CAIA Level I by Mark J. P. Anson

Author:Mark J. P. Anson
Language: eng
Format: epub
ISBN: 9781118282991
Publisher: Wiley
Published: 2012-03-21T16:00:00+00:00

Assume that the current price of the stock is $1,000 and the price of the convertible bond is $1,100. If the stock rises or falls $20, the convertible bond moves in the same direction but with half the magnitude (i.e., $10).2 The delta of the convertible bond is therefore 0.50, and the hedged position would be a long position of one convertible bond and a short position of 0.5 shares of stock. The hedged position is said to be delta-neutral. A delta-neutral position is where the value-weighted sum of all deltas of all positions equals zero. In this example, the sensitivity of the 0.5 short-sold shares to the equity price equals the sensitivity of one convertible bond to the equity price, offsetting each other and leaving the combined positions insensitive to small changes (i.e., a change of $20) in the stock price.

The last line of Exhibit 15.2 illustrates that the hedged position breaks even for very small changes in the stock price; the combined positions retain a constant value of $600. But the combined positions are profitable for either a $40 up or a $40 down movement in the underlying asset. This illustrates that even though the positions are delta-neutral, the hedge benefits from large movements in either direction. The profit is generated by the positive gamma of the convertible bond, wherein losses slow down when the stock declines, and profits accelerate when the stock rises. If a large price change in the underlying asset takes place, the hedged position makes a profit, and the positions are adjusted to be returned to being delta-neutral based on a new hedge ratio at the new price levels. If the underlying stock price does not move, the convertible bond will slowly decline to its par value at maturity, and the hedged position will fall to $500, illustrating the negative theta.

In a convertible arbitrage strategy, when the underlying stock price has changed and the positions (i.e., the hedge ratio) have been adjusted to bring the exposure back to being delta-neutral, it does not matter whether the stock price moves back to its original value or continues moving in the same direction. The reason it does not matter is that once the stock price has changed and the arbitrageur has reset the hedge to reflect the new hedge ratio by expanding or contracting the short position in the stock, the positions are returned to being delta-neutral. Once the positions are returned to delta neutrality, the positions return to the profit and loss exposures illustrated in Exhibit 15.2, and the arbitrageur returns to being able to profit whether the next move in the stock is up or down.

Note, however, that for the arbitrageur to make more money on gamma than is being lost on theta, which is known as time decay, the stock must keep experiencing substantial price changes. These price changes dictate the relationship between realized volatility and implied volatility. Realized volatility is the actual observed volatility (i.e., standard deviation of returns) experienced by an asset, in this case, the underlying stock.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.