1. Introduction
3.1 Defining Active Portfolio Management
Active portfolio management means allocation of funds based on expectations of future market developments. The strategy is performed against the MSCI Denmark as benchmark. This chapter introduces the main concept of active portfolio management and its instruments. We begin with the definition of active portfolio management:
Active portfolio management is the implementation of a dynamic investment strategy that over- and underweights the predefined investment opportunities over a long-term basis, with the single objective of outperforming the predefined benchmark at a predefined time in order to add value to the portfolio.
From this definition the importance of the benchmark for active portfolio management is evident. In terms of risk and performance measures, the use of benchmarks is important in order to obtain clear measurements in accordance with the investment strategy. In order to evaluate the performance of the investment strategy we will establish appropriate performance measures which aim at capturing the systematic risk adjusted return of the portfolio in comparison to that of the benchmark – the residual return – and measure whether it in fact adds value to the investor.
34
3.2 Performance Measure and Portfolio Added Value
Several performance measures for portfolio evaluation exist, such as the Sharpe Ratio and Jensen’s Alpha, and they are selected based on the purpose of portfolio management38. As portfolio performance in this thesis must be considered relative to the benchmark a relative rather than an absolute performance measure is required. Thus, we will employ a performance measure that captures the expected excess return of the portfolio in comparison to the benchmark – the active return. The information ratio provides such estimation39.
3.2.1 Information Ratio
We denote the active return as the difference between the portfolio returns and the benchmark return, which is illustrated in the nominator of equation 3.1. The mean of the residual returns is usually called return. SP-B is the tracking error, or the standard deviation of the residual return, measured as the squared difference between portfolio and benchmark return. Estimates for each three components are provided in chapter 4. According to Stotz (2005) with regards to the information ratio, the investment strategy ultimately seeks to either maximize the expected return of the active portfolio or minimizing the tracking error40. Since the portfolio is compared to the benchmark, active return determines the comparative capital gains, while the tracking error indicates how well the portfolio tracks the benchmark. In other words, active return determines whether the portfolio has outperformed the benchmark and the tracking error determines whether the information ratio is significant.
38 http://www.investopedia.com/terms/s/sharperatio.asp#axzz2ED7A5ucy http://www.investopedia.com/terms/j/jensensmeasure.asp#axzz2ED7A5ucy
39 http://www.investopedia.com/terms/i/informationratio.asp#axzz24eZnzbHn
40 Stoltz (2005): p. 264
35 3.2.2 Portfolio Value Added
Obviously, successful execution of the investment strategy involves over- and underweighting of the investment opportunities expected to perform well and poorly, respectively. The asset selecting approach only identifies the forthcoming winners and losers. Correspondingly, as shot selling is not allowed, the investor can allocate a proportion between 0% and 100% to a single asset. Hence, the amount of capital allocated to each asset need not be sophisticated, as it could just as well be equally weighted. However, if the mean of the active return of the portfolio is positive, the investor has actually beaten the benchmark, and whether the outperformance is significant or not is reflected in the information ratio, which will be investigated in chapter 6. Therefore, the information ratio should rather be seen as an indicator for the manager’s skill than a performance measure. denotes the excess return of the i-th investment opportunity. i,t denotes the beta of asset i at time t, and will be applied on a rolling basis rather than an overall average. Maintaining an average beta over the period is misleading as the environments in which companies operate change, leading the market risk, which they are exposed to change over time41. As the benchmark is treated as a single stock it only consists of n=1 investment opportunity, and will therefore not be submitted to reweighting at any time.
Furthermore, I will impose one constraint:
leaving the investor the opportunity to invest
in the optimal tangent portfolio or hold cash42. Given the relatively small size of the MSCI Denmark in
41 I will explain the basis for this application thoroughly in chapter 5
42 Borsen interview at time 8:45:
http://borsen.dk/nyheder/investor/artikel/1/246033/aktiv_kapitalforvaltning_for_de_tunge_investorer.html
36 terms of capitalization, it is neither broad nor representative and hence is not characterized as a market, as it carries market risk, as well as the sector indices, relative to the global stock market. In addition, the benchmark does not represent the investment opportunities, meaning they are not indices underlying the MSCI Denmark, but in fact larger in terms of capitalization, and have developed somewhat interdependently with regards to the benchmark. Nevertheless, the investor should still have the opportunity to invest globally within the limits of the investment strategy and opportunity set in order to provide opportunities for diversification. Hence, the benchmark beta does not represent a weighted average of the sector’s beta.
