I know what the old time readers are thinking: “Mike, this blog used to be indecipherable to all but 4 people. Now you are seriously going to ignore trying to value that knock-in option on the reverse convertible bond and posting distribution charts, and instead talk about policy recommendations? Sellout. Why don’t you just call this site the ‘Radio Friendly Finance-Opinion Unit Shifter’ blog?”
*sigh*. I know. Shameful. James caught this: “(The terms can depend on whether the stock ever went below the threshold and where it is at the end of the period, which makes the deal worse for the investor, but that’s the basic idea.)” But how much worse? Let’s go under the hood of this embedded option-within-an-option so I can show you what financial innovation looks like. It gets a little intense under the fold.
Refresher. Let’s model it like this. You put up $100 on day one. In one year you’ll get 10% interest payment plus the $100 unless an underlying stock, also worth $100, either (case 1) closes on the last day under the barrier or (case 2) closes on any day under the barrier. In this case you’ll get the stock, unless in (case 2) the stock is worth more than $100, in which case you’ll get $100. To get specific, in this case the barrier is $80. The (flat) interest rate is 5% and the (flat) vol on the underlying is 45%.
Sizing that extra knock-in option up as a financial engineer, the difference between (case 1) and (case 2), I’d say that has to be the juiciest bit of it, pure free cash to grab from the other guy. Or if you like, it’s the most innovative feature. People are poor at understanding embedded options, and this is an option embedded inside another embedded option. If the stock closes below the barrier on just one day, the final payment will either be the cash for the bond back or the stock, which is lower. I also have to imagine that difference is the easiest sell to naive investors. One a quick read, you may not even catch that it is there.
Now in practice you may think that this is not worth very much. If the stock crashes to $30, on day 2, it’s probably not coming back to $100. Grabbing some old monte carlo matlab code laying around the computer and adjusting the payouts to handle this bond can give us a headsup. Here is the code – not an actual investment tool! – the banks will use something similar, mostly getting very complicated with interest rates and vol measures. This’ll do for a quick read.
So for the instrument above, what is the expected return? Expected return discounted to T0 in (case 1) we expect $91.40 and in (case 2) we get $89.89. Just holding the stock is worth $100 (this is T0 timespace, sorry if confusing, old habit – the stock is worth much more at expiry too obviously – just multiple by exp(.05*1)). The difference is the value of the option. God I hope nobody paid retail for this hypothetical instrument; you’d do better putting it in a mattress.
Now these are made up numbers. What I want to really show you is the ‘innovation’ of the difference in the distribution between case 1 and case 2. Note that this is a difference naive investors may not catch at all unless if he or she didn’t understand the put option nature of the bond. Here are the histograms by $5 units by trials. (case 1 – Red) and (case 2 – Blue):
That is amazing. First off, look at all that glorious tail risk investors took on. Second, as we suspected, when things go bad they go bad; there isn’t much difference between red and blue at the tail end.
What is amazing is that a giant chunk of the number of full payment trials, the $100 + your interest, gets transfered over to the 80-100 range. Specifically, there are many trials where it goes below the barrier for a day but then ends in the $90 range. So what does the other side of this instrument do at the end? They take your $100 you gave them at the beginning, buy the stock for $90 and hand it to you, while pocketing your $10 (and they virtually did this on day 1 using market price options, very likely). The stock hasn’t collapsed. There was no tail risk insurance exercised. And these are options, so it’s zero sum – that $10 has to go somewhere, and it is going to them. They just took your $10 and are going to buy themselves a great night on the town because someone without a fiduciary responsibility to represent your interest told you you were buying a bond and you didn’t understand the fine print.
I have no problem with innovation. But it is very important for free market types to understand that financial innovation is often not of the Silicon Valley type, but of “how can I steal $10 from this guy and make it look like random market risk” type.
Rortybomb 
how many of these were sold?
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Do you know if they were dynamically hedging the reverse converts, or using market puts, or if there was some demand by someone else to buy the underlying knock in options as a cheaper form of insurance on the underlying? Was the packaging was a way to deal with something what they had directly sold to another client-the knock out puts?
I cannot figure out why you would have a client sell a knock-out put rather than a straight put here…
knock in not knock out 😦
Mike,
Thanks for the analysis. But I question whether you’ve set up (and obliterated) a straw man. Disclaimer: While I consider myself fairly well versed in the valuation of convertible securities, I’m not intimately familiar with reverse converts. So I may be dipping my toe into unfamiliar waters today.
The straw man I’m referring to is the comparison you’ve set up between an out-of-the-money put option (case 1) and an at-the-money put option with a knock-in. Is this germane to the comparison of a “vanilla” reverse convert and a knock-in varietal? Based on my read of how vanilla and knock-in reverse converts are typically structured (see here: http://seekingalpha.com/article/108107-reverse-convertibles-in-favor-of-the-issuer-not-the-buyer), the the embedded puts in vanilla structures normally appear to have at-the-money strikes, and knock-ins are also struck at-the-money but with an out-of-the-money trigger. If this understanding is correct, and we compare an at-the-money put to an at-the-money knock-in put, the former is clearly more valuable. That is, holding strikes constant, the presence of the knock-in diminishes the downside risk borne by the investor.
I support that name change. Also consider “The Money Will Roll Right In.wordpress.com”