Convertibles - Replication and Use in 'BVG' Portfolios

By Manuel Ammann, Axel Kind, Christian Wilde, Heinz Zimmermann, 18 May 2000

A study commissioned by Fisch Asset Management AG, Zurich, and carried out by the Swiss Institute of Banking and Finance of the University of St. Gallen

Executive Summary

Replication of convertibles

Convertibles are hybrid financial instruments with the characteristics of both bonds and equities. This part of the study examines whether convertibles can be replicated, similarly to the replication of options, through a dynamic trading strategy involving equities and bonds.

Two different valuation models underpin the replication analysis:

• First of all, a building-block model is employed that separates the convertible into an option component and a bond component. The option is replicated by using the standard method from options theory. This approach proves to be problematic from both a theoretical and an empirical perspective. Frequent contract specifications as well as implicit options hinder a meaningful separation into an option component and a bond component. Empirically, this approach also proves to be less than convincing.
• The second approach therefore employs a monolithic model that simultaneously values the bond component and the option component. Hence, at least from a theoretical perspective, a replication is fundamentally possible. In practice, however, there are also numerous difficulties with this approach. The sometimes very complex contract conditions of convertibles, such as implicit options and call rights, also complicate the modeling procedure here. Furthermore, the imperfection and illiquidity of the markets often impede the replication. For example, in the capital market, only in exceptional cases is a non-convertible bond traded with a similar payout structure as the convertible bond. For the replication, it is therefore usually necessary to employ another bond from the same company or often even a bond issued by another borrower or another interest rate instrument, which correspondingly affects the accuracy of the replication with respect to interest rate risks and especially credit risks. Even if suitable non-convertible bonds for replication purposes are available, there is a danger that they cannot be or may only partially be employed for the replication because of insufficient liquidity. All of these replication problems increase the risk of a significant replication error. By means of example, we illustrate the consequences that such inaccuracies can have on the success of a replication strategy. We come to the conclusion that the replication of convertibles is in fact fundamentally possible if specific prerequisites are fulfilled, but that in most cases the replication achieves only a very limited degree of accuracy. Whether or not the residual risk of the replication is acceptable depends among other things on the application.

Convertibles in 'BVG' portfolios

This part of the study looks at the question of whether the inclusion of convertible bonds in pension fund portfolios makes it possible to improve their position in the risk-return diagram. The examination period extends from 1 January 1994 to 1 February 2000. For this period, we can state that the returns and volatilities exhibited by convertibles were lower than those of equities but higher than those of bonds. This corresponds with the hybrid character of convertibles. The investment universe excluding convertibles consisted of indices for global equities, global government bonds, Swiss equities and Swiss bonds. To this group, we added a global convertibles index, a global convertibles index with at-the-money convertibles, and an index for Swiss convertibles.

We examined two different types of pension fund portfolios. The first type of portfolio is subject to investment restrictions under Swiss law ('Art. 54 BVV 2') with respect to the portfolio weighting of individual investment categories. The second type of portfolio is not subject to any such restrictions. We always assume, however, that it is not possible to engage in short positions or in borrowing in order to create a leverage effect.

For the portfolios with restrictions, it turns out that during the examination period, higher risk-return combinations could only be produced through the inclusion of convertibles. Especially for pension funds with the capacity to bear risk, it could therefore be sensible to conceivably replace part of their bond positions with convertibles.

For portfolios without restrictions, the addition of convertibles could slightly improve their position in the risk-return diagram. In this case, the optimized portfolios always contained convertibles. The convertibles thus always made a contribution to the diversification of the portfolio during the examination period. However, this assertion is only valid for the general global convertibles index. Neither the at-the-money index nor the index consisting of Swiss convertibles was part of the efficient portfolio. In the case of the restricted portfolio, however, these indices were also part of the efficient portfolio, but only for specific risk-return combinations.

Even if an ex-post portfolio optimization for a specific period cannot be used to project the optimal portfolio weighting for a later point in time, this examination still suggests that in specific instances the inclusion of convertibles can improve the risk-return structure of a portfolio.