportunity with the highest expected return. It is investments in corporate bonds referring to section 4.5.2 Portfolio One – The Minimum Variance Portfolio.

Compared to portfolio 2a, both the expected return and the volatility are lower. Investigating the Sharpe ratio it is concluded that portfolio 2b performs better than portfolio 2a with a ratio of 0,28 compared to 0,25. Comparing this portfolio to the actual portfolio instead, the optimised performance is higher than how the sector’s portfolio performs. All legal regulations are not included in the theoretical optimisation model. This will be elaborated upon later.

Portfolio 2b: Maximum return with legal restric.

Asset Class Optimal Portfolio

Danish Equity 70,00%

Foreign Equity 0,00%

Government Bonds 0,00%

Mortgage Bonds 0,00%

Inflation-Linked Bonds 0,00%

Corporate Bonds 30,00%

Total 100,00%

Expected return 7,06%

Standard deviation 13,66%

Sharpe ratio 0,28 Source: Own contribution

Table 4.5.3.2 Portfolio 2b

89 The final optimisation reflects the conditions, under which the pension fund sector operates, to the highest possible extent in the research setup. The aim of the optimisation is to maximise return subject to the two legal allocation restrictions like it was done in modelling portfolio 2b.

Furthermore, the volatility of the portfolio is restricted to reflect the corresponding volatility of the actual portfolio⁶⁷. The reason for equalling the volatility levels is based on the assessment that the pension fund sector carries out investments very conservatively. This means that the level of risk incurred in its portfolio somehow will reflect the low volatility under which they invest.

Indirectly, this indicates the sector’s risk aversion. Practically, when equalling the volatility level in the two portfolios compared, focus will solely be on the return opportunities and through that the performance of the two portfolios.

67 A small difference in the standard deviation occurs due to the fact that the Solver add-in in Excel could not find an exact solution to this problem, why a converged solution is provided.

Asset Class Optimal Portfolio

Danish Equity 17,33%

Foreign Equity 22,53%

Government Bonds 0,00%

Mortgage Bonds 0,00%

Inflation-Linked Bonds 0,00%

Corporate Bonds 60,14%

Total 100,00%

Expected return 6,02%

Standard deviation 5,27%

Sharpe ratio 0,54 Portfolio 2c: Maximum return with legal

Asset Class

Danish Equity 5,25%

Foreign Equity 14,43%

Government Bonds 19,02%

Mortgage Bonds 40,54%

Inflation-Linked Bonds 8,56%

Corporate Bonds 12,20%

Total 100,00%

Expected Return 3,75%

Standard deviation 5,25%

Sharpe ratio 0,11

Actual Portfolio

Source: Own contribution

Table 4.5.3.3 Portfolio 2c

When maximising the expected returns and imposing the two allocation restrictions, it is proven possible to hold a theoretical optimal portfolio performing better than both the optimal portfolio, not subject to forced diversification, and the actual portfolio held by the Danish pension fund sector.

90 From table 4.5.3.3, it is evident that the theoretical optimised portfolio achieves a higher expected return and thereby a higher Sharpe ratio corresponding to 0,54. The actual portfolio exhibits a ratio of 0,11. This shows that from optimising the theoretical portfolio, it is possible to achieve higher return, hence, a better performing portfolio in the sector than what it does.

The optimised portfolio, portfolio 2c, is not very diversified across the different asset classes, referring to table 4.5.2.6. Approximately 60% of the total investment is allocated to mortgage bonds and the remaining is invested in equity. Intuitively, without taking the data input into account, it is expected that the Danish pension fund sector at least will diversify its investments in bonds across the opportunities in this subgroup of assets. It was expected that the pension fund sector should invest in government bonds and mortgage bonds to larger extent than what portfolio 2c suggests.

It is evident from the actual portfolio that a relatively large amount of the sector’s actual investments are allocated to government bonds and in particular mortgage bonds. Government bonds are assessed to be the safest investment as the default risk on such investments is little⁶⁸. It would imply that the given economy, in which investments are made, goes bankrupt.

As mentioned in section 2.2 Regulations within the Danish Pension Fund Sector, the mortgage bond market is very important to the Danish economy and pension funds hold large positions in mortgage bonds. Mortgage bonds are considered safe investments and the 40% limit on investments in mortgage bonds is almost fully utilized in the actual portfolio (excl. the surplus of

“others”). Therefore, a high allocation in mortgage bonds was expected in the optimal portfolio.

