There are many cases where improper risk management has led investors to accumulate catastrophic losses. These cases highlight the importance of proper risk management. The purpose of risk management in this thesis is to identify and limit the type of risk the investor faces and set up risk measures in order to manage risk in a manner that secures reliable estimates for significant value added. In order to grasp what the concept of risk involves and how to measure it we will begin by considering investor utility as the first description of risk followed by Claus Vorm’s views upon risk and risk management. On that basis we frame
-2% 0% 2% 4% 6% 8% 10% 12% 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 Exp e cte d R e tu rn
Figure 4.5 Expected Return Estimates
Basic Materials Consumer Goods Consumer Services Finance
Healthcare Industrials Oil & Gas Technology
Telecommunications Utilities MSCI Denmark
47 a definition of risk in order to limit the types of risk factors the portfolio is exposed to, ultimately leading to identifying a measurement for the tracking error.
4.2.1 Investor Utility
The first systematic description of risk for financial problems is risk aversion, and I will now give a brief description of how investor’s utility is treated. A variety of different perspectives upon risk resides among investors and hence their levels of utility differ.
One of the major subjects of investigation is the relationship between risk and return. In contrast to usual utility evaluation, where individuals choose between two positive goods, in this case I consider return as a positive good while treating risk as a negative good as increase in the former increases the information ratio while increases in the latter decreases it. However, risk and return often comes hand in hand. Theory generalizes three different types of investors by their risk appetite: risk averse, risk seeking, and risk loving. The difference between investor types is their demand for compensation for taking on new risk. This rationale is commonly used in practice and is determined to be the general motive for the difference in investor’s preference when choosing stocks over e.g. bonds.
On the basis of these considerations that the investor regards risk and return as being a negative and positive good, respectively, diversification is required as a means for risk management. By spreading the investment into several investment opportunities the investor should be able to claim a higher risk adjusted return than any of the assets alone. Accordingly, diversification implies that the compensation for having risk is increased. Thus, there is a positive relationship between portfolio sectors and their associated return. Markowitz established the mean-variance approach in portfolio context on the basis of this relationship. We will ensure diversification with regards to portfolio construction with the objective for the investor to be compensated for any additional risk taken. We will therefore impose a constraint of maximum 20% portfolio weight to each sector index upon portfolio reweighting (Portfolio construction without such constraint will also be conducted). Chapter 5 will discuss the details of this constraint.
4.2.2 Professional Views upon Risk and Risk Management
Claus Vorm explained that a vast variety of risk exists, which the investor is exposed to and which dependents upon the investment objective. Thus, he acknowledges that risk is based on a point of view, as
48 is it dependent upon investor perception and the investment mandate the manager is given (being the investor himself or a professional manager). In that sense, proper risk management involves conducting investments submitted the constraints and risk preference of the investor. Thus, realized risk is obviously determined ex-ante and must not be higher than the risk permitted by the mandate.
Accordingly, in terms of measuring risk, measurements again depend upon the investor’s presumption of risk. Claus Vorm explained the variations of investor’s preference. Whether risk is measured as tracking error, beta or absolute risk is a question of investment objectives. In terms of active portfolio management the investor chooses an exposure to stocks and allows for a pre-defined tracking error. In order to control the tracking error, risk can also be controlled in an absolute sense, by setting specific boundaries in terms of short fall or volatility. However, actively managed portfolios have proven to deliver better performance with flexible investment mandates49, meaning providing the investor (or portfolio manager) with no specific investment constraints with regards to choosing risky investments over less risky investments. The long investment horizon allows for a flexible mandate as the investor has substantial opportunities for compensate potential losses incurred by potential gains from investments.
4.2.3 Risk Management and Risk Factors
From the discussion above we conclude there is no universal definition of risk and neither is there any one generally accepted definition of risk in specific environments. However, it is a common presumption among investors to link risk with uncertainty. In addition the definition of risk must allow for reasonable measurements. Therefore, for the purpose of active portfolio management we define risk as follows:
Risk is the exposure to some uncertain future events.
