earticle

영어

Structured derivatives markets, including equity linked securities (ELS), derivatives linked securities, structured notes and credit linked notes have grown dramatically since the mid-2000s in Korea, but little attention has been paid to how much these securities contribute to the improvement of investors’ performance from a portfolio perspective. This study fills the gap by examining the optimal portfolio choice of investors who are allowed to invest not only in stocks and bonds, but also in ELS (especially auto-callable ELS). As ELS are generally regarded as alternative assets to enhance portfolio performance, their economic benefits should be considered from a portfolio perspective rather than on a stand-alone basis. In addition, even though the majority of ELS in Korea include an auto-callable feature, there is little study for this specific type of product. This study is the first step in understanding the investment benefits of ELS. In our analysis, we first estimate the return distributions of the KOSPI200 index, a risk-free asset, and a typical auto-callable security linked to the KOSPI200 index. Taking the complexity of the payoff structure into consideration, it is very difficult to theoretically determine the return distributions of the auto-callable ELS. Unlike stocks and bonds, even from an empirical point of view, any standard statistical method to derive the empirical distributions from the observed historical returns cannot be applied to the auto-callable ELS as we do not have a large enough sample (i.e., independent or non-overlapping return data) to obtain a reliable estimate. For example, even if we assume that all of the auto-callable ELS issued during the past 10 years were exercised early on the first possible exercise date, the maximum number of independent returns we can observe is only about 20, and thus we cannot estimate the return distributions in a valid manner. To reconcile this problem, we estimate the GJR-GARCH (1,1) model from the observed returns of the KOSPI200 index from 2003 through 2015, and then derive the empirical return distributions of the ELS via Monte Carlo simulations using the estimated GARCH model. Second, we use three portfolio selection models to derive investors’ optimal portfolio choice given access to the ELS market: (1) the conventional expected utility theory, (2) the prospect theory of Kahneman and Tversky (1979), and (3) the safety first theory of Telser (1956), which is the cornerstone of the behavioral portfolio theory with mental accounts proposed by Das, Markowitz, Scheid, and Statman (2010). Our main empirical findings are as follows. First, auto-callable ELS are shown to be unnecessary for the construction of the optimal portfolio for all investors trying to maximize their expected utility, regardless of their degree of risk aversion. Second, the auto-callable ELS do not improve performance for the majority of loss-averse investors. That is, the auto-callable ELS are regarded as a redundant asset according to both expected utility theory and prospect theory. Third, we find that auto-callable ELS are valuable assets that play a key role in improving the portfolio performance of the majority of investors who make investment decisions based on the safety first theory. This suggests that auto-callable ELS can be a very effective investment tool for investors who try to maximize the expected returns of a portfolio with a restricted probability of failing to reach a pre-specified threshold return. The difference in our empirical results depending on the portfolio selection models arises fundamentally from the structural characteristics of the auto-callable ELS. Their risk and return profile indicates that losses occur infrequently, but when they do, the expected losses can be considerably large. Similarly, although gains occur frequently, they tend to be very marginal. These characteristics of auto-callable ELS are very similar to those of selling deep out-of-the-money (OTM) put options. In this sense, for investors assumed by safety first theory, who measure risk by the frequency rather than the amount of expected losses, auto-callable ELS can be effective in enhancing the investment opportunity set. However, for investors with expected utility theory or prospect theory preferences, the relative advantages of auto-callable ELS over common stocks and bonds are weakened as the portfolio risk is generally recognized and measured by the expected losses rather than the frequency of losses. Finally, our robustness test results indicate that the findings remain valid when we consider other types of auto-callable ELS, issuing costs, and the effect of the global financial crisis.

한국어

본 연구는 자동조기상환형 주가연계증권(Auto-Callable ELS; 이하 AC_ELS)의 투자 효용을 포트폴리오 관점에서 실증분석하였다. 즉, 무위험채권, 주식 및 AC_ELS에 대한 투자가 허용될 때, 기대효용이론(expected utility theory)/전망이론(prospect theory) /안전우선이론(safety first theory)에 따른 각 투자자들의 최적 포트폴리오를 분석 하였다. AC_ELS의 수익률 분포는 우선 주가 자료로부터 GJR-GARCH(1, 1) 모형을 추정한 후, 이를 토대로 몬테카를로 시뮬레이션(MCS)을 적용하여 도출하였다. 본 연구의 주요 실증결과는 다음과 같다. 첫째, 기대효용을 극대화하려는 투자자나 손실회피적 투자자를 가정하였을 때, AC_ELS는 최적 포트폴리오에 포함되지 않는 잉여자산 (redundant asset)에 불과한 경우가 대부분이다. 둘째, 안전우선이론을 적용하여 도출된 최적 포트폴리오에는 AC_ELS가 대부분 포함되며, 이 때 AC_ELS는 주로 채권의 대체재 로써 기능한다. 셋째, 발행구조를 달리 하거나, 발행 수수료 및 금융위기의 영향 등을 고려하더라도 전술한 실증결과에 본질적인 차이는 없다. 결론적으로 본 연구를 통해 포트폴리오 관점에서 AC_ELS의 경제적 효용은 특정 유형의 투자자에게만 발생함이 확인된다.