# Convertible Arbitrage. Thought of the Day 108.0

A convertible bond can be thought of as a fixed income security that has an embedded equity call option. The convertible investor has the right, but not the obligation, to convert (exchange) the bond into a predetermined number of common shares. The investor will presumably convert sometime at or before the maturity of the bond if the value of the common shares exceeds the cash redemption value of the bond. The convertible therefore has both debt and equity characteristics and, as a result, provides an asymmetrical risk and return profile. Until the investor converts the bond into common shares of the issuer, the issuer is obligated to pay a fixed coupon to the investor and repay the bond at maturity if conversion never occurs. A convertible’s price is sensitive to, among other things, changes in market interest rates, credit risk of the issuer, and the issuer’s common share price and share price volatility.

Analysis of convertible bond prices factors in three different sources of value: investment value, conversion value, and option value. The investment value is the theoretical value at which the bond would trade if it were not convertible. This represents the security’s floor value, or minimum price at which it should trade as a nonconvertible bond. The conversion value represents the value of the common stock into which the bond can be converted. If, for example, these shares are trading at \$30 and the bond can convert into 100 shares, the conversion value is \$3,000. The investment value and conversion value can be considered, at maturity, the low and high price boundaries for the convertible bond. The option value represents the theoretical value of having the right, but not the obligation, to convert the bond into common shares. Until maturity, a convertible trades at a price between the investment value and the option value.

A Black-Scholes option pricing model, in combination with a bond valuation model, can be used to price a convertible security. However, a binomial option model, with some adjustments, is the best method for determining the value of a convertible security. Convertible arbitrage is a market-neutral investment strategy that involves the simultaneous purchase of convertible securities and the short sale of common shares (selling borrowed stock) that underlie the convertible. An investor attempts to exploit inefficiencies in the pricing of the convertible in relation to the security’s embedded call option on the convertible issuer’s common stock. In addition, there are cash flows associated with the arbitrage position that combine with the security’s inefficient pricing to create favorable returns to an investor who is able to properly manage a hedge position through a dynamic hedging process. The hedge involves selling short a percentage of the shares that the convertible can convert into based on the change in the convertible’s price with respect to the change in the underlying common stock price (delta) and the change in delta with respect to the change in the underlying common stock (gamma). The short position must be adjusted frequently in an attempt to neutralize the impact of changing common share prices during the life of the convertible security. This process of managing the short position in the issuer’s stock is called “delta hedging.”

If hedging is done properly, whenever the convertible issuer’s common share price decreases, the gain from the short stock position should exceed the loss from the convertible holding. Equally, whenever the issuer’s common share price increases, the gain from the convertible holding should exceed the loss from the short stock position. In addition to the returns produced by delta hedging, the investor will receive returns from the convertible’s coupon payment and interest income associated with the short stock sale. However, this cash flow is reduced by paying a cash amount to stock lenders equal to the dividend the lenders would have received if the stock were not loaned to the convertible investor, and further reduced by stock borrow costs paid to a prime broker. In addition, if the investor leverages the investment by borrowing cash from a prime broker, there will be interest expense on the loan. Finally, if an investor chooses to hedge credit risk of the issuer, or interest rate risk, there will be additional costs associated with credit default swaps and a short Treasury position. This strategy attempts to create returns that exceed the returns that would be available from purchasing a nonconverting bond with the same maturity issued by the same issuer, without being exposed to common share price risk. Most convertible arbitrageurs attempt to achieve double-digit annual returns from convertible arbitrage.

## 3 thoughts on “Convertible Arbitrage. Thought of the Day 108.0”

1. About 15 years ago a friend I met was trying to learn a method of commodity trading based solely on the behaviour of charts: technical trading method that some guy developed in like the 1920s. I was a patented method, that you could tell what a market would absolutely do based in the various types of motion on the charts, with no concsideration of anything else.

Have you ever heard of this?

• I should say that there is a pattern recognition generally associated with how commodities could be traded based on the how charts flip flop, but am not sure of the method you are hinting at. But, for instance, there are these two types of patterns that generally develop on charts, the reversal pattern and the continuation pattern. Reversal patterns indicate that an important reversal in trend is taking place. Knowing where certain patterns are most likely to occur within the prevailing trend is one of the key factors in being able to recognize a chart pattern. Some of the most common reversal patterns include; the head and shoulders top and bottom, double tops and bottoms, triple tops and bottoms, key reversals, island reversals, rounding bottoms and tops, “V” formations or spike bottoms and tops.

• Those all sound very familiar. I remember looking at some of his lessons. The guy who cam e up with it became very wealthy and sold his method to someone before he died. That family promoted the method through trainings. Various combinations of moves, patterns predicted certain other moves. Yeah. It sound v similar to what you describe. Maybe this guys was the first one to figure out a way that worked.

But I would guess that perhaps it was a simple time back then, the 1920-30. but increased volume of trading based upon those knowable motions and patterns ( or at least the attempts) might have upset the method.

Who knows. With computers now days, the super-quantum fast trading puts and stuff; crazy. Maybe one day things will settle into predictable patterns that will destroy the potential to make money involved with markets.