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.

I put the above statement in a more mathematical framework. Considering the information ratio in equation 3.1 We let the return of the actively managed portfolio,R_P,t, and the benchmark R_B,t be defined by the following models:

(3.2)

10

1

, ,

,







ⁿ

i

t i t i t

P R

R  R_B,t _B,tR_i,t (3.3)

The investment universe consists of n=10 investment opportunities for the active portfolio and R_i,t 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:







 ¹⁰

1

, 1

n

i t i

p 

 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.





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, R_t^e≥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 R_t^e≤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 controls_P,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,R_t, 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, R_t. 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

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.