# Absolute Return Barrier Notes....evaluation?

The note is linked to an index and has a lower bound of .75 and an upper bound of 1.25. It’s an 18-month hold and has a final payoff of the absolute return provided the barriers aren’t broken, otherwise the payoff is return of principal. I set up a spreadsheet where it had the min/max going forward 18 months and peaks/troughs next to every observation day. So day 1, for example, the index is at 100 and the min is 76 (low was reached between day 2 and day 378*), max is 110 (max was reached between day 2 and day 378). These obesrvations are based on closing prices 18 months after the note was issued. In this situation, if at the close of the 18th month, the index is down 20%, the investor gets a +20% return. My question: Is this an EV play? The lower barrier was broken 1404 times and the upper barrier was broken 5093 times. The rest of the time (14533-5093-1404) the return was, obviously, under 25%. I pulled the Geometric mean of all issued notes and got 5.3% (includes 0% ,or return of principal, notes that broke the barrier)… *based on 252 trading days in a year.

So I buy this index-linked note for 100 and on day T the note is worth (1 + |% change in index through day T|)*100 unless this has ever been greater than 125 or less than 75 and then the note is worth 100. Is that right? So somehow you simulated this in Excel (I didn’t get how you did that) and found that the geometric mean of the returns was 5.3%. And then there’s this thing about “EV play”, whatever that means. So it seems to me that you are getting an ATM knockout call and and an ATM knockout put and the price for that is that you have to lend someone money for 18 months for no interest. So there are three things to price - the two knockout options are pretty simple (like there are even free web calculators to do it) and the interest-free loan is just the usual credit problem. What’s the problem here?

EV play = expected value. My calculation consists of daily returns of SPX. There were 1404 times the lower bound was broken and there were 5093 times the upper bound was broken (assuming one of these notes was issued every trading day for the last 50 years). Every time it’s broken the note defaults to original principal. Some returns, over the 50 year period, had zero growth and some had 24%… If I were to invest in one of these notes, what is a reasonable expection of return on my money? Is it the risk free rate due in 18 months? These notes are FDIC insured, by the way.

BTW - I think securities like this are useless. Sometimes there are legitimate risk transference reasons for issuing packages of exotic options, but it’s hard to imagine what that might be here (I can come up with some if there are accompanying knock-in notes). Usually there is no purpose for these things except that someone wants to have a math contest. Since you’re doing this in Excel and posting about it on AF, you probably shouldn’t be playing. In the end, if you do it right you’ll find out that you’re buying VIX at 45 or something.

Yep - it’s VIX. Those are ATM knockout options whose price depends on ATM S&P vol which of course is very transparent. FDIC insured means risk-free (I guess - don’t know much about FDIC insured paper). Figure out what the implied vol is on those options because you are giving up a really well-defined amount of money. Dollars to donuts it’s VIX * 1.5 or greater.

Also, since these knockout options have a fixed barrier there is an analytic solution to value them that was worked out in Merton (1973), one of the classic references for stock option pricing. This paper must be available somewhere on the web.

So actually my post was a little misleading - high vol makes these options worth less because it increases the probability of them being knocked out. At current VIX, the package of options is worth about \$2.50 per \$100. So this note is paying about a 1.6% interest rate. Sell.