# How Convertible Bond Arbitrage Works I

I've always been interested in low risk arbitrage in the stock market, but haven't done much research on the topic.  Luck may have it, Preet Banerjee a Bay Street Trader and blogger from WhereDoesAllMyMoneyGo.com, has written a great article for us describing convertible bond artibtrage.

I’m very excited that FrugalTrader has asked me to write a guest article for MDJ – here is what I came up with:

To speak about convertible bond arbitrage first we should look individually at convertible bonds and then separately at arbitrage itself. Once we have a handle on these two distinct concepts we can then put them together and have some fun! …uh, okay maybe fun is the wrong word. Replace that with “learn how people with lots more money than us make money way too easily”.

Convertible Bonds

A convertible bond is just like a regular bond except that it comes with what is known as a “conversion privilege”.  The “privilege” is the ability of the convertible bondholder to exchange his/her bond back to the issuer for common shares of the same company. There is also what is known as a “conversion rate” which is a formula which determines exactly how many shares you will receive for turning in your bond.

Let’s start with a quick example: You buy a \$1000 convertible bond from company ABC which is convertible to 50 shares of company ABC any time you want.  If you decide to exercise your conversion privilege then you surrender your bond back to ABC and they present you with 50 shares of ABC.  From this example you would expect that ABC’s stock is \$20.

Okay, so that is the BASIC mechanism by which a convertible bond works – but unfortunately it only gets much more complicated from there.  I should point out that a convertible bond’s conversion rate can be very simple (like the rate mentioned above) or very complex (involving mathematical formulas that are more complex and even vary with time).  Writing about this would take pages and I’ll assume that if you are really that interested in these types of hybrid-securities then you will do much more than read this PRIMER level post.  The philosophy is basically the same, so for the sake of learning about converts (one nickname) we will forego exploring all variations of each feature.

So now we have to look at how a convertible bond is valued.  To cut to the chase: it can behave like a bond or like a stock option depending on the price of the underlying common stock.  It will behave more like a bond (sensitive to interest changes) when the underlying common stock is priced too low to make exercising your option to convert to common shares a profitable decision.  If, on the other hand, the common stock is increasing in value then there will come a point where the convertible bond’s value will start to fluctuate more in line with the value of the common share.

The Floor Value or Intrinsic Value

The convertible bond will never fall below a certain price – the intrinsic value of the bond. So let’s look at what that value would be of a straight bond so we have an understanding:

Let’ say that ABC decides to issue a 1 year bond that has a 5% coupon rate.  So on the first day of trading it has a par value of \$1,000 and if you held it to maturity (1 year) you will have collected \$50 of interest. Now, let’s say that interest rates increase to 6% the day after that bond has been issued.  Well, if an identical company called XYZ wanted to issue a bond the day after ABC, then they would offer a \$1000 bond with a 6% coupon rate since that is now the “going rate”.  No one would rationally buy ABC’s 5% coupon bond for par (\$1,000) when they could now buy XYZ’s 6% coupon bond for \$1000.  This is why bond’s fall in price when interest rates increase and rise in price when interest rates go down.  If you wanted to match the yield of 6% (the going rate) then you would only pay \$833.33 for ABC’s bond now since the coupon payment of 5% is based on the par value of the bond.  In other words, no matter what happens, ABC has promised to pay \$50 of interest for the year to the holder of the ABC 5% bond.  ABC doesn’t care who you sell the bond to, or for what price.  But the buyers/sellers DO care.  The buyer of this bond would not pay more than \$833.33 for this bond because \$50 in interest on a \$1000 bond is 5%, but \$50 in interest on a \$833.33 bond is a 6% yield.

Remember how I just said that you wouldn’t pay more than \$833.33 for ABC’s bond right now? I lied.  You probably have figured out why you WOULD pay more – not only do you have the coupon payment coming in – but you now have a capital gain.  If you did indeed pay \$833.33 for a bond maturing in 364 days – then at maturity you will have accrued a 20% capital gain in one year and last time I checked the bond market wasn’t made up of idiots – i.e. no one will sell that bond for that price.

It would be somewhat closer to \$990. Let’s do the math:

1. Interest payment is \$50 for the year.
2. Capital gain for the year would be \$10 (Maturity Value of \$1000 less Purchase price of \$990).

