1. Introduction
6.2 Analysis of Value Added
71 Table 6.2: Regression Results
The timing coefficient does not provide evidence that either portfolio possesses a timing ability. It is negative and significantly different from zero at a 95% confidence level in both regressions. From the t-scores, both below ±1,96, we cannot consider the process of quarterly portfolio repositioning to be a skilled investment strategy. Thus, market exposure of both portfolios is not statistically significant. The mean-variance model has not utilized the opportunity to construct portfolios with systematic risk at market level,P,t 1, and at the same time generate a significantly higher return. Thus, in statistical terms, tactical portfolio investment under the condition of quarterly repositioning has not proven to be a more skilled investment strategy compared to investing in the world market index.
In defense of quarterly portfolio repositioning, we cannot ignore that investment opportunities have proven to be stationary. The implication that follows is that identifying points in time of market inefficiency, at which to reposition the portfolios without superior information becomes a difficult process. Whether the portfolios had provided different levels of return, had we changed the repositioning process to e.g. every month, is therefore unknown. However, in such case, transaction costs would certainly have been higher resulting in diminishing realized portfolio return.
72 The portfolios were optimized according to the information ratio in equation 5.4. This portfolio realizes a return of RP,T in the subsequent quarter while the benchmark index yields a return of RB,T. We referred to the difference between these two returns as the active return of the portfolios:
) 1 . 6
, (
,t Bt
P
t R R
R
In order to measure whether the investment strategy has added value to the investor, we provided the information ratio consisting of value added and the ex-ante tracking error for portfolio evaluation. As the active portfolios were repositioned quarterly over a period of 20 years (240 months) they are evaluated on an average monthly basis by the ex-post information ratio:
*
(6.2)*
* 240
1
1
2 , , 2 , , 2
, , 2011
, ,
i
t B t i e
t B e
t i i
e t B e
t P Dec
t
t B t P t
R R w
R R
R
If alpha, the numerator of equation 6.2, is significantly greater than zero, the active portfolio strategy has added portfolio value compared to benchmark investment. Applying optimization from equation 3.3, the active returns were adjusted for CAPM systematic risk in order to investigate the presence of portfolio added value.
Figure 6.2 Information Ratio
The development of the information ratio reflects the conclusion that timing skill is not present in active portfolio management. Evidently, no clear development in information ratios can be detected as spikes occur occasionally. In addition, 57 and 66 observations for the unrestricted and restricted portfolio,
-0,75 -0,50 -0,25 0,00 0,25 0,50 0,75 1,00
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Information Ratio
Figure 6.2b Unrestricted Portfolio
Source: Own Creation, Appendix 6 -3,00
-2,00 -1,00 0,00 1,00 2,00 3,00 4,00
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Information Ratio
Figure 6.2a Unrestricted Portfolio
Source: Own Creation, Appendix 6
73 respectively, carried an information ratio of zero. For these observations, portfolio beta was lower than benchmark beta but active return was positive. The interpretation is that the investor has overestimated the market risk and underestimated future active return which is not an act of skill, but neither something that should be penalized as it still contribute with positive portfolio return.
Table 6.3: Results of Value added and Information Ratio
Panel A of Table 6.3 displays overall value added, between portfolios and the benchmark index66. Panel B shows the corresponding results for the average information ratio. In general active portfolios achieved monthly residual return, or value added of 1,56% and 1,16% on average. The observed residual returns are both economically and statistically significant as all t-values for both portfolios exceed 1,96, and no p-value exceeds 5%. Grinold and Kahn (1995) suggest that significant information ratio indicates that the portfolio performance is due to skill rather than luck, as the probability of observing such large alpha by chance is only 5%67. That basically means that any significantly positive value added is a sign of investment skill. We previously attributed the source of skill to the timing of portfolio reweighting, however, we could not determine skill as the source of the performance of the investment strategy. Considering the information ratios can, however, determine which investment strategy is considered most skilled.
