ارزیابی ایمن سازی مشروط

This paper tests the effectiveness of contingent immunization, a stop loss strategy that allows portfolio managers to take advantage of their ability to forecast interest rate movements as long as their forecasts are successful, but switches to a pure immunization strategy should the stop loss limit be encountered. This study uses actual daily transactions in the Spanish Treasury market covering the period 1993–2003 and uses performance measures that accounts for skewness and kurtosis as well as mean variance. The main result of this paper is that contingent immunization provides excellent performance despite its simplicity.

The aim of this research is to test the effectiveness of contingent immunization techniques. The pioneer works in this field, Leibowitz and Weinberger, 1981, Leibowitz and Weinberger, 1982 and Leibowitz and Weinberger, 1983, developed contingent immunization as a midpoint in a risk-return framework between pure immunization and active bond management strategies. Contingent immunization is a stop loss strategy that allows portfolio managers to take advantage of their ability to forecast interest rate movements as long as their forecasts are successful, but switches to a pure immunization strategy should the stop loss limit be encountered. Specifically, contingent immunization consists of forming a bond portfolio with a duration larger or smaller than the investor’s planning period depending on interest rate expectations. If the investor thinks that interest rates are going to rise more than the market expects she would buy a bond portfolio with a duration smaller that her planning period and vice versa. However, if interest rates move opposite to the investor’s expectations and the portfolio value falls to a given stop loss limit then she would immunize and guarantee this lower limit for the eventual portfolio return. This strategy gives contingent immunization an option like feature:1 limiting losses but preserving upside potential if interest rates movements are favourable. Therefore contingent immunization strategies represent an attempt to capture positive (or avoid negative) skewness. While prior work is supportive of immunization, the accuracy of the results is affected by the assumption that portfolio weights are adjusted periodically rather than when a payment is made from the underlying portfolio. For instance, Fooladi and Roberts, 1992 and Ventura and Pereira, 2006 assume semi-annual rebalancing while Soto, 2001 and Soto, 2004 assumes quarterly adjustments. Late rebalancing can lead to poor results because immunization can be applied late after the stop loss limited is violated. Late rebalancing therefore can have an important impact on the assessment of contingent immunization as a viable strategy especially if interest rates fluctuate sharply as in the case of the Spanish market during the period 1993–1998. This paper makes a number of contributions. First this paper makes a high computational effort in measuring the holding period returns of all strategies as realistic and exact as possible by rebalancing the portfolio each time payments are due instead of periodically and checking the portfolio value every day to determine whether the stop loss rule should be implemented. Consequently this paper makes the most accurate assessment of contingent immunization to appear in the literature so far. Second, we borrow from the recent hedge fund literature to include the mean, variance, skewness and kurtosis in our assessment of performance. This is especially important for contingent immunization because, as mentioned earlier, the stop loss limit inherent in contingent immunization can be seen as a deliberate attempt by investors to capture moments of the distribution other than mean and variance. Moreover we examine the performance of not only a variety of contingent immunization strategies, but also classical immunization, active bond and passive equity strategies. Third, we employ an extensive data set of actual daily transactions in the Spanish Treasury market covering a 10-year period from January 4, 1993 to January 3, 2003. We find that contingent immunization strategies implemented via Fisher and Weil (1971) duration provide excellent results, as these strategies are able to capture upside potential while the stop loss limit is by and large effective in preventing large losses. Using a second order duration measure to implement contingent immunization strategies improves the effectiveness of the stop loss limit. We find that by adjusting performance measures for skewness and kurtosis the relative ranking of contingent immunization strategies do improve suggesting that contingent immunization strategies do improve the distributional properties of holding period returns. Moreover these attractive results are achieved without the need for interest rate derivatives that are often illiquid and require complex valuation methods.2 This paper is structured as follows. First, we describe the data. Then we determine the structure of the portfolios and propose a model to implement alternative contingent immunization as well as active and pure immunization strategies. In implementing contingent immunization we mainly use traditional Fisher–Weil duration measures but we also consider two factor duration measures that adjust for changes in the level and slope of the yield curve. Third we introduce traditional and innovative portfolio performance measures, specifically the Shape ratio and adjusted Sharpe ratio that account for mean variance, and the modified Sharpe ratio that accounts for four moments of the distribution of holding period returns. Then we present and comment on the results and finally summarize the main conclusions.

This paper is the first to make a great computational effort to mimic the behaviour of actual contingent immunization strategies by rebalancing portfolios every time a cash payment is made from the underlying portfolio and testing every day whether the stop loss limit is violated. Therefore this paper makes the most accurate comparison amongst contingent immunization, active management and pure immunization strategies to appear in the literature to date. The main conclusion is that contingent immunization does indeed provide a mid point between pure immunization strategies and active bond portfolio management. As claimed by the earlier studies, contingent immunization allows investors to carry on active management but the stop loss limit is effective in limiting losses derived from failures in predicting future interest rates. Just as important however is that contingent immunization adjusts the distribution of holding period returns. Clearly the distributional characteristics of bond holding period returns are important as not only can performance be seen as better but the relative ranking of what is the “best” strategy can change once the impact of skewness and kurtosis is recognized. We conclude that one should recognize the impact of skewness and excessive kurtosis when measuring the performance of contingent immunization strategies. One drawback of these strategies is inherited from the effectiveness of immunization itself to guarantee a target return due to non-parallel shifts in the yield curve. Additionally contingent immunization strategies do experience violations of the stop loss limit although these violations are limited in both frequency and size. This limitation of the immunization strategies can be partially resolved by using strategies based on duration vectors. Indeed, this alternative is also tested in this paper providing better results in the case of the pure immunizations strategies. Moreover the effectiveness of the stop loss limit in preventing large losses if the active part of the contingent immunization strategy goes wrong improves by using a two factor rather than a single factor duration model to implement the contingent immunization strategy. It is important to note that these strategies are very simple to implement and monitor. They provide a very flexible method to adjust the degree of risk assumed by the investor while simultaneously giving the investor much of the upside potential available from the more risky active management strategy. Moreover contingent immunization achieves an attractive distribution of returns without the need for complex valuation models and hedging strategies requiring the use of often illiquid interest rate derivatives.