ایمنی درجه اول و ارزش فوق العاده بهینه سازی دوجانبه پرتفوی ایالات متحده و مکزیک در سراسر بحران پزو و پیمان نفتا در سال 1994

High volatility can motivate safety-first portfolio optimization in emerging markets. Mexico is a case in point, as the December 1994 Mexico peso crisis followed the high positive expectations from the ratification of NAFTA earlier that year. This study examines safety-first and extreme value optimization for bilateral U.S.–Mexican portfolios in U.S. dollar (USD) and Mexican peso (MXN) around the crisis, and compares these to Markowitz mean–variance optimization. It finds that these approaches result in substantial differences for the optimal investment weights in Mexico, with these generally higher under safety-first pre-1994 and lower post-1994 than under mean–variance optimization, whether in MXN or USD. Safety-first objectives do not inhibit investment weights that are higher than the minimum variance optimization weights for Mexico in the non-crises pre-1994 period. But following the 1994 financial crisis, safety-first optimization requires more of an exit from Mexico than even minimum variance optimization.

Safety-first has greater relevance in the high volatility environment in emerging markets, with the December 1994 peso crisis in Mexico providing a good case study. Positive expectations were high following the ratification of NAFTA on January 1, 1994, making North America the largest trading block in the world. But shortly after, Mexico endured one of its worst economic crises. The peso crisis that followed highlight the attendant risks that accompany investing in emerging markets like Mexico, even in the midst of positive expectations, regardless of whether investors are domestic (Mexican) or foreign (U.S.). Similar crises and risks have appeared elsewhere, including Asia in 1997 and Russia in 1998. In these, risk managers must worry that portfolios may suffer from “extreme” events, even if they lie outside the range of available observations. The safety-first criteria of Roy (1952) operationalized with use of extreme value theory as applied by Arzac and Bawa (1977) and Jansen, Koedijk, and de Vries (2000), and most recently, Haque, Hassan, and Varela (2004), is useful in these cases. Extreme value theory (EVT) provides a firm theoretical foundation for statistical models describing extreme events, and offers risk managers a seemingly objective tool to examine portfolio behavior under extreme circumstances. The analysis is undertaken by trying to “fit” the tail of the returns’ distribution of a portfolio, because the tails of a continuous statistical distribution generalize to a Pareto distribution as one examines further into the distribution's extremes. The use of EVT lies principally in the manner in which it can quantify estimates of the probability of extreme events, and the way portfolios behave under such occurrences. It is applicable to fat tailed and asymmetric distributions, making it advantageous over models that assume symmetry (such as t, normal, ARCH and most GARCH-like distributions), because most financial returns are asymmetric. The present study applies safety-first using EVT to portfolios of Mexican and U.S. equities from both Mexico and U.S. points of view during the period surrounded by the Mexican peso crisis in 1994, and by default NAFTA. It examines how these portfolios differ from Markowitz mean–variance portfolios, and draws lessons in the application of safety-first during such crisis in emerging markets. The study is divided into the following sections. Section 2 presents the literature review and Section 3 the sample and data. Section 4 discusses exceedence values and extreme value theory and Section 5 the safety-first methodology. Section 6 presents the empirical findings and Section 7 concludes the study.

The December 1994 peso crisis in Mexico provides a good safety-first case study, as this crisis quickly followed the high positive expectations from the ratification of NAFTA in January 1994, showcasing high volatility in emerging markets. This study examines bilateral U.S.–Mexican portfolios with returns in U.S. dollar and Mexican peso denominations around this peso crisis under safety-first and extreme value optimization, and compares this to traditional Markowitz mean–variance optimization. The entire study period runs from January 1, 1988, to May 28, 2001, with pre--1994 period and post-1994 period also examined. There are substantial differences between the optimal safety-first and traditional minimum variance portfolios. The weights in Mexico for the entire and pre-1994 periods are higher under safety-first (using extreme value theory), regardless of whether the analysis is based on the USD or MXN. In the post-1994 period, safety-first leads to no investment in Mexico, whereas the traditional minimum variance invests 5% in Mexico based on a USD and 30% based on an MXN perspective. The pre-1994 period is the most attractive for U.S. safety-first risk-averse optimization (from a USD perspective) in Mexico, when the weight in Mexico was 60% and in the U.S. 40%. A dramatic changed occurred post-1994, when this investment weight in Mexico fell to zero, just like for Mexican safety-first risk-averse optimization (from a MXN perspective) in Mexico. The safety-first and highest Sharpe ratio results are also the same post-1994, regardless of whether in USD or MXN. The peso and financial crisis in Mexico post-1994 required substantial shifts in equity investments from Mexico to the U.S. both for U.S. and Mexican safety-first optimization, with these shifts leading to the highest Sharpe ratios. Safety-first objectives do not inhibit investment weights that are higher than the minimum variance optimization weights for Mexico in the non-crises pre-1994 period. But following the 1994 financial crisis, safety-first optimization requires a greater withdrawal from the market than under minimum variance optimization. We end with a caveat and suggestion for future research, with our thanks to the referee for providing motivation. This paper has an ex ante perspective, in stating what should be a portfolio's distribution before and after a crisis using optimization criteria established by Markowitz and safety-first objectives. However, the fact that the resulting portfolios are optimized does not mean that they are necessarily the portfolios constructed by investors, creating a problem in using ex post data to test these models’ predictive powers. Indeed, a home country bias compared to Markowitz's optimization in portfolio construction is well known. This bias also appears for our safety-first optimization results, that suggests that domestic Mexican investors should have been fully invested in Mexico before the crisis (a complete home bias) and fully out of Mexico after the crisis (a complete foreign bias). An interesting extension of the present paper is to examine the impact of a home country bias, and other possible factors such as capital market constraints, in explaining why investors do not follow the optimizing results of both Markowitz and safety-first. After neutralizing these other factors, then comparing these two models’ prediction to ex post data could produce interesting results.