The difference in information ratios is highly significant. Considering the risk factors of the ex-post tracking error, the unrestricted portfolio tracks the benchmark more appropriately as it recognizes the benchmark as a single index with changing return and beta estimations. This occurs generally at levels above the investment opportunities, and conducts asset allocation accordingly. As a result, portfolio
67 Grinold & Kahn (1995): p. 323
t-score P-value
5,78 <0,0001 4,94 <0,0001
6,02 <0,0001 5,95 <0,0001 Source: Own Creation, Datastream, MSCI Barra Appendix 6
Restricted Portfolio
Average Value 1,56%
Panel A. Value Added
Unrestricted Portfolio Panel B. Information Ratio
Restricted Portfolio Unrestricted Portfolio
1,16%
33,14%
6,41%
74 corner solutions then emerges as the mean-variance model tracks benchmark beta and select the investment opportunity with the beta best matching benchmark beta. In periods where benchmark beta is higher than any given investment opportunity, the mean-variance model allocates as much funds as possible into the investment opportunity which best matches the benchmark beta. However, as portfolio beta is limited to 1 the mean-variance model cannot allocate 100% funds to one sector index with beta above 1, but instead distributes the remaining funds into low beta sectors. Restricting maximum portfolio positions presents a tradeoff. The restricted portfolio cannot eliminate active beta as it can only allocate 20% funds into high beta investment opportunities. Thus the restricted portfolio cannot track benchmark beta as effectively as the other portfolio. However, diversifying investment positions provides better conditions for eliminating the other risk factor, active risk, as spreading investments would compensate losses in some investments by gains in others. As the historic performance of the benchmark has proven superior to both portfolios, tracking active return is a far more difficult task. Thus, the tracking error is minimized by eliminating active portfolio beta, and the unrestricted portfolio is more successful in doing so, making it the most preferred portfolio.
In summary, both portfolios yielded inferior cumulative return compared to the benchmark, and analysis could not detect any form of investment skill. Investigating whether value was added to the portfolio, we found that the unrestricted portfolio and the restricted portfolio yielded significant residual returns of 1,56% and 1,16%, respectively. These positive returns add value to the investor, resulting in significant information ratios of 33% and 6%, respectively. The information ratios are quite different indicating the unrestricted portfolio tracks the benchmark more successfully than the restricted portfolio.
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7. Conclusion
In this thesis the mechanics of active portfolio management was addressed based upon the motivation that an investor attempts to outperform a benchmark, the MSCI Denmark. Chapter 1 to 4 established the investment strategy which involved the determination of a strategic long-term investment opportunity set and conducting tactical short-term asset allocation by means of Markowitz’ mean-variance portfolio model. The model was applied each quarter from 1992 to 2011. The asset allocation was conditional on return and covariance estimations. Two portfolios were constructed: one portfolio upon which was imposed a restriction of maximum 20% representation of investment opportunities.
The second portfolio was not subject to any constraint with regards to asset allocation.
To answer the superior research objective four sub-questions were identified. Conclusions with respect to each question and the overall conclusion will be presented in the following based on the findings of chapter 5 and 6.
How does the mean-variance portfolio model conduct asset allocation in the context of active portfolio management?
The mean-variance portfolio model was applied for conducting tactical asset allocation in chapter 5. The model was submitted to three constraints: no short selling, no financial gearing, and a maximum level of systematic risk constrained to market level,P,t 1. The model conducted asset allocation with regards to optimization of the information ratio, which measures relative performance of portfolio versus benchmark. A historical increase in market integration have seen stock markets increase correlation and hence their covariance towards other markets. Thus, as the investment opportunities display comparable historical return patterns the mean-variance model primarily selects stocks based upon their expected return estimates and systematic risk.
Based on the findings in chapter 5, we conclude that optimizing the portfolios against a strong performing benchmark prescribes concentrated portfolios. In periods of high expected benchmark return, investment funds need to be allocated to a combination of investment opportunities with both very high and very low systematic risk, in order to maximize portfolio expected return and retain systematic risk at market level.
