# 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!

-> If you would like to read more articles like this, you can sign up for my free newsletter service below (we will not spam you).

About the author: 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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{ 29 comments… add one }
• FrugalTrader September 26, 2007, 9:02 am

What do you guys think of topics like this? Too complex?

• Henry September 26, 2007, 9:08 am

I actually like topics like this. My question is for Preet. How does one go about purchasing “convertible bonds”? Do discount brokerages offer them? How do you know if a bond listing is “convertible”?

• FourPillars September 26, 2007, 10:26 am

Hey, I was going to write about this very topic next week! Just kidding…

I don’t mind complexity – some of my posts involve detailed spreadsheet analysis of topics that I’m sure while most of the readers are interested in the topic, they aren’t interested in knowing all the details of the analysis – hopefully they will at least read the conclusions of what I’ve come up with.

Personally I don’t have much of an interest in different types of bonds for my own investment strategy but I still found this post quite interesting.

From what I understand of the bond market, you need big bucks to play and it’s hard to know things like spreads since it’s not as open as the stock market.

Preet – from the point of view of a small investor, is a convertible bond sort of like a GIC with an equity component? I’m just thinking that if someone wanted to replicate a convertible bond for an index they might do it by buying a GIC or bond ETF and then maybe a call option on that index. That’s not the same as owning a convertible bond for a specific company or government but again, as a small investor that might not be practical? Feel free to tell me if I have this all wrong.

Mike

• FrugalTrader September 26, 2007, 11:13 am

FP, do you use bonds as part of your asset allocation? I personally use bond indexes instead of individual bonds because it’s easier.

• FourPillars September 26, 2007, 11:29 am

FT, I use mainly XSB (short term bond ETF) as well as some GICs. I may look into buying individual bonds when we have more money invested…but then again I might not.

Mike

• WhereDoesAllMyMoneyGo.com September 26, 2007, 1:23 pm

Henry: I just put a few calls in to some bond traders and the retail desk because I honestly don’t know where to look for converts off a discount platform. I have a discount brokerage account that is still active from my pre-career days and I just logged into it to try and find them and I couldn’t find any specific categories.

Personally, I just log into our intranet and click on the inventory and it lists it all – then I lot into our fixed income trading conduit and place the order to the bond desk. :) I guess that’s why I give half my income to the bank… lol

I hope to have an answer for you by Friday – unfortunately today and tomorrow are a bit hectic… Sorry!

• WhereDoesAllMyMoneyGo.com September 26, 2007, 1:52 pm

FourPillars: Excellent question! I remember asking the same sort of question when I was first pitched a principal protected note. Specifically I asked why not just buy a strip bond at 70 cents on the dollar and use 30 cents to buy a call option. If the underlying security to the call goes down then you would just let the call expire and collect your par on the bond at maturity. So you at least get your money back no matter what happens to the equity component, but if the equity component goes up then you exercise your call (or sell) and you get the leverage effect since it is a derivative.

The answer was that it would be hard to find a call option that lasts long enough that you could pay enough of a discount-to-par on the fixed income component to allow you enough money to make your investment in the derivative worthwhile.

I just read that last paragraph to myself and realized it warrants further explanation. :) If you are buying a strip bond, it will be cheaper the longer the remaining term. Since they appreciate at 5% per year (or whatever) their current price is mainly a function of term-to-maturity. On the other end, when you buy the call option – you want to make sure that you are putting enough of your money into it to make it worthwhile if it pays off – so the longer the term-to-maturity of the strip bond, the cheaper, which means more money that is able to be put towards the call option.

It seems that the average length of options is not long enough to be able to implement that kind of strategy on one’s own.

But back to your question: They would behave somewhat similarly to an equity-linked GIC, yes. BUT the second part of your question: buying a GIC or Bond Index ETF and then call options on the index: personally I would rather buy the actual index you are interested in and buy puts on that index if you want to “insure” your portfolio against losses and appreciate in the gains. You would effectively accomplish the same thing and you could be more selective on when you buy puts (i.e. if the market just had a correction, would you really want to buy more puts?). LONG TERM – I think this will reduce your fees paid while still giving you short term piece of mind.

With the other version – you are linking the majority of your gains to a lower risk, lower returning portfolio and constantly rolling over call options with a smaller portion of your portfolio. The opposite strategy (majority of your portfolio in the higher risk, higher long term returning assets and rolling over (selectively) put options) I think will offer you more returns long term, offer the same downside protection, and cost you less.

