1. Introduction
4.1 Expected Return in Active Portfolio Management
4.1.1 Asset Pricing in an Active Setting
38
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.
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:
) 2 . 4 ) (
var(
) , cov(
M M i
i r
r
r
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
0 2 4 6 8 10 12
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.
) 3 . 4 (
*
Premium , USequity risk premium Risk
Equity Market
f t B
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:
) 4 . 4 ( )
( , , ,
,t Mt f t it
i e
B R R
R
Here,RM,t Rf,t is the monthly risk premium calculated above and i,t is the consensus expected excess return of the benchmark. The latter is a 19 years rolling historical average, as consensus of benchmark 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 can expect to gain a reward for selecting seven of the ten sector indices, which is however not large enough for the investor to increase expectations for the return estimations. Expected active returns indicate that none of the investment opportunities will be able to outperform the benchmark individually.
For more details of active returns, see Appendix 4.
BMATR CNSMG CNSMS FINAN HLTHC INDUS OILGS TECHN TELCM UTILS Active Return Premium -0,0005 0,0014 0,000 -0,002 0,003 0,000 0,003 0,002 0,000 0,000
t-score -0,18 0,60 0,09 -0,90 1,48 0,12 0,95 0,55 -0,04 -0,14
P-value 0,86 0,55 0,93 0,37 0,14 0,90 0,34 0,58 0,96 0,89
Source: Own Creation, Datastream, MSCI Barra, SAS Enterprise Guide
45 From figure 4.4 exceptional benchmark return has been the least stable of the three. For example, around the period of the dot.com bubble in late 2000 and the financial crisis in late 2008 and 2009 the investors experienced increasing returns relative to consensus. The important takeaway here is that the applied procedure of calculating risk premium includes current expectations about future return, which is very beneficial from the investor’s point of view, as it enables dynamic asset allocation which is not constrained by historic performance. This also explains why the association between exceptional benchmark return and the risk free rate is somewhat clear, but deviates substantially during the periods of the dot.com bubble and the financial crisis.
Concluding the analysis of estimating expected return we review the relationships estimates for expected return. Figure 4.4 graphs the historic development of these estimates.
0,00%
0,20%
0,40%
0,60%
0,80%
1,00%
1,20%
1,40%
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Premium
Figure 4.4 Estimated Premuims
Government Bond Rate Market Risk Premium Exceptional Benchmark Premuim
Source: Own Creation, Datastream MSCI Barra, Statistikbanken
46 As a result of rolling beta estimates and risk premiums, from figure 4.5 we see how expected returns are by no means stable. This is particularly evident by the dot.com-bubble which saw Technology stocks boom to extraordinary high levels of return. In addition, other investment opportunities are expected to exhibit correlation within an interval between approximately 1% and 4%. During the financial crisis from late 2008 most sectors plunged increasing their correlation, and from 2009 they converge back to higher return levels, but maintained a strong pattern of inter-correlation, as a result of market systematic risk levels becoming more integrated across industries. Expected residual return estimations between each investment opportunity and the benchmark are illustrated in Appendix 5.