Add those together and you have your \$60 for the year – just like what you would get for XYZ’s 6% bond offering.

From this point forward (assuming no other changes to the interest rates) the value of the bond will slowly start to drift towards \$1000 by the maturity date.

The value of a convertible bond will never fall below this intrinsic bond value because if you never exercise your privilege to convert to common shares, then once you reach the maturity date of the bond – you will receive the maturity value of par.

Okay, so now we have established the “floor” value of the convertible bond. Let’s look at the other end of the range, which we’ll name the “conversion” value.

The Conversion Value

This is the value the convertible bond takes if the underlying common stock goes up in value sufficiently so that it would make sense to convert your bond to shares (i.e. when it becomes profitable to do so).

If we go back to our example company ABC – we have a convertible bond issued at \$1000 and convertible to 50 shares of ABC common shares whenever the bondholder desires.  Let’s assume that ABC’s stock is trading at \$20 for the time being. (I should point out that normally when a convertible bond is issued the issuing company will make sure that no one would buy it and then immediately convert it – i.e. the conversion rate might be 40 shares for this particular bond which would mean that the stock price would have to go up to \$25 before converting makes sense – otherwise they’d be better off just issuing new shares!).

If ABC’s stock price rises to \$25 then the convertible bondholder could exercise their conversion privilege and receive 50 shares of ABC’s stock (we’re back to using the 50:1 conversion rate for our example remember).  50 shares at \$25 is worth \$1250. So if the convertible bondholder bought the bond at issue (i.e. paid \$1000 for it) he/she has made a \$250 profit (assuming they then turn around and sell the common shares). If instead they decide that they want to sell the bond, they could command \$1250 for the bond – since we’ve just determined it’s worth. Truth be told, he/she might be able to get a *little* bit more than \$1250 since the bondholder still collects the coupon payments!

If ABC’s stock price drops to \$15, then what happens? Well if we do the conversion math, 50 shares @ \$15 is worth \$750.  So does the value of the convertible bond fall to \$750? NO – Remember: if this happens you could simply never exercise your right to convert to common shares, collect your coupon payments and your original principal at maturity.  Like I said above – the convertible bond will never be priced below it’s intrinsic value (think of this as the value the bond would have if it was a straight bond).

So from all of this information, you have by now figured out that buying a convertible bond offers you the ability to participate in the price appreciation of a common stock of a company with the added sweetener that you have a high degree of principal protection built in as well.  If the underlying common stock performs well – you can either sell the bond or convert to the common.  If the underlying stock performs poorly – you’ve at least made a small positive return.

Tomorrow we'll get into arbitrage and some case studies on convertible bond arbitrage.  Stay tuned!

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FT is the founder and editor of Million Dollar Journey (est. 2006). Through various financial strategies outlined on this site, he grew his net worth from \$200,000 in 2006 to \$1,000,000 by 2014. You can read more about him here.
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fc
7 years ago

A year from now the price of the 5% bond would be 1050. If interest rates rise to 6% right before you bond matures, then the value of the bond is 1050/1.06= 990.5.

How you get the bond price for a 1 year bond

ct
8 years ago

The theoretical prices of the bond may never fall below the floor but that doesn’t mean the bond holder is then safe from the default risk of the underlying company.

Professor Don Abrams
11 years ago

What a great primer for greater things ahead!

Convertible bonds, if properly strategized, can produce amazing results.

Yet, as you have aptly explained, they are also normally more secure than common stock.

So why not combine the convertible with a short sale ?

Isn’t this dangerous?
Dangerous – no. Smart thinking – yes.

Allow me to explain.

Through the joint operation of the convertible bond and the short sale, your best offense, and, defense, is a battle plan against financial loss.

A case in point is the convertible bond Ford Motor Company, 4.25% of 2036.

By combining this bond with the speculative short sale of the common stock, paradoxically, you reduce your risk.

A case in point are the returns posted on Professor Smarba’s SCOREBOARD.

This is the fruition of utilizing a ladder approach to the convertible bond.

If interested, the totally transparent results dislosed on the website, http://www.profittaker.info.

The first plan was completed with an amazing 382% annualized profit.

The second Ford plan is now operating with a 62% annualized profit.

By teaming up these two investment techniques, you’ll practically eliminate the risk of buying the convertibles alone, at the same time avoiding the usual dangers of short selling.

Working together – It works

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