Delta Hedging.

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The principal investors in most convertible securities are hedge funds that engage in convertible arbitrage strategies. These investors typically purchase the convertible and simultaneously sell short a certain number of the issuer’s common shares that underlie the convertible. The number of shares they sell short as a percent of the shares underlying the convertible is approximately equal to the risk-neutral probability at that point in time (as determined by a convertible pricing model that uses binomial option pricing as its foundation) that the investor will eventually convert the security into common shares. This probability is then applied to the number of common shares the convertible security could convert into to determine the number of shares the hedge fund investor should sell short (the “hedge ratio”).

As an example, assume a company’s share price is $10 at the time of its convertible issuance. A hedge fund purchases a portion of the convertible, which gives the right to convert into 100 common shares of the issuer. If the hedge ratio is 65%, the hedge fund may sell short 65 shares of the issuer’s stock on the same date as the convertible purchase. During the life span of the convertible, the hedge fund investor may sell more shares short or buy shares, based on the changing hedge ratio. To illustrate, if one month after purchasing the convertible (and establishing a 65-share short position) the issuer’s share price decreases to $9, the hedge ratio may drop from 65 to 60%. To align the hedge ratio with the shares sold short as a percent of shares the investor has the right to convert the security into, the hedge fund investor will need to buy five shares in the open market from other shareholders and deliver those shares to the parties who had lent the shares originally. “Covering” five shares of their short position leaves the hedge fund with a new short position of 60 shares. If the issuer’s share price two months after issuance increases to $11, the hedge ratio may increase to 70%. In this case, the hedge fund investor may want to be short 70 shares. The investor achieves this position by borrowing 10 more shares and selling them short, which increases the short position from 60 to 70 shares. This process of buying low and selling high continues until the convertible either converts or matures.

The end result is that the hedge fund investor is generating trading profits throughout the life of the convertible by buying stock to reduce the short position when the issuer’s share price drops, and borrowing and selling shares short when the issuer’s share price increases. This dynamic trading process is called “delta hedging,” which is a well-known and consistently practiced strategy by hedge funds. Since hedge funds typically purchase between 60% and 80% of most convertible securities in the public markets, a significant amount of trading in the issuer’s stock takes place throughout the life of a convertible security. The purpose of all this trading in the convertible issuer’s common stock is to hedge share price risk embedded in the convertible and create trading profits that offset the opportunity cost of purchasing a convertible that has a coupon that is substantially lower than a straight bond from the same issuer with the same maturity.

In order for hedge funds to invest in convertible securities, there needs to be a substantial amount of the issuer’s common shares available for hedge funds to borrow, and adequate liquidity in the issuer’s stock for hedge funds to buy and sell shares in relation to their delta hedging activity. If there are insufficient shares available to be borrowed or inadequate trading volume in the issuer’s stock, a prospective issuer is generally discouraged from issuing a convertible security in the public markets, or is required to issue a smaller convertible, because hedge funds may not be able to participate. Alternatively, an issuer could attempt to privately place a convertible with a single non-hedge fund investor. However, it may be impossible to find such an investor, and even if found, the required pricing for the convertible is likely to be disadvantageous for the issuer.

When a new convertible security is priced in the public capital markets, it is generally the case that the terms of the security imply a theoretical value of between 102% and 105% of face value, based on a convertible pricing model. The convertible is usually sold at a price of 100% to investors, and is therefore underpriced compared to its theoretical value. This practice provides an incentive for hedge funds to purchase the security, knowing that, by delta hedging their investment, they should be able to extract trading profits at least equal to the difference between the theoretical value and “par” (100%). For a public market convertible with atypical characteristics (e.g., an oversized issuance relative to market capitalization, an issuer with limited stock trading volume, or an issuer with limited stock borrow availability), hedge fund investors normally require an even higher theoretical value (relative to par) as an inducement to invest.

Convertible pricing models incorporate binomial trees to determine the theoretical value of convertible securities. These models consider the following factors that influence the theoretical value: current common stock price; anticipated volatility of the common stock return during the life of the convertible security; risk-free interest rate; the company’s stock borrow cost and common stock dividend yield; the company’s credit risk; maturity of the convertible security; and the convertible security’s coupon or dividend rate and payment frequency, conversion premium, and length of call protection.

Option Spread. Drunken Risibility.

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The term spread refers to the difference in premiums between the purchase and sale of options. An option spread is the simultaneous purchase of one or more options contracts and sale of the equivalent number of options contracts, in a different series of the class of options. A spread could involve the same underlying:

  •  Buying and selling calls, or
  •  Buying and selling puts.

