Yesterday, Preet Banerjee from WhereDoesAllMyMoneyGo.com explained the basics behind convertible bonds. Today he will continue to explain how convertible bond arbitrage works along with some case studies.
Okay, so yesterday we explained the CONCEPT of convertible bonds. Let’s quickly define Arbitrage:
Arbitrage is when you are long and short two related securities (or the same security in some cases) in order to make a gain when the price changes. I realize that it sounds counterintuitive – the best way to explain is to show an example. Hmmm… I wish I had a security that lends (no pun intended!) itself well to arbitrage… Hold the phone! I do: The Convertible Bond!!!! Let’s take a look:
Convertible Bond Arbitrage
Like I said the best way for me to explain is to dive right in with an example – and then you can work backwards to make sure it makes sense.
Let’s start out with our convertible bond at issue time. It is being issued at $1000, with a coupon payment of 5% and let’s say that it is a 2 year bond (not common, but for the sake of the example). It has a conversion rate of 50:1 – so you can exercise your conversion privilege anytime and receive 50 shares of the underlying common stock. Right now the share price is $20.
To engage in Convertible Bond Arbitrage you have to buy and sell (at the same time) two related securities – and in this case you are buying the convertible bond for $1000 and at the same time you are shorting 25 shares of the common stock – you’ll note that you are shorting HALF the amount of shares that the bond could be converted to, which is 50. (If you are not familiar with shorting – stop now and look it up – then come right back here.) Now we will look at three cases: 1) No change in the share price for 1 year. 2) Share price goes up after 1 year. And 3) Share price goes down after 1 year. In all three cases you MAKE a gain (all else being equal).
Case 1: Share price does not change for the year
You have received $50 in interest for the year (coupon payments on the bond). You have also received interest on the proceeds of the short sale for one year (when you short a stock you are selling it which means you have cash on hand that you can gain interest on – we’ll say your brokerage account pays 2% on cash balances). Since you “sold” 25 shares at $20 you have $500 earning the 2% interest – which equals $10. There is also the interest you have to pay for borrowing the shares from your broker to sell – let’s say this is 1% – so you have a COST of $5 to borrow the shares you shorted. Your running total so far is $55 in your pocket.
Now, remember nothing has happened to the share price, so your convertible bond is still worth $1000. At day 366, you cover your short and you sell your convertible bond. In other words you have completely unwound the strategy.
So at the end of the day you earned 5.5% for the year (Interest on the bond plus the interest on the short sale proceeds less the cost of borrowing the shorted stock). Not bad for 5% bond, right?
Case 2: Share price rises to $25 after 1 year.
50 Shares at $25 is worth $1250 – so your convertible bond has made you money ($250 gain). You have to subtract your loss on your short position (you lose money if a shorted stock goes up in value). In this case, when you unwind your short you have essentially sold it for $20 at the beginning and bought it back for $25 when you cover your position at the end of the year. Therefore you have a loss of $5 per share ($20 Shorting price less $25 Covering price) which for 25 Shares equals a $125 loss on your short position. We still have the interest on the proceeds of the short position ($10) and the interest charged to borrow the stock from your broker to establish a short position (-$5). This leaves you with $250 (Capital Gain on the convertible bond) + $50 (Interest earned on the bond) – $125 (Loss on the short) + $10 (Interest earned on the proceeds of the short sale) – $5 (Interest charged on the borrowed securities for the short) = $180 at the end of the year.
So in this case you have earned 18.0% for the year because the share price went up.
Case 3: Share price decreases to $15 after 1 year
Okay, so your convertible bond is worth $750 since 50 shares x $15 = $750? WRONG – Remember – the value of the convertible bond won’t fall below it’s intrinsic value – or what it would trade like if were just a bond. So in this case it is still worth $1000. You are break even on the bond. BUT you have made money on your short position. Since the stock has gone down in value you have effectively sold it at $20 and bought it for $15 when you cover your short position for a gain of $5 per share. Multiply that by 25 shares are you have a gain of $125 on your short sale. We still have the same interest on the short sale proceeds for the year of $10 and a cost of interest on the borrowed securities from your broker of $5. Add all that up and we have $0 + $125 + $10 – $5 = $130.
So in this case you have earned 13% for the year because the share price went down.
The End – Now don’t go out there and do it
This concludes my guest article on Convertible Bond Arbitrage – I would suggest not rushing out and immediately implementing this strategy just yet – do a LOT more research – because the conversion rates can be complex formulas for convertible bonds and you need to examine the effects of each of the three scenarios I just went through with the conversion math of the convertible bond issue you are looking at. I made up a fictitious convertible bond example with an accompanying fictitious stock example.
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