Worst-of Step-Down ELS: Autocall, the 45% Barrier Cliff, and Fair Value at Issue
A bank branch sells investor Seo, 58, a three-year, three-underlying worst-of step-down ELS for 100 million KRW. The note pays 6.50% per annum, simple, paid on redemption, and autocalls on any quarterly observation if the worst-of the three underlyings is at or above a step-down level: 90% at months 6 and 9, then 85%, 80%, 75%, 70%, and 65% at month 36. If it never autocalls, principal is repaid in full only if the worst-of at maturity is at or above 45% of its initial level - a knock-in barrier observed only at maturity. Below 45%, the investor loses 1% of principal for each 1% by which the worst performer is below its initial level. Initial levels: KOSPI200 350.00, S&P500 5,200, EURO STOXX 50 4,650. At the first observation the levels are KOSPI200 336.00, S&P500 5,460, and EURO STOXX 50 4,330. Seo believes the worst-of design means he is 'diversified across three markets' and that the 45% barrier 'protects 45% of my money.'
1. Determine the outcome at the first observation date and explain how the worst-of mechanic actually allocated the risk.
Read the worked answer
Normalise each underlying to its initial level:
- KOSPI200: 336.00 / 350.00 = 96.00%
- S&P500: 5,460 / 5,200 = 105.00%
- EURO STOXX 50: 4,330 / 4,650 = 93.12%
Worst-of = 93.12%, versus a month-6 autocall level of 90%. The condition is met, so the note autocalls.
Redemption: 100,000,000 × (1 + 0.065 × 6/12) = 103,250,000 KRW. Seo earns 3.25 million over six months, an annualised 6.5% - the headline coupon, but only for half a year.
How the risk was allocated: diversification never happened. The payoff is driven by the single worst performer, so the note is short a basket option on the minimum of three indices, not long three exposures. The S&P500 being 5% higher contributed nothing. The practical consequences:
- One weak market is enough to block the autocall at every later date.
- The more names, the lower the correlation benefit to the investor - a worst-of on three indices yields a higher coupon than a single-index note precisely because the worst-of is more likely to be bad.
- The investor is effectively long correlation: a fall in cross-market correlation widens dispersion and raises the chance that one index lags badly, which is exactly what erodes the note's mark-to-market.
2. Suppose the note had not autocalled (worst-of at month 6 = 88%) and at maturity the KOSPI200 sits at 44% of its initial level while the S&P500 is at 120% and the EURO STOXX 50 at 70%. Compute the redemption and explain the barrier cliff. Then compare with a final KOSPI200 level of 45.1%.
Read the worked answer
Worst-of at maturity = KOSPI200 at 44%. Because 44% is below the 45% knock-in barrier and the barrier is observed at maturity only:
- The knock-in is triggered.
- Redemption = 100,000,000 × 44% = 44,000,000 KRW, with no coupon.
- Loss versus principal: 56 million KRW (-56%), despite the S&P500 being up 20%.
The cliff. Compare with a final worst-of of 45.1%: barrier not breached, so the investor receives par plus the full accumulated coupons - roughly 100m + 19.5m = 119.5 million KRW. The difference between 45.1% and 44.0% is a swing of about 75.5 million KRW on a 1.1-point move in the index.
This is the defining feature of a European knock-in observed at maturity: the payoff is discontinuous at the barrier. A 1% move just below the barrier destroys roughly 56% of principal, because the investor goes from full protection to 1:1 downside participation in a single step. Seo's belief that the barrier 'protects 45% of my money' is wrong in both directions - it protects nothing below the barrier, and it is not a gradual buffer.
Risk-management point: a holder who cannot tolerate this cliff should not hold to maturity. Once the worst-of approaches the barrier with the note deep out of the money, the position is a leveraged bet on a specific index recovering before a specific date, and the issuer's early-redemption quote will be far below par.
3. Seo asks why the note was worth less than 100 million KRW on day one, and what could make the secondary-market value collapse later. Explain the economics and the credit dimension.
Read the worked answer
Why fair value at issue is below par. The 100 million is not invested in a 100-million asset. Roughly:
- Distribution fee to the bank: about 0.5–1.0%.
- Structuring margin and hedge cost kept by the issuer: about 1.0–1.5%.
- Hedging: the issuer immediately sells a down-and-in put on the worst-of to its derivatives desk, and the 6.50% coupon is funded by that premium plus the issuer's funding advantage versus the 3.5% area risk-free rate.
A realistic fair value at issue is therefore 97.5–98.5 million, and the secondary quote from the issuer will be inside that, net of its own bid-ask. The 6.5% coupon is not free money: it is the price the market pays for selling volatility, selling a barrier put, and taking issuer credit exposure.
What can make the mark collapse:
- The worst-of falls toward the barrier. Delta is small far from the barrier, then gamma explodes near it; the mark falls sharply and non-linearly.
- Implied volatility rises. The investor is short the embedded option; a volatility spike raises the value of the issuer's hedge and lowers the note's mark.
- Correlation falls. As above, dispersion increases the value of the worst-of put and hurts the holder.
- Issuer credit deterioration. The note is an unsecured obligation of the issuing securities firm or bank, not a deposit and not deposit-insured. If the issuer's rating falls, the note's value falls even with the underlyings unchanged - a risk Seo was almost certainly never told about.
- Liquidity. There is no exchange; early exit depends on the issuer's quote, which widens with volatility and time.
Selling point for the branch: the disclosure must cover the fee drag, the short-volatility and short-correlation exposure, the credit risk, and the barrier cliff - not just the coupon and the three famous index names.