We compare active beta and active return as two separate factors in order to measure value added.
Holding high beta investment should only add value to the investor if the return is correspondingly high an vice versa.
P,t B,t
* te (3.4)t R
a
The mechanics of active portfolio management is seen from equation 3.4. It represents a cornerstone for measuring value added, or residual return, and tracks any value added by active portfolio management.
For the case of a non-negative active return, Rte≥0, the exposure of the investor should at least be as big as the exposure of the portfolio, P,t B,tin order for active portfolio management to add value on average. Accordingly, for the case Rte≤0, in order to obtain value added P,t B,tso a positive alpha is maintained. Thus, the beta adjustments to the excess active return tracks any value added from active investing. Hence, if a positive alpha is maintained active investing has added value to the investment.
These equations show that security selection and market timing are the same, because in both cases the investor controlsP,tin order to add value to the portfolio.
The beta portfolio is constrained in order to limit the amount of risk the investor can take upon his investments. Investing in high beta stocks is likely to generate high returns, but its risk deteriorates the investment value for the investor as well. Pursuing high beta investments, such as the benchmark is a risky way to generate high returns. Therefore, the crucial point for successful security selection and market
37 timing is the correct prediction of the active return,Rt, hence estimates for expected return for the portfolio and the benchmark.
Note from equation 3.3 that the correct prediction of security return is not the only source of alpha. It was previously argued that the significance of the outperformance of an investment strategy is reflected by the information ratio. By now we have shown that the information ratio can be increased by better predictions of security prices, Rt. Obviously, the information ratio may also be increased by variances in residual return, provided that the mean residual return remains the same. Minimizing the residual risk hence, becomes important as well for maximizing the information ratio.
Treynor and Black (1973), describes systematic active portfolio management approach, coupling the identification of alpha, and risk management43. Traditional portfolio theory does not distinguish between active portfolio management and optimal portfolio construction. This thesis will not attempt to fill this gap, meaning portfolio construction is conducted with the sole purpose of outperforming the benchmark on a risk adjusted basis. Whether, a deviation from the investment strategy could in some way have provided the investor with higher residual return than realized remains hypothetical and will not be investigated. However, what all active portfolio strategies have in common is that outperformance has to be gained through altering investment positions, which is emphasized in the definition above.
This chapter provided a review of the framework of active portfolio management. The important takeaway for the pending analysis is the need for expected return estimations and measures for risk. We will then have the necessary input to conduct portfolio construction.
43 Treynor, Black (1973): p. 69
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4. Risk and Return in Active Portfolio Management
In accordance with the information ratio as the performance measurement of active portfolio management, emphasis is required on active risk and return. This chapter establishes valid estimates for expected return and risk measures appropriate for portfolio construction. The investment strategy requires estimates every time the portfolio is to be reweighted. An exposition of the capital Asset Pricing Model (CAPM) will provide such estimates. Furthermore, we investigate the risk factors the investment is exposed to in order to determine risk warranting the return.
4.1 Expected Return in Active Portfolio Management
Based on the assumptions of Markowitz portfolio theory Sharpe (1964), have derived the Capital Asset Pricing Model (CAPM)44. The importance and relevance to this thesis of the CAPM model is derived from its terminology, i.e. its use of the Greek letters ɑ and β, which is widely used in the context of portfolio management today.
The CAPM seems to be an attractive approach to the active portfolio management. It has, however, received extensive criticism, particularly from Farma and French (2004), arguing against its empirical foundation implying that most implications of the model are invalid45. Nevertheless, I will in this chapter set up the CAPM model.
