This book analyzes several investment strategies that are applied to an international equity portfolio. The evaluated strategies are: the Simple Crossover Moving Average, the Equally Weighted Portfolio, the Minimum Variance Portfolio, the Certainty Equivalent Tangency Portfolio, the James Stein Estimator and the Black Litterman Model. Besides the applied methodology part which demonstrates how to implement the considered strategies, the empirical section shows from the viewpoint of a European investor whether the final performance parameters are mainly due to returns of foreign markets or through exchange rate developments. The investigation is carried out from an ex ante as well as from an ex post perspective. In order to examine the time window of a strategy, the in- and the out of the sample periods are varied. The empirical investigation indicates that – the relative young more sophisticated approaches are superior to the traditional strategies, the impact of exchange rate developments cannot be ignored in an equity portfolio, nearly no conclusion can be drawn in the context of a superior in- and out of the sample period.

Textprobe: Text Sample: Chapter 3.4.1, Crossover Simple Moving Average: The idea that the performance of the MVP, the CET, the JSE and the BLM are only compared to the development of the MSCI World might seem a bit insufficient. It is truly unproblematic to compare the mentioned strategies, which are all built on the same fundamentals of Markowitz, with the MSCI and therefore show if the step from a passive management to an active portfolio management results in a better performance. However, it might be interesting to know how another strategy performed which does not rely on the ideas from Markowitz. Therefore, beside these strategies, which are static because the analyst or the investor needs to specify a certain estimation period, the Crossover Simple Moving Average (CSMA) as a dynamic strategy has been applied as well. However, an obstacle arises because the two different approaches cannot directly be compared. Further, if to a certain degree short positions are allowed, then the portfolio weight optimization of the Markowitz based strategies do not always result in corner solution with the maximum short or long position. Therefore, the direct evaluation of the resulting moments might be a flawed because it is like comparing ‘apples and oranges’. However, the application of the CSMA strategy comes with one major advantage – we can see if the same dataset lets a simple dynamic strategy seem to be superior to the more sophisticated static ones. A CSMA strategy results from taking two Moving Averages (MA) in which each is based on the different length of time. The MA formed by the shorter of the two periods is called the fast MA, while the MA that arises through the longer time period is the slow MA. As the price changes over time, the fast MA reflects these changes by moving up or down with the price faster than the slow MA does. Therefore, from time to time the two different MA cross each other. When the fast MA crosses over the low MA, it is a buy signal. On the other side, when the fast MA crosses under the low MA, it is a sell signal. This strategy works well in trending markets but does not in consolidating ones. In other words, if markets tend to continue to rise or fall, the strategy is appropriate but in markets which quickly trade back and forth, it is not. In cases where the fast MA is below the low MA a sell signal was anterior. In order to receive in these periods a return as well, the endowment is invested in the Euribor. In other words, in case of an upward trend, the endowment is invested in the index, while in periods of a downward trend the investment is in the Euribor. Since there are ten indices in the total portfolio, each index has been allocated 10 percent of the total endowment. Therefore, the final return- and standard deviation magnitudes are based on the 10 indices. Equally Weighted Portfolio: As the name suggests, the Equally Weighted Portfolio (EQW) consists of all indices in an equal amount. Since this analysis contains 10 markets, each index contributes 10% to the total portfolio performance. The EQW can be considered as a portfolio, which achieves the benefit of international diversification without taking the information on expected return, variances and covariances into account. An EQW performs well if markets move countercyclical at the length of one periods time. In the beginning of a period each asset in the EQW is worth 1/N because of the equal amount, however, through the stochastic element of a risky asset, the end of the period wealth is different. Assets which showed good performances relative to other assets in the portfolio are worth more than 1/N at the end of a period. Therefore, the adjustment in each new period leads to an increase in the weight of the losers while at the same time the weight of the winners is reduced. Minimum Variance Portfolio: The Minimum Variance Portfolio (MVP) is defined as the portfolio with the lowest possible variance. The MVP is solely calculated by the variances and the covariances of the indices. It is the global risk minimum of the mean-variance efficient frontier. The MVP is suitable for a highly conservative investor whose risk aversion converges to infinity. In other words, in a (..) diagram, the utility functions of MVP investors are straight lines which are parallel to the y-axis. The MVP approach is solely based on the second moments of the assets in the portfolio the parameters of the expected returns are not included for the determination of the optimal weights. This implies that by moving away from the MVP and entering a small amount of additional risk, a large amount of additional expected return is obtained. Therefore, the MVP has to be regarded as a purely hypothetical approach. The optimal weights of the MVP are calculated according to the following minimization problem.

• Portfolio Management

• International Asset Allocation

• Stock Market Returns

• Exchange Rate Risk

Gerhard Wörtche is a PhD at the Complutense University of Madrid. He holds a Master in Banking and Financial Management from the University of Liechtenstein and a Bachelor in Economics from Cardiff University.