Equity-linked notes (Hong Kong examples)

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• Equity-linked notes (Hong Kong examples)
• Callable dual accrual cash or share security
• Early redemption equity-redeemable warrants
• Super certificate (lookback minimum and lock-in
  level)
• Target redemption notes
• Guaranteed equity bonds

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24 Month Callable Dual Accrual Cash or Share
Security On Wal-Mart Stores, Inc and Intel
Corp. issued by Merrill Lynch (Feb. 9, 2006)

• Payment/delivery on the maturity date
• If the settlement prices of BOTH the underlying
  stocks are higher than or equal to the
  respective exercise price, each warrant holder
  will receive 100 of the notional amount per
  warrant held.
• If either one of the settlement prices is lower
  than the respective exercise price, each holder
  will receive per warrant physical delivery of a
  number of the Worst performing stock equal to
• Notional amount / exercise price of worse
  performing stock
• It is a forced conversion when the share prices
  decline (opposite effect to that of a convertible
  bond).

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Issue size 10,000,000 warrants Minimum
subscription 100,000 warrants Notional
Amount USD 1 per warrant Issue Price 100 of
the Notional Amount Trade Date Feb. 9,
2006 Issue Date Feb. 23, 2006 Valuation
Date Feb. 11, 2008 Maturity Date Feb. 19,
2006
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• Underlying stocks (uncorrelated)
• Reference price Exercise price
• Wal-Mart Stores Inc. USD 45.48 USD 39.5676
• Intel Corp USD 20.77 USD 18.0699
• Exercise price 87 x reference price
• Terminal payoff min (1, min(S1(T)/S1,S2(T)/S2)
  )
• 1- max(1 -
  min(S1(T)/S1,S2(T)/S2), 0),
• where A1 and S2 are the reference prices of
  asset 1 and asset 2.
• The investor shorts a put on the minimum of two
  assets.

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Additional coupon (accrual feature) Unless the
warrants have been called, over each observation
period (3-month period), the holder receives
4.075 x n /N of notional amount where N
number of New York Business Days in the period in
the applicable Observation Period
n number of New York Business Days in the
applicable Observation Period on which the
closing prices of BOTH the Underlying Stocks
are at or above the respective Exercise
Price. This is like an accrual note with the
underlying index being the minimum of two share
prices. The accrual feature can be viewed as a
series of daily binary options which pay
4.075/N x notional amount when
min(S1(T)/S1,S2(T)/S2) gt 1.
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• Overall description
• The investor believes that the prices of BOTH
  underlying shares at maturity will remain at a
  level above or equal to their respective
  Exercise Prices, earning an enhanced yield.
• The warrant pays out a fixed 4.075 coupon for
  the first quarter.
• The coupon received would depend on the trading
  path of BOTH underlying stocks due to the
  accrual feature.

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• Issuers Call On any of the Observation Date,
  provided that BOTH underlying stocks are greater
  than or equal to the reference prices, the
  issuer can call by paying 100 of the Notional
  Amount. This occurs when the value of the
  embedded put is less than the present value of
  the enhanced yield over the remaining period.
  This call right given to the issuer is like a
  Bermudan put option.

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• Risks
• Market risks underlying shares
• Credit risk default of Merrill Lynch
• Liquidity risk will not be listed on any
  securities exchange and do not expect a trading
  market with only Merrill Lynch as a possible
  buyer.
• Interest rate risk bond component par plus
  coupons and issuers call.
• warrant bond (series of binary options
  accrual feature)
• - European put on minimum of
  two uncorrelated stocks
• - issuers call (Bermudan put)

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• 2-Year JPY Early Redemption Equity-Redeemable
  
• (ER) Warrants Linked to a Basket of Japan
  
• Equities (Japan Basket ER Warrants)
• Type of investor
• He holds the belief that over the next two
  years the prices of all of the shares in the
  Japan Share Basket will not decline by more than
  12.00 from their respective Reference Price.
• He must be willing to take delivery of the
  worst two performing shares if any of the shares
  in the basket falls below their respective
  Strike Price at the Valuation Date.

This product is not principal-protected.
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Japan Share Basket A basket made up of the 5
shares as shown in the table below
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Issue Size 1,000,000,000 warrants Minimum
Subscription JPY 10,000,000 Notional
Amount JPY 1,000,000,000 Issue
Price 100 Trade Date 14 June 2005 Issue
Date 28 June 2005 Maturity Date 28 June 2007,
subject to the following business day
convention Periodic payment Payable quarterly
in arrear on each Periodic Payment Date and
accruing on 1 30/360 basis at the Periodic
Payment Rate
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Reference Price Executed price of each Share in
the Share Basket on Trade Date Settlement
Price Closing price of each Share in the Share
Basket on the last Observation Date, as
determined by the Calculation Agent Strike
Price 88.00 of the Reference Price of each
Share in the Share Basket Trigger Price 98.00
of the Reference Price of each Share in the Share
Basket
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Periodic Payment Rate
For the first period, from the issue date to the
first Periodic Payment Date, 10.00 p.a. fixed in
the first period Thereafter, 10.00 p.a. if the
closing prices of all the Shares in the Share
Basket are at or greater than their respective
Strike Prices on an Observation Date. Otherwise,
the Periodic Payment Rate is deemed to be 1.00
p.a..
Early Redemption by Issuer
If the closing prices of all the Shares in the
Share Basket are at or greater than their
respective Trigger Prices on an Observation Date,
the Warrants will be redeemed in full at 100 of
the Notional Amount together with accrued
interest on the related Periodic Payment Date.
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Worst Performing Share
The Share in the Share Basket which has the
lowest value on Valuation Date according to the
following formula
(Settlement Price / Reference Price) - 1
On the last Observation Date (1) If the
Settlement Prices of ALL the Underlying Stocks
are higher than or equal to their respective
Strike Price, each holder of the ER Warrant will
receive 100.00 of the Notional Amount per
warrant held.
Redemption at Maturity Date
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• If the Settlement Price of ANY of the
  Underlying Stocks are lower than their respective
  Strike Price, each warrant holder will on the
  maturity Date receive per Warrant physical
  delivery of the Worst Performing Share equal to
• Any fraction of a trading lot of the Shares to be
  delivered shall be paid out in JPY cash at a
  price calculated using the relevant Settlement
  Price.