4.1.1 Asset Pricing in an Active Setting
The CAPM model plays an important role when selecting portfolios according to mean-variance optimization. When using the CAPM forecasts of expected return to construct optimal mean-variance portfolios, those portfolios will consist simply of positions in the market and the risk free asset. In other words, optimal portfolios constructed under mean-variance optimization will differ from the market portfolio and cash if the forecasted excess return differ from the CAPM excess return. As we adopt tactical asset allocation I add components to the asset pricing model. Thus, the expected return, in this thesis is built on five factors: the risk free interest rate, the sector specific risk adjustment, the market risk
44 Sharpe (1964): p. 436
45 Farma (2004): p. 26
39 premium, a premium for exceptional market return, and an expected residual return. Note, the residual return is, ai, is a constant.
From these four factors the CAPM in active portfolio management takes the following form:
* R ,
, (4.1)
e
t M, ,
, ,
,
,t f t it Mt f t it it
i R R R a
R
E
Here, E(Ri,t) is the expected return of asset i. Rf is the risk free rate, βi,t is the systematic risk of sector i, RM
is the market return. Exceptional market return,
i,t
e t
RB, and the expected residual return, ai,t extend the traditional CAPM model for the investment opportunities only. As the purpose of active portfolio management is to obtain the highest portfolio residual return possible, the portfolio should not only be maximized with regards to its own standard deviation, but also with regards to the risk adjusted return of the benchmark, in order to improve the information ratio. Therefore premiums for selecting the investment opportunities over the market and benchmark are warranted.
4.1.1.1 The Risk Free Interest Rate
To estimate the risk free rate, Rf, I consider two Danish government default-free bonds. Obviously, no bonds are default free. However, the selection of the Danish default- free bond is based upon the obvious reason that the investor is assumed to be Danish and since these bonds are considered safe investments46. The 10 year government default-free bond rate is commonly used, particularly in valuations as the maturity of the bond, the market and the forecasting period will be close to each other. Figure 4.1 illustrates the 5 year Danish government bond rate against the 10 year Danish default-free bond rate.
46 http://www.jyskebank.dk/wps/portal/jfo/finansnyt/struktureredeprodukter/danmark2015
40 The 10 year default free rate has a lower standard deviation than the 5 year default free rate. Thus, if we were to use the 5-year default free rate, we would experience marginally larger deviations in the expected return estimates, than by using the 10-year default free rate.
4.1.1.2 Systematic Risk
According to the CAPM the expected return of an asset is driven by its systematic risk, βi, which indicates how much on average the stock return change for each additional 1% change in the market return. Beta is calculated as the covariance between asset and market return divided by the variance of market return as follows:
It is important to consider the beta of the benchmark as well. As the Danish index is relatively small on a global scale it is exposed to systematic risk as well and as beta is a main driver of the expected return estimation we cannot presume a constant benchmark beta. Therefore, we consider the systematic risk of both sector indices and benchmark with respect to MSCI World Index.
Estimating beta on a rolling basis is a reasonable approach. Peter Sjøntoft explains that companies change their strategy in accordance with the altering environment in which they operate. Therefore, the
1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Percent
Figure 4.1 Danish Default Free Government Bonds - 5 vs. 10 years
Danish default free government bond rate - 5 years Danish default free government bond rate - 10 years Source: Own Creation, Statistikbanken
41 corporate strategy of many international companies is by far not the same as it was ten or twenty years ago. Thus, markets respond to these changes and their sources. Companies entering new markets conduct mergers and acquisitions or are subject to sectorial bull or bear markets often takes upon them a varying amount of risk, and given the long time frame, sectorial risk cannot be submitted to a single average risk estimate. However, estimating beta on a sectorial basis makes it less sensitive to the market risk of the underlying companies. Closing this discussion on beta we continue by measuring beta as a rolling estimation of each investment opportunity. Rolling estimates are obtained by calculating each beta based on 1 year monthly returns. Figure 4.2 illustrates the rolling beta estimates based on 12 months rolling average.
Sector betas converged in 2008 and had before that with exceptions such as Technology, trended towards common beta averages between 0 and 247, which is also illustrated in figure 4.3. The R-square values are, however quite low, as they indicate beta values fluctuating substantially around average. Initially, such result seems disappointing, as systematic risk appear to be difficult to control.