Combining puts and calls into groups of two or more makes it feasible to design derivatives with interesting payoff profiles. The profit and loss outcomes depend on the options used (puts or calls); positions taken (long or short); whether their strike prices are identical or different; and the similarity or difference of their exercise dates. Among directional positions are bullish vertical call spreads, bullish vertical put spreads, bearish vertical spreads, and bearish vertical put spreads.

If the long position has a higher premium than the short position, this is known as a debit spread, and the investor will be required to deposit the difference in premiums. If the long position has a lower premium than the short position, this is a credit spread, and the investor will be allowed to withdraw the difference in premiums. The spread will be even if the premiums on each side results are the same.

A potential loss in an option spread is determined by two factors:

  • Strike price
  • Expiration date

If the strike price of the long call is greater than the strike price of the short call, or if the strike price of the long put is less than the strike price of the short put, a margin is required because adverse market moves can cause the short option to suffer a loss before the long option can show a profit.

A margin is also required if the long option expires before the short option. The reason is that once the long option expires, the trader holds an unhedged short position. A good way of looking at margin requirements is that they foretell potential loss. Here are, in a nutshell, the main option spreadings.

A calendar, horizontal, or time spread is the simultaneous purchase and sale of options of the same class with the same exercise prices but with different expiration dates. A vertical, or price or money, spread is the simultaneous purchase and sale of options of the same class with the same expiration date but with different exercise prices. A bull, or call, spread is a type of vertical spread that involves the purchase of the call option with the lower exercise price while selling the call option with the higher exercise price. The result is a debit transaction because the lower exercise price will have the higher premium.

  • The maximum risk is the net debit: the long option premium minus the short option premium.
  • The maximum profit potential is the difference in the strike prices minus the net debit.
  • The breakeven is equal to the lower strike price plus the net debit.

A trader will typically buy a vertical bull call spread when he is mildly bullish. Essentially, he gives up unlimited profit potential in return for reducing his risk. In a vertical bull call spread, the trader is expecting the spread premium to widen because the lower strike price call comes into the money first.

Vertical spreads are the more common of the direction strategies, and they may be bullish or bearish to reflect the holder’s view of market’s anticipated direction. Bullish vertical put spreads are a combination of a long put with a low strike, and a short put with a higher strike. Because the short position is struck closer to-the-money, this generates a premium credit.

Bearish vertical call spreads are the inverse of bullish vertical call spreads. They are created by combining a short call with a low strike and a long call with a higher strike. Bearish vertical put spreads are the inverse of bullish vertical put spreads, generated by combining a short put with a low strike and a long put with a higher strike. This is a bearish position taken when a trader or investor expects the market to fall.

The bull or sell put spread is a type of vertical spread involving the purchase of a put option with the lower exercise price and sale of a put option with the higher exercise price. Theoretically, this is the same action that a bull call spreader would take. The difference between a call spread and a put spread is that the net result will be a credit transaction because the higher exercise price will have the higher premium.

  • The maximum risk is the difference in the strike prices minus the net credit.
  • The maximum profit potential equals the net credit.
  • The breakeven equals the higher strike price minus the net credit.

The bear or sell call spread involves selling the call option with the lower exercise price and buying the call option with the higher exercise price. The net result is a credit transaction because the lower exercise price will have the higher premium.

A bear put spread (or buy spread) involves selling some of the put option with the lower exercise price and buying the put option with the higher exercise price. This is the same action that a bear call spreader would take. The difference between a call spread and a put spread, however, is that the net result will be a debit transaction because the higher exercise price will have the higher premium.

  • The maximum risk is equal to the net debit.
  • The maximum profit potential is the difference in the strike
    prices minus the net debit.
  • The breakeven equals the higher strike price minus the net debit.

An investor or trader would buy a vertical bear put spread because he or she is mildly bearish, giving up an unlimited profit potential in return for a reduction in risk. In a vertical bear put spread, the trader is expecting the spread premium to widen because the higher strike price put comes into the money first.

So, investors and traders who are bullish on the market will either buy a bull call spread or sell a bull put spread. But those who are bearish on the market will either buy a bear put spread or sell a bear call spread. When the investor pays more for the long option than she receives in premium for the short option, then the spread is a debit transaction. In contrast, when she receives more than she pays, the spread is a credit transaction. Credit spreads typically require a margin deposit.