Case 013Volatility, options and convertiblesCore

The Ushar Capital-Protected Note returns 100% of capital after three years plus 60% of any index gain. Three-year rates are 7% and a three-year at-the-money call costs 18% of notional. Decompose the note and say whether 60% participation is fair.

The situation

A distributor is selling the Ushar Capital-Protected Note to wealthy clients. For every Rs 100 invested, the note pays back Rs 100 after three years, plus 60% of any rise in an equity index over those three years. If the index falls, the investor still gets Rs 100 back.

Three-year rates are 7% a year, compounded annually. A three-year at-the-money call option on the index, priced from the dealer market, costs 18% of notional. The note pays no coupon. A volatility fund asks you whether the note is fairly priced.

Your task

Break the note into its parts, work out what participation the money could buy, and judge whether 60% is fair.

Quick check

Roughly what participation could the issuer afford to give at these prices?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The note is a 81.6 zero-coupon bond plus 18.4 of option budget, enough for about 102% participation, so 60% leaves the issuer about 7.6 per 100, roughly 2.5% a year. The capital protection is simply the bond; the upside is a set of calls. At these prices the investor pays for a full call and receives 60% of one. The note is not fair unless the issuer's costs or credit explain the gap.

Step 1What is the note actually made of?

Every capital-protected note is two things glued together. Think of a fixed deposit that matures at exactly the amount you started with, with the interest spent on lottery tickets. The protection is a zero-coupon bond that grows back to 100, and the upside is call options bought with whatever is left. At 7% for three years, the bond costs 100 divided by 1.07 cubed, about 81.63. That leaves an option budget of 18.37 per 100.

The relationship
B=100(1.07)3=81.63budget=100−B=18.37pfair=18.3718=102%B = \frac{100}{(1.07)^3} = 81.63 \qquad \text{budget} = 100 - B = 18.37 \qquad p_{fair} = \frac{18.37}{18} = 102\%
Bthe price today of a three-year zero-coupon bond paying 100
budgetwhat is left to spend on options
p_fairthe participation the budget buys at 18 per at-the-money call
What it says in wordsThe guarantee costs the bond price, and the leftover money divided by the call price is the participation it can buy.
Unbundle the note: a bond, some calls, and what the issuer keeps100Investor paysper 10081.6Zero-coupon bond100 / 1.07^310.8Calls bought60% x 187.6Issuer keeps2.5 a yearBudget18.4buys 102%
Of each 100 invested in the Ushar note, 81.6 buys the zero-coupon bond that returns the capital, 10.8 buys calls for 60% participation, and the issuer keeps 7.6, about 2.5 a year.
Step 2So is 60% fair?

Compare what the investor pays for with what the investor gets. The option budget of 18.4 buys about 102% participation at 18 per call; the note gives 60%, which costs 10.8, so the issuer keeps about 7.6 per 100. Over three years that is about 2.5% a year, far more than the fee on a typical equity fund. Some of it is legitimate: the issuer has to hedge, distribute and carry the product. But an investor who bought the bond and the calls separately would get roughly the full index gain for the same money.

The floor is real; the upside is where the 7.6 goes80100120140160-40%-20%0%+20%+40%+60%Index change over three yearsPaid at maturity, per 100the index itselffair: 102% of the gainUshar: 60% of the gainfloor 100
The Ushar note pays 100 if the index falls and 100 plus 60% of any gain, while a fairly priced version would pay about 102% of the gain; after a 50% index rise the note returns 130 against about 151 for the fair version.
Step 3What else would you check before calling it expensive?

Two things change the arithmetic. First, the note is unsecured debt of the issuer. If the issuer's own borrowing rate is above 7%, the bond part is cheaper for it, the option budget is larger, and the note is even less fair; the protection is only as good as the issuer. Second, the index in such notes is usually a price index, so the investor gives up dividends, which the call price already reflects. For the volatility fund the view is clear: the embedded option is being sold to retail buyers at a large markup, so the relative value is in the dealer market, not in the note. Nothing here is a view on whether the index will rise.

Where candidates lose it

The trap is admiring the protection. Capital back after three years sounds valuable, but it is just a bond; at 7% a year, the investor's money would have grown by about 22% in a plain bond instead of 0%. That forgone interest is what pays for the calls.

The second miss is forgetting issuer credit. Capital protected means protected by the issuer's promise, and if the issuer fails, the investor is an unsecured creditor.

What the interviewer asks next

  • Rates fall to 5%. What participation could the same note offer?
  • How would a cap on the index gain at 40% change the fair participation?
  • Why might the call be cheaper for the issuer than the 18% the dealer market charges?

Company names and figures are illustrative.