47 Koller et. al. (2010): p. 246 -2
-1 0 1 2 3 4 5 6 7 8 9 10
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Beta
Figure 4.2 Rolling Beta Estimates
Basic Materials Consumer Goods Consumer Services Finance
Healthcare Industrials Oil & Gas Technology
Telecommunications Utilities MSCI Denmark MSCI World
Source: Own Creation, Datastream, MSCI Barra
42 There is a trade-off, however, as volatile beta estimates improves the opportunities of tactical asset allocation. Portfolio repositioning is conducted frequently based on the expectation that return on investment opportunities will change between repositioning. This is a reasonable assumption, as sector returns are stationary, meaning returns fluctuate around their long-term average return. In order to change return estimations, beta must change correspondingly. Therefore, in order to provide the investor with incentive to reposition the portfolio, we allow for fluctuating sector beta, hence expected return changes between months.
4.1.1.3 Market Risk Premium
Two methods are applicable for estimating market risk premium: ex-ante and ex-post. The ex-post method calculates the historic market return and then subtracts the risk free interest rate. Applying the ex-post method presents two complications. First, even though this thesis investigates a historical development, historical data alone is not a reliable indicator of future market expectations. Second, the market risk premium depends on the periodic time frame which can expose the method to selection bias.
The second method is calculating the risk premium ex-ante.
The country default spread is measured as the relative equity market volatility for the benchmark. We obtain this measurement by dividing the standard deviation of the benchmark equity market by the standard deviation of the 10 year Danish default free government bond rate. This ratio is then multiplied
0,35
0,09 0,08 0,08 0,04 0,30 0,25
0,00 0,00 0,09 0,35 0,00
0,40 0,80 1,20 1,60 2,00
Figure 4.3 Average Beta and R-Square for Each Sector as Regressed on MSCI World
Beta R-square Source: Own Creation, Datastream, MSCI Barra
43 by the long term risk premium of the US equity market, in order to obtain an estimate comparable to other major stable national Indices.
)
Premium , USequity risk premium Risk
Here, σM,t is the rolling standard deviation of the market – at time t and σf is the standard deviation of the risk free rate. The US equity premium is estimated to be 5,5%48.
4.1.1.4 Exceptional Benchmark Premium
I have added the exceptional benchmark return to the CAPM model as a measure that takes into account the deviation from the market and the benchmark. A premium is presented to the investor when the market portfolio is expected to deliver higher return than the benchmark, meaning that investing in other stocks than the benchmark delivers superior return. This premium is measured by the difference between the excess return on the market and the consensus benchmark return, which is a long-run estimate, as investors possesses only available market information must rely on historical performance. In other words, the exceptional benchmark return measures the benchmark timing, and as the issue of timing refers to the tactical asset allocation, this estimate will be considered on a short term basis, meaning estimates will change between months. Thus the exceptional benchmark return is estimated as follows:
) performance among investors represents the current presumption (at time t) of benchmark return.
4.1.1.5 Selection Premium
We conducted stock selection as an ex-ante investment decision as the opportunity set was limited to ten sector indices with no possibility of substituting indices. Thus a premium for taking such risk is warranted and determined by the ex-port performance of each sector relative to the benchmark measured by regression. Thus, it represents the reward for selecting each index into the investment opportunity set. Its
48 Fernández et.al. (2011), p. 3
44 value will therefore be applied as a constant for every time t in the period. The premium will be determined by a simple one-factor regression model based on the traditional CAPM. The applied regression model is the following:
Ri ai i (RB Rf ) et (4.5)E
RiE and (RBRf) represents the expected return of sector i and the benchmark risk premium, respectively. A regression of the historical sector return against the benchmark from 1992 to 2011 yields a constant,ai, which represents the intercept of the regression line. In other words, it represents the expected return of sector i when the risk adjusted benchmark return is zero, which is the expected long-term active return. Table 4.1 shows relevant summary statistics of the residual return.
Table 4.1: Summary Statistics for Residual Return Regression
Results are slightly different among sectors. With the exception of Basic Materials, Finance, and Utilities, all sectors show positive active return. However, no sector shows significant residual return on a 95%
confidence level, as all p-value of all sector indices are above 5%. This means, theoretically the investor
confidence level, as all p-value of all sector indices are above 5%. This means, theoretically the investor