The investments in mortgage bonds will possibly be limited further due to the coming solvency II directive requiring a maximum of 15% originating from one issuer. If this rule is enforced, it will

68 At least this was the assessment before the Greek, Irish, Portuguese and not to forget the US cases.

Depicting the level of risk aversion in the sector by equalling the volatility contained in the portfolios and maximising expected return, it is proven possible to achieve higher return and a better performing portfolio by optimising the portfolio theoretically.

91 affect the investments strategy of the Danish pension fund sector because of the limited number of issuer of mortgage bonds. This might affect the sector’s ability in utilizing the 40% limit.

All in all, it was expected that more investments should be allocated into mortgage and government bonds in the optimised portfolio, 2c. The explanation of why the theoretical optimal portfolio does not diversify across the different bonds is reasoned by the data set. This will be addressed in section 4.6 Addressing the Actual vs. the Theoretical Optimised Portfolio.

A comparison of the asset allocation of the two portfolios shows, that a higher proportion of equity is held in the optimal portfolio, 39,86% whereas the actual portfolio only allocates approximately 20% of investments to equity. From this it is concluded, that the pension sector should allocate more to risky assets since it is assessed that such investments contribute to the higher return.

Even though the proportion of equity is higher in the optimal portfolio, it is seen that the limits of how much the investor maximum must invest in equity and mortgage bonds are not close to be reached in the optimal portfolio.

Holding portfolio 2c would imply a higher expected return with the same volatility compared to the actual portfolio. This is assessed partly caused by the fact that the solvency requirements (article § 159(1) in the Financial Business Act described in section 2.2.1 The Danish Legislation

When depicting the investment environment to highest possible degree and maximising expected return, the two allocation restrictions, imposed by law, are not close to be reached.

When depicting the investment environment to highest possible extent and maximising expected return, the theoretical optimal portfolio allocates more investments to equity, than is done in the investment strategy of the Danish pension fund sector. The pension funds should allocate more investments to risky assets.

92 – The Financial Business Act) is not incorporated in modelling the optimal portfolio. Therefore, it is found reasonable to conclude that the solvency requirements limit the possibility to achieve higher returns.

It is assessed that the rather tight risk management in terms of the traffic-light system and the current draft of the solvency II directive has an effect on the investment strategy of the Danish pension fund sector. At least a part of the excess return and better performance obtained in the theoretical optimal portfolio stems from a different and less restricted investment strategy with respect to risk management.

Having conducted a number of theoretical optimisations and compared the outcomes to the actual portfolio, different interesting conclusions have emerged. The different optimisations were conducted in order to investigate how different investment environments possibly affect the outcomes of the theoretical optimal portfolios. A sum up all outcomes is presented in table 4.5.3.4.

Actual

Portfolio # Actual Portfolio 1a Portfolio 1b Portfolio 2a Portfolio 2b Portfolio 2c

Expected Return 3,75% 4,78% 4,78% 8,00% 7,06% 6,02%

Standard Deviation 5,25% 3,05% 3,05% 19,44% 13,66% 5,27%

Sharpe Ratio 0,11 0,52 0,52 0,25 0,28 0,54

Equity Ratio 19,68% 5,22% 5,22% 100,00% 70,00% 39,86%

Minimum Variance Maximum Return

Source: Own contribution

Table 4.5.3.4 Key Points from the Actual and Theoretical Optimised Portfolios

The high focus on risk management in investment strategy, as a result of the traffic-light system and coming Solvency II directive, hamper the performance of the Danish pension fund sector.

The solvency requirements imposed to the investment strategy of the Danish pension fund sector, limits the possibility to achieve higher returns.

93 The table clarifies and gathers the outputs from the optimisations conducted in this section. The foundations of the optimisations; minimising variance or maximising return, affect the outcomes.

Different restrictions imposed (the two allocation restrictions and - in portfolio 2c - the equality in variance) imply different outcomes both in relation to the performances of the portfolios and the proportion of allocation to equity. The portfolio showing the lowest performance is actually the actual portfolio with a Sharpe ratio of 0,11. As concluded in this chapter, this means that it is possible to hold better performing portfolios than the sector does. The highest performing portfolio is portfolio 2c with a Sharpe ratio of 0,54. Compared to the remaining optimised portfolios, this shows higher allocations in equity than portfolio 1a and 1b and lower equity ratio than portfolio 2a and 2b with its level of 39,86%. This comparison between the different theoretical optimised portfolios should not be taken literally, since different restrictions are imposed to them individually, making them incomparable.

The next section addresses different factors relevant to comment on in relation to the analysis conducted so far.

In document Benefitting Pension Contributors – An Analysis of the Danish Pension Fund Sector (Sider 92-99)