Only an event that has a dependency on the portfolio may influence its risk. In many cases of risk management, probabilities of possible future events are estimated. We do not presume to know these probabilities as the referred events may not even be known. We will therefore apply an ex-ante measure for the tracking error with regards to portfolio optimization, and evaluates portfolio performance by means of an ex-post measure. The focus in this chapter will be on the ex-post measure, and the ex-ante tracking error will be highlighted with regards to portfolio optimization in chapter 5.
49 We will refer to ex-post risk management from Claus Vorms statements above. He suggests that risk can be limited to one or a few measurements, and in that regard we consider risk factors relevant to adding portfolio value. Based on the fact that the investment universe is limited to stocks, we consider only the risk within the area of investments. In order to model asset risk, for simplicity, we consider two risk factors also included in value added:
Systematic risk
Active sector risk to the benchmark.
As a consequence of estimating the tracking error ex-post, the systematic risk is the only risk factor the investor is able to control. Restricting the portfolio beta to P,t 1 provides the option to move from a portfolio that is fully invested in equities to one that incorporates a proportion of risk equivalent to holding cash. In a declining market, for example, cash provides a safe haven helping the investor to ride out a down turn while positioning the portfolio to take advantage of opportunities as they arise. In down markets high proportions of cash level risk can help the investor to produce milder declines and lower volatility than the benchmark. In a strong positive market the investor can revert to a more fully invested portfolio, which will help keep pace and potentially outperform as the benchmark rises.
Estimating the tracking error ex-ante proscribes controlling realized portfolio return deviation from the benchmark. However, as outlined in chapter 1 the investment opportunities and the benchmark have shown quite high correlations, and we can therefore expect somewhat similar return development between the investment opportunities. When returns between investment opportunities and the benchmark appear to have deviated, the tracking error increases.
4.2.4 Financial Risk
The risk measure with regards to the risk factors and utility seeks to increase risk adjusted return by diversification. However, we still need a tangible measurement relevant for the investor which incorporates the risk factors, market risk and idiosyncratic benchmark risk, in order to conduct specific ex- post estimation of the tracking error. Additionally, it is relevant to adopt a procedure for risk estimation that reflects the active holding of the investment opportunities. As the portfolio is actively managed, the investor seeks to acquire residual return and hence also takes active risk upon his investments.
50 One could argue that for the investment opportunity set, active risk is proportional to the capitalization of each sector. Thus the market weight for e.g. Industrials may be 12% (see Appendix 2). Position limits of 6% and 18% may be set with the idea that this is a 50% underweighting and 50% overweighting. So the active exposure of Industrials is limited to ±6%. However, throughout the later investigations we will treat active risk as being dependent upon active exposure, and not the holdings of each asset. So, while there may be cost and liquidity reasons for emphasizing large stocks, we do not believe it to be true that an active position in a large sector is less risky than an active position of the same amount in small sectors.
With respect to the considered risk factors, beta and idiosyncratic risk, we decompose the market risk and the relative benchmark risk in estimating the tracking error for value added. This possibility is enabled as the introduction of additional risk premium in our return estimations makes beta and realized returns are somewhat uncorrelated. The applied estimate for the portfolio to track value added from benchmark investing is stated in equation 4.6.
*
(4.6) * 1 2 , , 2 , , 2
i t B t i e t B e t i i P w R R
Here,
P is the portfolio tracking error, wi is the asset weight, Bet et
i R
R, , is the residual excess return and )
(i,tB,t is the residual beta. The point of this estimation is to provide an estimate of the additional risk the exposure of the sector Indices adds to the risk of benchmark investment. E.g. investing in the benchmark yields zero active exposure (replace Rie,tbyRBe,t). Note, that investor risk aversion is not
incorporated into the tracking error, as active portfolio management will not be submitted to specific risk preference, but rather a general framework of risk reduction, due to the basic consideration of risk being a negative good.
51
5. Portfolio Construction
Implementing the investment strategy involves portfolio construction and repositioning. This chapter constitutes the final steps of active portfolio management which enables evaluation of portfolio performance. The primary focus of portfolio construction concerns the process of determining the amount of funds allocated to each investment opportunity and that process relies on the applied portfolio model. The process of repositioning simply comprises the timing of when the model conducts asset allocation as a repetitive exercise.