Model Performance

63 sector distribution may change completely between quarters depending on return and covariance estimates.

64 Healthcare, Technology and Utilities are the most attractive investment opportunities for the unrestricted portfolio, as the model has allocated most funds into these sectors. Given the average beta estimates in figure 4.3 the model seems to favor a combination of high and low beta sectors in the unrestricted portfolio, as Utilities and Technology possess the lowest and highest average beta, respectively.

Furthermore, a positive relationship between beta and realized return is evident from table 5.3, as Utilities possess the lowest Sharpe Ratio and the Technology the second highest. Thus, imposing the restriction of a portfolio beta,_P 1, the model combines sectors with both high and low beta and realized return.

Such condition is unfortunately likely provide portfolio return inferior to the benchmark, but opportunities to add significant value remain as the low return is compensated by low beta. The same condition is evident with regards to Oil & Gas, which constitutes the second largest represented sector with the second highest beta and the highest Sharpe Ratio. Note that Basic Materials, Consumer Goods, and Consumer Services provide the lowest average portfolio positions for both portfolios. These sectors possess only mediocre beta and expected return estimates, and due to high correlation among sectors, we do not expect their covariance to be small enough to impact the asset distribution process.

High average asset allocation is a result of two possible scenarios. First, the portfolio model allocates sectors consistently over the period with a high and stable portfolio proportion, resulting in a low asset allocation spread. Second, the model conducts minimum asset allocation to a portfolio sector, and occasionally provides solutions with a substantial overweight to the given sector, which results in a high spread in asset allocation.

Figure 5.5 Average Sector Position

y = 0,831x - 0,0434 R² = 0,8243

0%

5%

10%

15%

20%

0% 10% 20% 30%

Average Sector Position

Standard Deviation Figure 5.5a Unrestricted Portfolio

Source: Own Creation, Appendix 7

y = 1,0824x + 0,0061 R² = 0,046

0%

5%

10%

15%

20%

0,00% 2,00% 4,00% 6,00% 8,00% 10,00%

Average Sector Position

Standard Deviation Figure 5.5b Unrestricted Portfolio

Source: Own Creation, Appendix 7

65 Figure 5.4 illustrates a positive relationship between average asset allocation and their standard deviation.

The unrestricted portfolio is, however, much more successful in explaining the variation of the observations. In other words, the regression line for the unrestricted portfolio matches the data points by 83% versus 5% for the restricted portfolio. For the unrestricted portfolio, sectors with high average weights have constituted portfolio corner solutions, as they carry standard deviations above their average meaning the position in given periods for these sectors have fluctuated between very high and low values.

Healthcare, Technology and Utilities, possessing the highest average portfolio positions, have either dominated the portfolio claiming very high portfolio weight (up to more than 90%, respectively) upon their introduction in some periods or been excluded by the mean-variance model in others.

The distribution pattern is less visible for the restricted portfolio. Imposing a maximum portfolio weight upon the sectors decreases the standard deviation, resulting in a steeper but much less representable regression line in figure 5.5. Sector weights therefore fluctuate less in the restricted portfolio, and retains average values at approximately the same level as the unrestricted portfolio, meaning their distributions are obviously kept more stable over time as opposed to the unrestricted portfolio.

Note the difference in sector standard deviation. It is not surprisingly higher for the unrestricted portfolio compared to the restricted portfolio. Any allocation restriction above zero limits the allocation spread, meaning the lower the restriction of sector distribution the lower the standard deviation is likely to become. Evidently an equally weighted portfolio would have a zero standard deviation of average positions⁶³.

Based on the existence of a positive relationship between average portfolio weights and their respective standard deviation, corner solutions are indeed present in the unrestricted portfolio, which is in fact a rather disappointing result, given the aim of applying the mean-variance was to secure high risk adjusted return through diversification. However, tactical asset allocation is based upon expectations of future return, and estimates showed that benchmark return estimates retained higher levels of return than many of the investment opportunities. Since the mean-variance model optimizes with regards to which assets are expected to outperform the benchmark, i.e. the information ratio, only few investment opportunities might exist, leaving portfolios with only few assets expected to outperform the benchmark.

63 If each sector had a portfolio weight of 10% at all times standard deviations would be zero.

66 5.4.2 Portfolio Returns

The distributions from table 5.2 lead to the following performance of the two portfolios.

Table 5.3: Portfolio Performance

The Benchmark yields higher returns than both portfolios and the market. Both portfolios have yielded higher return than the market, and since the 20% restriction has led the portfolio to conduct asset allocation to a larger number of sectors, portfolio standard deviation is slightly lower, which does, however, result in lower Sharpe Ratio. Thus, in terms of absolute performance, the unrestricted portfolio has delivered marginally superior performance as opposed to the restricted portfolio. The next chapter will investigate whether it has done so with regards to its residual return and in that regard evaluate the portfolio strategy.

Portfolio Return Excess Return Standard Deviation Sharp Ratio Panel A. Portfolio

Unrestricted Portfolio 0,37% -0,06% 4,94% -1,16%

Restricted Portfolio 0,34% -0,08% 4,66% -1,76%

Panel B. Benchmark and Market

MSCI Denmark 0,65% 0,22% 5,92% 3,69%

MSCI World 0,34% -0,09% 4,47% -1,96%

Source: Own Creation, Datastream, MSCI Barra, Appendix 6

67

6. Performance Evaluation of the Investment Strategy

This chapter analyzes the results of portfolio construction, and seeks to investigate three findings:

comparative absolute return between portfolios and benchmark, presence of investment skill and finally the extent to which active portfolio management has added value. Chapter 5 concluded that benchmark investing provided superior active return to the portfolios. However, a timing skill and value added may still be present as the portfolios did in fact outperform the market index and carried systematic risk restricted to market level, meaning active return needs be adjusted for systematic risk.

All results are analyzed and explained in terms of theoretical models and parameters.