Convertible Bond Hedging Jane Buchan

1. Economics 437 Behavioral Economics March 24, 2011 Convertible Bond Hedging Jane Buchan

2. What is Convertible Hedging? Which one should I buy????

3. Okay, but this is an economics course…….. • Traditionally, Convertible bond hedging is the purchase of a convertible bond while simultaneously hedging the bond’s exposure to the stock market leaving exposure to the remaining risk factors.

4. Why do we care? • If you can understand convertibles, it is easier to understand other complex securities (it is the same approach) • Convertible Bond Hedging is an interesting strategy (and many other strategies are similar) • There are interesting “clientele” effects in this market (and this is a behavioral economics class) • Professor Burton is in charge and gives us our grades!

5. So, what is a “plain vanilla” convertible bond? • It is a corporate debt security issued by a company • BUT it gives the buyer of the bond, the right, typically at the buyers choice, to exchange the bond for the company’s stock • So in some respects it is like a bond – but you can CONVERT it into a pre-specified amount of stock

6. Corporate Bond Basics Review • When interest rates go up, bonds go down • So there is INTEREST RATE RISK • When companies default (go into bankruptcy), you may not get all your money back • So there is CREDIT RISK

7. For Convertible Bonds • In addition, since the convertible bond buyer has the “option” to convert it into stock, there is also EQUITY RISK • So the price of a convertible = f (interest rates, credit, and stock prices)

8. Convertible Bonds/ Credit Risk CB price Bond floor Value of the firm

9. Convertible Bonds/ Value of the Firm Perspective Parity CB price Bond floor Conversion ratio Value of the firm

10. Convertible Bonds/ Stock Price Perspective CB price Parity premium CB price Bond floor Conversion ratio stock price

11. Convertible Bonds Out of the money At the money In the money Junk Discount Equity-like CB price Parity Bond-like premium CB price Bond floor Conversion ratio stock price

12. Example Airtran AAI 5.5’s of 04/15/15 Current Price 205.1250 Par $100 Adj. Conversion ratio 26.04167 shares Stock $7.32 per share Conversion Value (26.04167 * $7.32) $190.625

13. Convertible Bonds have an embedded option --- Why? Out of the money At the money In the money Junk Discount CB price Parity CB price Bond floor stock price

14. Let’s go back to the Airtran Example Note: the model price of the bond at $7.64 has been adjusted to make the point clear. Stock $ 7.00 $ 7.32 $ 7.64 5½’s of 15 204.38 205.12 206.48 Conv. Value 182.29190.63198.96 Difference 22.09 14.49 7.52 “Option Value”

15. So, if I wanted to capture the option value – how would I do it? Short sell the stock!!!!! Why??? Because when you short a stock you make money when it goes down and vice versa

16. If I short 3 shares of stock then Stock $ 7.00 $ 7.32 $ 7.64 5½’s of 15 204.38 205.12 206.48 Stock Value 21.00 21.96 22.92 Bond Profit $ -0.74 $ 1.28 Stock Profit $ 0.96$-0.96 NET 0.22 0.32

17. If I do this…I am practicing Convertible Bond Hedging CONGRATULATIONS You are now an arbitrageur!!!!!!!

18. Wait!!! Stop!!!!! You need to ask the most important question What risks am I running? the price of a convertible = f (interest rates, credit, and stock prices)

19. The Corporate Bond Risks • Interest Rates • As rates go up bond prices go down • When am I exposed to this??? • Corporate Credit Spreads • As spreads widen bonds go down • When am I exposed to this???

20. So if I hedge all my risks, I can the difference between the lines Out of the money At the money In the money Junk Discount CB price Parity CB price Bond floor stock price

21. Embedded “Option Value” If the market was perfectly efficient, then this option value would be perfectly priced and then doing all this hedging activity might be FUN But, you would not earn any excess profits!

22. New Subject Why does this “arbitrage” exist???? I am in a behavioral economics class??? ??? Could they be linked

23. Trading Basics Dealer 2 Dealer 3 Dealer 1 Buyer Exchange Traded Over-the-counter Traded Dealers tend to keep inventories of securities in order to facilitate trading

24. Why have inventories??? Stock Mutual Fund Dealer Bond Mutual Fund Hedge Fund Insurance Company Index Fund From a dealer’s perspective

25. Pulling this all together…. These are called “clientele” effects The different market participants are trading convertibles in different ways and when the convertibles have different characteristics So, unlike traditional economics, there is not a ready buyer/seller for every financial asset…….which makes the prices non-efficent

26. Convertible Bond Hedging Summary • Long convertible bond • Short equity(Delta-adjusted) • Buy credit protection • Sell treasuries Hedges equity price risk Hedges credit risk of bond Hedges interest rate risk Goal: Find “cheap options” or mispriced volatility Makes money when realized volatility is greater than the implied volatility at purchase

27. Busted convertibles Bond-like converts; more of a credit play as the option has little value Index arbitrage Index volatility mismatched with the underlying components of the index Event/ Merger arbitrage Capitalize on specific events which result from merger/ spin-off activity Other Hedging Trades