Portfolio Optimization Employed

As countries and economies drive closer and closer due to globalization, many investors are looking at international investment as an additional way of diversifying the risk without jeopardizing the returns (Fonseca et al. 2008). Ever since the Markowitz (1952) seminal presentation on portfolio optimization, many academic researchers continue to carried out further investigations into the portfolio optimization and international investment.

One among the first researchers to depict the gains made from international investments was Grubel (1968) who concluded that international diversification of portfolios could bring in a new source of gains and at the same time a positive impact on policy making among nations. This is because international capital movements are  function not only of interest rate differentials but also depend on the growth rates of asset holding in the countries.

On examining the results on gains made exclusively from foreign currency holdings, Levy (1978) reported that  the alternative way of reducing the foreign exchange risk is by using a portfolio balancing approach because since the collapse of the Bretton Woods System  early 1970s, exchange rates had gained the ability to flout freely at the global market. As a result, Levy observed that (between early 1971-late 1973) US investors made significant gains by holding only foreign currencies.

However, Eun and Resnick (1988) argue that both studies from Grubel (1968) and Levy (1978) overstate the actual gains made from international diversification as they do not account for parameter uncertainty, which affects estimation of returns. They argue that the risk inherent to foreign exchange rates can eliminate or reduce the gains made on an international portfolio due to volatility and their positive correlation with stock returns.  

This paper seeks  empirically and theoretically to examine various models that are used to optimize the portfolio of foreign currencies with a focus on the currencies of the G10 countries. The data analysis for this study is focused on G10 countries because of the economic stability of these countries and the fact that their currencies are most traded at the foreign exchange market.

Most of the studies on currency portfolio optimization focus on simple, equal-weighted portfolios. The choice of simple portfolios could be because there is substantial evidence indicating that they outperform out-of-sample more than complex optimized portfolios. Optimized portfolios are a closer reflection of the uncertainties faced by investors in real time, i.e. they have to choose what signals to use, how to weigh each signal, and how to address estimation error and transaction costs (Barroso & Santa-Clara 2012). Therefore, our primary concern is how to decrease the risk of the portfolio returns regarding international currencies.

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The paper will extend the growing literature on modern portfolio theory of Markowitz (1952) and provide a brief description on each model from portfolio-choice literature considered. The models discussed include: Naïve portfolio, Mean-Variance (Tangency) portfolio, Minimum-Variance portfolio, and Bayes-Stein Shrinkage portfolio as discussed in DeMiguel, Garlappi, and Uppal (2009) financial study paper.

This study combines the parametric portfolio approaches of DeMiguel, Garlappi, and Uppal, (2008); Gronlund and Pedersen (2008); Kroencke, Schindler, and Schrimpf, (2011) and test the relevance of each variable in forming currency portfolios as applied at the FX markets. A pre-sample test is used to study which features are significant for investment purposes. Then a comprehensive out-of-sample exercise is conducted with 16 years of monthly returns.

Any rational investor desires to gain the highest returns from  investment. Every time that the investor adds foreign assets to his/her portfolio, he/she will automatically be exposed to foreign exchange fluctuations. Sometimes a positive return from a foreign invested asset can be cancelled by a depreciation of the currency in which the asset is traded. The return on such investment is therefore not only influenced by the performance of the business venture, but also by the performance of the currency at the foreign exchange market.  In most cases the returns from an investment has to counterbalance with risks that are associated with investment that the investor is willing to take. Unfortunately, the higher the returns are, the higher the risk associated with that investment.  The portfolio is normally typified using the expected return and the risk measured by variance (or standard deviation).

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The fact that majority of investors are risk-averse implies that investors hold well-diversified portfolios instead of investing their entire wealth in a single or a few assets. Diversification is across several business organizations within the same country is good because one firm may experience different challenges that the other firm is better in tackling them. Consequently, diversification in different business organizations in different foreign countries is even better because firms within the same country may be subjected to similar economic, socio-cultural and political turbulences. Therefore, as Levy and Sarnat (1970) reveals, portfolios diversified across different countries have better risk-adjusted returns than portfolios consisting only of US stocks.

The objective in this paper is to understand the various models used to optimize the portfolio of foreign currencies and how to improve the mean-variance optimization. In order to achieve this, the researcher will explain the meaning of optimal portfolio of currencies; analyze various known models of portfolio optimization for G10 countries  and discuss both theoretical and empirical studies on the performance of different portfolio strategies at the foreign exchange market.

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The initial results from the main analysis were very positive. The initial tests for prime assets suggest that international stock market investments are only beneficial for a U.S. investor when the exchange rate exposure is hedged meaning that Sharpe ratio rises from 0.29 p.m. in non hedged case to 0.33 p.m. for the hedged case. The baseline results are obtained for FX portfolio strategies constructed from 24 very liquid and frequently traded currencies, from the G10 countries. The role of transaction costs is also considered which typically occur due to re-balancing of currency positions in the FX portfolio strategies in order to provide the most realistic analysis of international diversification investments.

Based on the analysis as first documented by Kroencke, Schindler and Schrimpf (2011), there are several important findings. First, considerable improvements in the portfolio optimization can be achieved by investing in FX markets. All the three FX strategies for foreign portfolio optimization increase the Sharpe ratio to 0.44 p.m., which is a substantial increase relative to the prime asset classes (Sharpe ratio: 0.33 p.m. U.S. bonds, U.S. stocks plus fully hedged international stock market portfolios). Second, these results also hold after correcting for transaction costs that are implied by re-balancing the FX portfolio strategies. Third, using the rolling windows in the out-of-sample setting, the researcher applies portfolio optimization rules as well as naïve formation rules for prime assets and an augmented asset class with investment strategies. The overall results in this paper suggest that there are significant improvements when U.S. investor focus on international portfolio diversification based on FX strategies at the foreign exchange markets, both in the statistical and most importantly in the economic sense as documented earlier by Kroencke, Schindler, and Schrimpf (2011).

The rest of the paper is laid out as follows: chapter 2 introduces the basic framework for discussing the various portfolio optimization theories and other foreign exchange concepts. Chapter 3 summarizes the most essential findings from the vast body of the academic literature concerning the returns in the foreign exchange markets and related theories and models on portfolio maximization. Chapter 4 describes the portfolio methodology and data employed and also provide some important definition of terms for future reference. Chapter 5 discusses how FX index is constructed basing on various FX investment theories. Chapter 6 looks at portfolio optimization analysis and defines the prime asset classes used as a benchmark for analysis and interpretation. Chapter 7 summarizes the findings of prime asset classes and augmented FX investment strategies. Chapter 8 gives the conclusions basing on the findings. Chapter 9 gives details of the entire references used to compile this report and finally, Chapter 10 shows the Appendix that describes other tables, graphs and additional information being useful in the study.

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