Equity-linked notes are popular instruments in the over-the-counter equity derivative market. ELNs are also known as high-yield notes or reverse convertibles. A typical term sheet of an ELN looks something like this:
Good deal? Well, it depends on your view. Yes if you don't think there is much upside for China Mobile (a major telecom stock listed in Hong Kong), but you like the fundamentals. You will pocket a handsome 38% per annum return in cash if the stock does not fall below HKD75; otherwise you will end up with a long position in the stock.
How to reverse-engineer the ELN
Usually these structures involve embedded options to make the payoff more attractive. In this case, the investor takes a long position in China Mobile shares when the stock falls below HKD75. In other words, the investor has sold a put option, struck at HKD75, to the issuer. Therefore an ELN is
Where is the high yield from?
The extra yield comes from the option sold to the issuer. The option premium is paid to the investor in the form of interest on the ELN. In fact, if p is the put option premium and x is the issue price of ELN, these proceeds together should generate the par value at maturity at the money market rate (r), that is
and the actual yield (y) for the investor who paid x for the ELN is
Hence we have an equation for the yield (y):
which shows that the put option premium (p) works both in the numerator and denominator to pump up the yield.
Put-Call parity (PCP) states a no-arbitrage relation between the call and put premiums. In one form, it states
The notations are K = strike price, S = spot price, c/p = call/put option premiums. Many other forms of PCP are possible by permuting the terms in the above form and they all have different financial interpretations. For example, a long call position plus a short put position is like a forward struck at K. Hence present valuing the equality will give
See Chance's book1 for more fun with PCP. Now we claim equation (1) is the proper form of PCP to understand the ELN. Recall that an ELN is a time deposit + a short put option position; therefore the left-hand side of (1) is the current price of the ELN (with K = 100). The right-hand side of (1) is saying that the note price is also equal to the current stock price minus the premium for the corresponding call option. That means holding a ELN is the same as holding a stock and selling a call option on the stock. Put it yet another way, buying a deposit-like ELN is equivalent to writing a covered call option by PCP equation (1). In hindsight, it is a straightforward result: with a covered call position, you get to keep the stock if it doesn't go above the strike price; otherwise the stock will be called away by the option holder and you are left with the strike price (the par amount). This is exactly what the ELN gives you.
The above argument serves as further evidence of Put-Call parity. Not only that, PCP tells you a do-it-yourself way to create an ELN. In particular, for investors that already have the stock in their portfolio, all they need to do is to sell a call at their local exchange. This may be a better deal if the options at the exchange are more fairly priced.
1. Don Chance, "Essays in Derivatives", Frank J. Fabozzi
Associates, 1998.
This week's Learning Curve was written by Wai-yan Cheng, assistant professor in the Economics and Finance department of City University of Hong Kong.
