When +30 = -100 or The Power of Monte Carlo or Valuing Callability or Both Sides Now
On October 15th, Barclays offered this note. How should we value it as of issuance or on any day between now and maturity?
The investor delivers 100 dollars to Barclays, which Barclays uses as it sees fit. All returns to the investor should be discounted to reflect present value.
There is some non-zero chance that Barclays will be unable to meet its obligations, so the investor is implicitly short a credit default swap.
Barclays holds a European put on Hertz Corporation and may choose to exercise it. This is a knock-in set for final valuation date at 70% with a strike of 100%. Expressed in prices of HTZ: since HTZ was 22.14 on the initial valuation date, the strike price is 22.14 and the knock-in barrier is 15.50. If, at maturity, HTZ closes above 15.50, the put expires worthless.
Barclays will pay the investor 3.75 dollars at the end of every quarter (i.e., each valuation date, January 9th, April 9th, July 9th, and October 9th ) for the next two years, as long as HTZ is above 15.50 on those dates.
This note is callable on any valuation date. Barclays can choose to stop paying the 3.75 and return the investor’s 100.
Some Implications of General Discussion
The best case for the investor would be for HTZ to hang around just above 15.50 for the next two years so that Barclays keeps thinking its put will pay off. That way Barclays pays all 30 dollars in coupons and the investor winds up with 130 dollars.
If HTZ drops immediately to zero, Barclays never has to pay a coupon, and the investor loses everything. Other, intermediate, results for HTZ are not quite so disastrous for the investor, but can still result in losses.
One thing we do know is that this note will never be worth more than 103.75. The worst case for anyone who sold it higher than that would be paying one coupon, then calling the note and pocketing the difference.
The Discount Rate
In the current environment, we could use rates somewhere in the neighborhoods of one or two percent. We are not sure, for the moment, of the principal amounts or of the duration's that should actually apply to our situation. Toward the end of this blog we will talk about how to match dollar payoffs with their duration's and with the corresponding probabilities of those payoffs at those duration's. Then we can multiply by the appropriate discounts.
We could price two-year insurance on Barclay's. Instead of shopping around, we could even use Black-Scholes for an estimate. However, the most likely scenario is that Barclay's will choose to call after one valuation date, so for the most part it is three-month insurance that is relevant. In any event, we need some probability-weighted technique to adequately reflect the cost of a default.
We can calculate the value of a two-year knock-in put. It is worth x1, which by itself would be enough to bring down the putative 15% yield on this note to x2. Unfortunately, this callable contingent coupon note that we are examining is much more complicated than that. In most cases the issuer will sacrifice the put in order to exercise his call and stop paying out the 3.75 each quarter.
We know that HTZ could spend some time during the next two years trading below 15.50. If it does, then some of those (eight, at most) coupons will not have to be paid. We calculate that this contingency by itself would bring the annualized yield to x3.
Far and away the most likely outcome for this note is an early call. In isolation, this is so valuable that it alone brings the annualized yield down from 15% to x4%. Again, however, there is no closed formula for how this call interacts with the note’s other features. For example, if HTZ sinks fast enough, then the issuer will choose to sacrifice this extremely valuable callability because he is tempted to realize the value of the put. In some cases, this will result in the issuer paying all thirty dollars of coupons even though he could have gotten out much earlier.
What Is to Be Done?
As with so many products, the only viable resource here is Monte Carlo. This technique will generate thousands of random walks of possible price changes for HTZ. With these we can arrive at the correct strategies for the issuer—when to call, when to wait it out for one more quarter… We can also use Monte Carlo to help us gauge the impact of a BCS bankruptcy on our expected returns.
It is true that we could extend Black-Scholes to estimate the probability of HTZ sinking below 15.50 or of BCS heading toward zero. And we could think about deep-in-the-money calls on stocks paying a 3.75 quarterly dividend and whether those calls should be exercised (corresponds to the issuer calling the present note). Nonetheless, even if we had totally precise values for all the features that benefit the issuer, we could not know the value of the note. They cannot all work simultaneously to his benefit or to the investor’s detriment. The only way to account for the interactions of all the note features is to run a Monte Carlo. So that is what we have done.
In its prospectus, Barclay's stated the note’s initial value as $959.70.
Our work tells us: $x5.