Marta Szymanowska†, Jenke ter Horst‡, and Chris Veld‡‡

December, 2003

PLEASE DO NOT CITE OR QUOTE WITHOUT THE PERMISSION OF

THE AUTHORS

JEL classification: G10 and G19

Keywords: alternative investments, reverse convertible bonds, option

pricing, behavioral finance, framing

Abstract

The question regarding the deviation of the values of assets from their

fundamental levels has gained a lot of interest in the financial literature.

The recent increase in the global demand for derivatives has shifted the

attention from common stocks to derivatives. We focus on one type of

derivatives, namely reverse convertible bonds. These are bonds that give

right to a high coupon rate and at maturity the issuer has an option to either

redeem the bond at par in cash, or to deliver a pre-specified number of

Introduction

The question concerning the deviation from rational values of assets has

gained a lot of interest in the financial literature. Episodes of significant

overvaluation in the Treasury bond market were documented in e.g Cornell

and Shapiro (1989); Jordan and Jordan (1996). They found significant

overpricing over a certain period and potential arbitrage opportunities that

could not be attributed to changes in fundamentals.

Recently, the global equity derivatives market has become popular and is

growing rapidly. According to the Bank of International Settlements its

volume of trade has expanded by 52% in the period from June 1998 till June

2001. Among the derivatives, the convertible instruments have reached

their global issuance peak in 2001. This was driven by strong demand from

private customers as well as from hedge funds and corporations (Green,

2002). As a consequence of such a shift in the interests of investors, the

market was flooded with a large number of novelty derivative products.

With time plain vanilla products became less popular as investors were

demanding more sophisticated capital protections, and the derivative

products started to include barrier clauses reducing downside risk.

In this context reverse convertible bonds became very popular, especially in

countries such as Japan, UK, France, Italy, Germany and the Netherlands.

A reverse convertible bond (RC) is a bond that can be exchanged into shares

of common stock at the option of the issuer. In fact, it is a bond in

combination with a written put option. In order to compensate investors for

the possible loss due to written put option, the bonds carry very high coupon

rates. These rates vary according to the conversion conditions and to the

nature of the underlying shares; however, coupon rates as high as 20% have

been observed in this market. The market for the reverse convertibles

started originally with plain vanilla bonds. Lately, these bonds often include

a knock-in or knock-out clause. By appropriately specifying the barrier

level such clauses may reduce the downside risk of the investor’s.

The risk profile of plain vanilla reverse convertibles is similar to risk of

redemption in cash in a bearish market. Moreover, during the lifetime of the

bond the investor receives a relatively high coupon. The knock-out reverse

convertible works in the opposite direction. It starts as a plain vanilla

reverse convertible but it turns into a “normal” bond after the pre-specified

barrier has been reached.

Yet, some of the investors seem not to be able to realize the true riskiness of

reverse convertibles. Ignoring the risk component has a significant impact

on the perception of these products. Given that investor observes a high

coupon rate, while they ignore the risk of possible redemption of the bond

below its par value, it becomes less surprising that they have gained a large

popularity. Reverse convertibles offer a high yield, which is desirable by

investors especially in economies with a low interest rate. Moreover, if the

market is bullish — it is less likely that the underlying value will fall below

the exercise price of the option — the investor receives a high coupon for the

bond that most probably will be redeemed at the full value. Such reasoning

may be misleading as in principal, the bond might be redeem below its par

value. The risk of reverse convertibles is present in the option part: it is the

issuer who can decide at the maturity, whether to redeem the bond at or

below par value. Buying a reverse convertible issued on some common

stock is equivalent to buying a coupon-paying bond of the same issuer and

selling the put option on the same stock.

In line with the above argument the practical literature often suggests that

reverse convertibles are overpriced1. In this paper we study the pricing of

the Dutch reverse convertible bonds. In the Netherlands, the reverse

convertible bonds are very popular, especially with private persons2. This is

remarkable, since in the tax system that prevailed until 2001 they were taxed

very unfriendly3. Moreover, the practical literature also suggests that

reverse convertibles are often bought by “bond investors”, while their risk

profile is closely related to stocks4.

In order to investigate the pricing of reverse convertibles, we compare the

market price with the theoretical price induced by the bond and long term

put option. Furthermore, we investigate a broad set of possible explanations

Furthermore, we also investigate other explanations that go beyond

rationality. Behavioral finance literature shows that investors may not be

“fully” rational in their decisions. They might rather be “under influence”

and this bias may create market inefficiency in the shape of mispricing

(Hirshleifer, 2001). According to Shefrin and Statman (1993) different

evaluation of reverse convertibles could be attributed to the design of this

product. As a reverse convertible is pronounced to be a bond, it is likely

that investors underestimate the risk attached to this investment.

Until now, two papers studied such new financial products. Roberts et al.

(2002) studied stock-index linked debt in France. They found that the

issuance of stock-index linked debt had significantly positive announcement

effects on the issue date. They contributed their results to the market

completion story: index-linked bonds complete the market; for instance,

insurance companies gain access to equity markets by using index-link

bonds. They also found that the stock-index linked bonds are overvalued.

Ter Horst and Veld (2002) studied call-warrants in the Netherlands. They

found that call-warrants are overpriced compared to call options that are

issued on the same underlying stock. Their results cannot be explained by

market completeness argument, since there are call options available on the

same underlying stocks. They also found that there are no other rational

factors, such as transaction costs, that could explain their results. Based on

Hirshleifer (2001), they contributed the overpricing of the call warrants to

behavioral factors.

In this paper, we document a significant overpricing of Dutch reverse

convertibles issued from January 1, 1999 to December 31, 2002. On

average they are overpriced by more than 23% with a median of around

19%. Plain vanilla reverse convertible bonds are overpriced more than

knock-in with averages of 29% and 19%, and medians of 22% and 15%

respectively. To calculate the overpricing we used 2 different model

specifications and we found that the difference between these models is

negligible. Moreover, the documented overvaluation is robust with respect

to the estimation errors of the parameters and is persistent for approximately