1. Introduction
6.1 Return-Based Performance Analysis
67
6. Performance Evaluation of the Investment Strategy
This chapter analyzes the results of portfolio construction, and seeks to investigate three findings:
comparative absolute return between portfolios and benchmark, presence of investment skill and finally the extent to which active portfolio management has added value. Chapter 5 concluded that benchmark investing provided superior active return to the portfolios. However, a timing skill and value added may still be present as the portfolios did in fact outperform the market index and carried systematic risk restricted to market level, meaning active return needs be adjusted for systematic risk.
All results are analyzed and explained in terms of theoretical models and parameters.
68 losses, meaning volatility has been higher providing higher uncertainty with regards to its performance.
The advantage of portfolio diversification comes into view as the spread between the 95th and 5th is higher for the benchmark than the portfolios. The standard deviations from table 5.5 support this observation (benchmark standard deviation was 5,9% and unrestricted and restricted portfolio standard deviation were 4,9% and 4,6%, respectively).
Figure 6.1 considers the investment timeframe, and shows the impact of using cross sectional comparison.
We compare the two portfolios and the benchmark by their cumulative return. Such comparison is conducted by calculating the percentage difference between portfolio and benchmark cumulative return:
Value Index Benchmark
Value Index Benchmark Value
Index Portfolio Comparison
turn
Cumulative
Re
Over the 20 year period the portfolios have accumulated a return of 41% and 42% inferior to the benchmark, the unrestricted portfolio performing marginally better as previously concluded. The mean-variance model provides portfolios performing almost equally well over long time frame (20 years). In addition, had the investor limited the time horizon to 1999, 2001 or 2003 at least on portfolio would have provided a positive cumulative active return. However, we must keep in mind that the beta restriction on the portfolios prevents the investor from taking systematic risk above market level, limiting opportunities
-60%
-40%
-20%
0%
20%
40%
60%
Cumulative Return
Figure 6.1 Cumulative Return Comparison 1992-2011
Unrestricted Portfolio vs Benchmark Restricted Portfolio vs Benchmark Source: Own Creation, Datastream, MSCI Barra, Appendix 6
69 for realizing a superior return. Systematic risk has been lower, and returns are consequently lower as well as the investment cannot refrain from selecting low beta investment opportunities. The active investment evaluation will later investigate whether the superior return of the benchmark to the two portfolios is warranted by its market risk.
From figure 6.1, similar cumulative return development between portfolios is in fact significant, since the findings of chapter 5 indicated very different patterns of average sector allocation. As a result, identifying investment opportunities showing different return patterns at a given time, and conducting asset allocation accordingly, becomes a fairly redundant process. High covariance resides among investment opportunities, which makes the ability to identify points in time where some stocks have proven to perform better than others a difficult task. Such ability refers to skill on the part of the investment strategy.
6.1.2 Market Timing
Benchmark and portfolio investment both provided positive active return to the world market index. This subsection seeks to investigate whether such returns are generated as a result of investment skill. With regards to the portfolios, the influence the quarterly portfolio reweighting, or market timing, have had on realized portfolio return, meaning how successful the investment strategy has been.
6.1.2.1 Regression Analysis
To examine whether the portfolio return is a result of skill rather than luck we turn to the statistical tool, Ordinary Least Square (OLS) method. The model below should provide a conclusion to whether benchmark and portfolio investing can actually be considered a skill, appropriate for the investment strategy.
0, ( )
( )* ) (
* )
(t R t Max R t t
RP P M P M P
We introduce the variable P to determine whether investment strategy possess any timing skill. The model includes a down beta,P, and a beta in positive market returns P. If Pis significantly positive, we say there is evidence of a timing skill, meaning market exposure is significantly different in cases of positive and negative market returns. The variable Max
0,RM(t)
assumes the value zero or any positive70 market return at time t. If Pis positive and significant there is evidence that quarterly repositioning is a timing skill, meaning market exposure is significantly different in up and down cases.
With regards to the error term,P(t), the model’s quality and value depends heavily on the behavior of the residuals. Consequently, we need to check whether the residuals behave as the OLS assumptions required.
The error term at different time stages, must be uncorrelated, in order to maintain an unbiased variance of the betas, ensuring the reliability of the t-tests, which measures parameter significance. Furthermore, as the regression model contains more than one explanatory variable and these variables have a good chance of being highly correlated a problem with multicollinerity arises, as we will not be able to separate the effects of the individual variables64.
The models test hypothesis is stated below:
H0: Max
0,RB(t)
0 : Portfolio performance is a result of investment skill H1: Max
0,RB(t)
0 : Portfolio performance is not a result of investment skillBefore testing the hypothesis, we test for autocorrelation in the regression model. Autocorrelation is a representation of a degree of similarity between the time series, applied in the regression model, and a lagged version of themselves over successive time intervals65. Testing the model for autocorrelation using the Maximum Likelihood test with 4 lags, we find that neither portfolios show significant sign of autocorrelation in the error term. As a result we can draw reliable conclusions from the t-statistics of significance. We therefore bring to a close that the models do not contain a problem with regards to autocorrelation, thus conclude that the OLS assumptions are fulfilled. The models results are described in table 6.1
64 Multicollinearity is present if there is a linear relationship between the explanatory variables:P ,Max
0,RM(t)
65 Gujarati et.al (2009): p.413
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.