76 How does active portfolio management perform compared to MSCI Denmark between 1992 and 2011?
Chapter 6 analyzed the results of portfolio construction. By means of tactical asset allocation and the mean-variance portfolio model the unrestricted and a restricted portfolio provided average monthly return of 0,37% and 0,34%, respectively. The MSCI Denmark provided an average return of 0,65% per month. The market return was 0,34%. Neither portfolio outperformed the benchmark, but both outperformed the market. High covariance and correlation was detected among investment opportunities, and given different representation of investment opportunities between portfolios, restricting portfolio representation has not proven to alter portfolio performance.
The choice of time frame is a contributing factor in determining the success of active portfolio management. Limiting the timeframe to 1999, 2001 and 2003 would have provided cumulative portfolio return superior to the benchmark, but from 1992 to 2011 cumulative portfolio return was 41% and 42%
below benchmark, respectively.
Based on the findings in chapter 5 and 6, we conclude that MSCI Denmark has provided the investor with higher realized return as opposed to active portfolio management. This conclusion is based upon respective performances from 1992 to 2011. Selection of time frame is, however, important to determine the success of active portfolio management.
Does active portfolio management performance indicate investment skill on the part of the investor?
In order to determine whether the investment strategy indicates investment skill we considered the timing of portfolio repositioning and turned to the statistical tool Ordinary Least Square. Market return was regressed on portfolio return and a second explanatory up-market variable containing only positive market returns was introduced. The purpose of this variable was to determine whether portfolio market exposure was significantly different in the event of positive and negative market return. The up-market variable was statistically significant but negative.
Based on the findings with regards to market timing in chapter 6, we conclude that quarterly portfolio repositioning cannot be attributed as a timing skill. Even though both portfolios provided return superior to the market index, market exposure of portfolios is not statistically significant.
77 With regards to the systematic risk of portfolio and benchmark, does active portfolio management add value to the investor?
Portfolio value added, or alpha, is present under the condition of positive active beta and positive active return or vice versa. The rationale behind this condition is that the investor is only rewarded for taking higher systematic risk than the benchmark if active return is positive. On the other hand, negative active return still adds value to the portfolios, given the portfolio beta is lower than the benchmark beta. The unrestricted and restricted portfolio added value by providing monthly average residual return of 1,56%
and 1,16%, respectively. As a result of the unrestricted portfolio possessing concentrated sector positions, this portfolio was more successful in tracking the benchmark performance resulting in a superior information ratio of 33% against 6%.
Based on the findings of chapter 6, we conclude that active portfolio management has added significant value to the investor as opposed to benchmark investment. Restricting the portfolio beta to,P,t 1, provides the investor with the ability to control market exposure of the portfolio, leading higher portfolio systematic risk to be warranted by a higher realized return. On the other hand, leading lower realized return to be justified by lower systematic risk.
The overall conclusion from this thesis is: the investment strategy of active portfolio management provides inferior return to investing in the MSCI Denmark. However, maintaining a fixed level of systematic risk upon portfolio repositioning, portfolio return inferior to the benchmark is justified as the benchmark demands higher systematic risk in order to generate higher return. In addition, given portfolio systematic risk exceeds benchmark systematic risk portfolio return is in such case positively significant. In that regard active portfolio management adds value to the investor.
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8. References
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Books
Benninga S. (2008): Financial Modeling, Massachusetts Institute of Technology, Third Edition
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80 Databases
Datastream
MSCI Barra
Statistikbanken
Publications
Da Silva A., Lee W., Pornrojnangkool B. (2009): The Black-Litterman Model for Active portfolio Management, Forthcomming in Journal of Portfolio Management, Winter 2009
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Fernández P., Aguirreamalloa J., Corres L. (2011): US Market Risk Premium used in 2011 by Professors, Analysts and Companies: A Survey with 5731 Answers, Working Paper, IESE Business School, University of Navarra
Lee W. (2000): Advanced Theory and Methodology of Tactical Asset Allocation
MSCI Barra (2010): MSCI Global Investable Market Indices Methodology; MSCI Barra Index Methodology
Sparinvest (2007): Strategisk Asset Allocation - kort fortalt, Second Edition
Websites
www.borsen.dk
www.euroinvestor.dk
www.ft.dk
www.investopedia
www.jyskebank.dk
www.msci.com
www.proinvestor.com
www.sec.gov
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