Equity-linked note -- Chapter 01 - YouTube

This Chapter 1 reviews the process of structuring an equity-linked, principal protected note

via the purchase of a fixed-rate bond and a call option.

We begin by assuming that an investor has given you $100, and has asked you to provide

her with a vehicle for investing in Microsoft shares for a 3-year time horizon.

Recognizing however that Microsoft shares are volatile and could expose much of her

investment to a loss, the investor also asks that your bank guarantee the return of her

principal in 3 years’ time.

Finally, the investor specifies that she would like to receive a coupon, paid annually, equal

to 1% of her principal.

You can probably recognize right away that to provide the guaranteed coupon of 1%, and

the principal at maturity, you will need to invest a large portion of the investor’s

money in some sort of fixed-income security.

You therefore call up your funding desk and ask them how much it would cost to purchase

a 3-year bullet bond, with a 1% coupon, bearing the credit risk of your institution.

Worksheet Bond shows the next few calculations.

We assume for this exercise that the US treasury yield curve is flat at 5.50% , and that your

bank’s credit spread over the US treasury curve is 75 basis points for all maturities.

This means in turn that the appropriate discount rate to apply to cash flows carrying your

bank’s credit risk is 6.25%.

For the sake of simplicity, we are assuming that all payments are made annually.

Excel permits us to calculate the present value of a 3-year bond, carrying a 1% coupon,

issued by your bank, with the result appearing in Cell E15.

You can look up the formula behind this Cell E15 by clicking on INSERT, then FUNCTION,

whereupon the PV function opens in front of you.

The PV function requires you to input 100 for FV, which is the face value of the Bond,

C11* 100 for PMT (which is the coupon relative to the stated face value), C10 for Nper (which

is the number of periods), and, perhaps most importantly, C8 for Rate, since this is the

appropriate discount rate as explained above.

Many people are tempted to input C11, which is the coupon, for Rate, since they associate

the word Rate with the concept of a coupon; but Excel uses the word Rate to denote the

discount rate for the bond’s cash flows.

It is next to PMT, we remind you, that you input the actual coupons.

The present value – i.e. the price of the bond you need – turns out to be $86.03,

leaving you with $13.97 to invest in something else.

This something else that you are looking for can be either a direct investment in MSFT

shares, or an investment in call options on MSFT, since either of these alternatives would

give you upside exposure to MSFT shares.

Pros and cons of each are discussed a little later, but for now you decide to go ahead

with the call options.

Please click at this point on the Worksheet labeled Option Prices.

A European call will be sufficient for your purpose, since the investor is concerned only

with the final price of MSFT shares at the end of the 3-year time period.

The worksheet models European calls and puts using the Black-Scholes pricing model.

Pricing a call option on shares requires you to input the share’s spot price , its volatility

, the strike of the option , the option’s maturity, or tenor , the risk-free interest

rate and the dividend yield of the stock , which

happens to be zero in this instance.

Note that the risk free interest rate has been converted from 5.50% , which was an annually-compounded

rate, to 5.35% , which is the continuously-compounded equivalent rate required under the Black-Scholes

model.

The process of converting an annual rate into one that is continuously-compounded is discussed

in some of our other modules.

You will quickly see here a pattern that should be familiar: the higher the strike of the

call option, the lower the price , since the probability of a gain for the buyer becomes

smaller the more we increase the strike.

The opposite is true for put options . We will not be needing the put option prices

during our discussion, but you will use them to answer some of the quiz questions at the

end.

Remembering that you have only $13.97 to invest, you choose the strike 60 call option , which

costs $13.15 and leaves you with $0.82 as your profit margin.

In effect, you would be offering the investor a package – which we will henceforth refer

to as the “ELN”, or “Equity-Linked Note” – whose price is 100, but whose fair value,

on its issue date, is in fact only $99.18.

Going forward, we will refer to the 1% Bond as the “Bond”, and the Strike 60 Call

Option as the “Option”.

The term sheet for the ELN you offer your customer would look as follows:

The formula for the Redemption Amount shows the receipt of the guaranteed $100 from the

maturity of the Bond on that day, plus the contingent payment under the Option, which

would be the excess if any of the final stock price over $60.

This completes Chapter 1.