• FourPillars September 26, 2007, 2:30 pm

Thanks for the response Preet – your suggestion of buying the index plus puts should be a lot more tax efficient than buying a gic + call option.

Mike

• FatboyJim September 26, 2007, 2:43 pm

FT,
I think that these more complex topics (complete with examples to help explain things) are great! I’ve always been interested in exactly what opportunities are available for those with higher available capital (compared to us nickel-and-dime investors), and this is very interesting.
Thanks for the great article, Preet; I’ll be checking out your website during lunch!
Cheers,
FJ

• Telly September 26, 2007, 2:59 pm

FT: Too complex for me, but I’m just a girl. ;)
Ok, seriously, I like to keep things fairly simple when it comes to our investments. If it takes too much effort to understand then I figure it’s not for me (I like Buffett’s thinking on this) but with your large base of readers, there is something for everyone here.

I say keep up the variety of posts, especially when written by knowledgable guests (such as Preet).

• FrugalTrader September 26, 2007, 3:07 pm

Ok, good to hear that you guys enjoy the more complex articles also.

Telly, based on your comments around the blog world, you keep up with the best of them. I’m surprised that you haven’t started your own blog yet.

• Gates VP September 26, 2007, 3:21 pm

Hey FT, I love this stuff, but I do have one comments that’s a little off the wall:

I like pictures! I know they’re really time-consuming, I’ve posted Excel charts to my own blog and I know they can be a time-sink. But as the examples become more complex the pictures become more valuable. I know that the “less than hardcore” will be sitting there with their scratch pads trying to draw ABC vs. XYZ.

And as you dig deeper into complexity, you’re going to lose more and more readers who simply won’t be able to keep up without some visual aids.

Again, I know that pictures are a pain, so these are just my \$0.02.

• FrugalTrader September 26, 2007, 3:26 pm

Great idea Gates. I seldom use pictures in my posts just because of that reason, it’s so time consuming. But if readers enjoy pictures, who am I to argue? :)

• FourPillars September 26, 2007, 4:28 pm

This is a bit off topic, but Preet’s comment about buying the index + puts made me think that this might be a more tax efficient way to reduce volatility in a non-registered portfolio (like an SM portfolio for example). Normally someone might decide to have an asset allocation of say 75% equity / 25% fixed income if they thought 100% equity was too risky, but outside the rrsp (or 401k) they will get nailed on income taxes on the fixed income interest.

Perhaps an alternative is to have most of the money invested in equities and then a small percentage (2%?) invested in puts on the relevant indexes. I don’t know enough about puts to know if this is practical or cost efficient but from a tax perspective it would be much better than fixed income if you are in a high tax bracket. Assuming losses on the puts are capital losses then they could be applied against gains.

Who would this apply to? Well most Canadians have enough rrsp assets to shelter their desired fixed income portion but for someone who is mega rich and has most of their money outside their rrsp or for that matter someone who is doing the SM and wants to reduce the risk of their leveraged portfolio could do something like this which could lower their equity risk and maintain the tax deductibility of their loan.

FT – I nominate you to do a post on this!

• nobleea September 26, 2007, 7:59 pm

I second that nomination!

• WhereDoesAllMyMoneyGo.com September 28, 2007, 5:48 pm

Henry: I spoke to a broker who used to be a bond trader for many, many years. He had a couple of things to say – namely that if you know enough to invest in convertible bonds you’ll know how to identify them. He’s a bit blunt, but I agree. One should have a very deep grasp of their investments if they are going to go it on their own.

Essentially, if you were to purchase a bond, you would have looked up the terms of the bond offering before purchasing it and known whether it is convertible or not, if it has a sinking fund, etc.

He also said that the easiest way would be to call your support line for your discount broker and ask them where the inventory of convertible bonds is listed.

Many debentures are convertible. If you find a list of debentures, you could look up the terms of the offering and confirm – but MANY debentures that I have seen are convertible. Understand debentures are riskier than bonds due to not being secured by real assets, but rather by cashflow and credit instead. Because of this tradeoff they will have higher coupon rates than similar bonds however.

I believe you would find terms of offerings on SEDAR – I don’t know for sure – again, I just call our bond desk for all that stuff. :)

I hope this answered your question Henry…

• Professor Don Abrams September 23, 2009, 3:43 pm

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

• ct September 20, 2012, 5:52 pm

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.

• fc January 24, 2014, 7:41 pm

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

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