Settlement Currency JPY
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Payout at any Observation Date
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Payout at Maturity if not Early Terminated (i.e.
Warrant is held to Maturity Date)
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• Summary
• Juicy coupons for potential short life if stock
  prices stay above the trigger prices (98). The
  juicy coupons in the early coupon represents
  the premium of the put option sod to the issuer.
• When the stock prices fall below the strike
  prices (88), the coupon reduces to 1 pa. In
  addition, the investor receives the worst
  performing stock at maturity.

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2-Year USD Super Certificate Plus (with lookback
minimum and lock-in Level) Linked to Basket
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Share Amount If the Worst Performing Share is
denominated GBP (HKD), Share Amount shall mean a
quantity of the Worst Performing Share equal to
(a) an amount in GBP (HKD), equal to the Note
Denomination converted into GBP using the Final
Reference Exchange Rate for EUR, divided by (b)
the Reference Price of the Worst Performing
Share rounded to the nearest integer. If the
Worst Performing Share is denominated USD, Share
Amount shall mean a quantity of the Worst
Performing Share equal to the Note Denomination
divided by the Reference Price of the Worst
Performing Share rounded to the nearest
integer.
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Monitoring Period The period from and including
the Launch Date to and including the Valuation
Date. Barrier Event A Barrier Event is deemed
to have occurred if the price of at least one
Share at the Valuation Time is at or below its
corresponding Barrier Price on any Exchange
Business Day during the Monitoring
Period. Look-back Period The period from and
including the Launch Date to and including 21
December 2005. Call Strike Level (b) Means the
lowest daily closing price level observed as
compared against the corresponding Initial Spot
Price during the Look-back Period, subject to a
minimum of 90 and a maximum of 100.
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where and where is the lowest
daily closing price observed in respect to the
ith Share during the look-back Period.
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Lock-in Event A Lock-in Event is deemed to have
occurred if the prices of all Shares, at the
Valuation Time on an Exchange Business Day during
the Monitoring Period, are at or above their
corresponding Lock-in Prices in respect of a
particular Lock-in Level such Lock-in Level is
then deemed to have been reached. For the
avoidance of doubt, more than one Lock-in Event
can occur during the Monitoring Period. Actual
Lock-in Level The highest Lock-in Level reached
among the Lock-in Levels reached in respect of
all Lock-in Events where applicable.
(PerformanceLocked)
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Redemption Amount (Case 1) If the at least
one lock-in Event has occurred during the
Monitoring Period, the Issuer shall pay the Note
holder the following amount in respect of each
Note held on Maturity Date. Case 1 occurs
when at least one share has increased by more
than 10. This is called a lock-in event. In this
case, it is principal protected plus extra
percentage based on the stock performance.
at maturity
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(Case 2) If Lock-in Event has not occurred
during the Monitoring Period and that (Case
2a) Barrier Event has not occurred during the
Monitoring Period, the Issuer shall pay the Note
holder the following amount in respect of each
Note held on Maturity Date.
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(Case 2b) at least one Barrier Event has
occurred during the Monitoring Period. (Case
2b-i) and if Performanceworst? 0, that is the
Worst Performance is greater than or equal to
zero, the Issuer shall pay the Note holder the
following amount in respect of each Note held on
Maturity Date.
or
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(Case 2b-ii) and if Performanceworstlt 0, that
is the Worst Performance is less than zero, the
Issuer shall pay to the Note holder the Share
Amount (fractional entitlement will be subject to
cash settlement) AND shall pay the Note holder
the follow amount (if the amount is greater than
zero) per Note in respect of each Note held on
Maturity Date.
where
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1. To the note holder, it is most desirable to
have (a) A small value of b. This occurs
when there are drops in the share prices
during the lookback period. (b) A higher
performanceLocked value (which can be greater
than 10). It is easier to be achieved
when the share prices are more correlated. 2.
Cases 2a and 2b-i are principal protected. 3.
When knock-out event occurs and performanceworst
lt 0 Case 2b(ii), the note holder acquires
the share plus some cash compensation. In this
case, the note is not principal
protected. Remark Complexity almost for the sake
of complexity. The structures are opaque for
both parties cannot really work out where the
value lies. Product controllers have trouble
marking to market.
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Target redemption notes
Example 7.5 USD Target Redemption Index Linked
Deposit (issued by Bank of East Asia, 2004)
Selling points - Enjoy potentially higher returns
with Index Linked Deposit

• 100 principal protection plus 7.5 guaranteed
  coupon return over a maximum of 5-year investment
  period.
• 1st year annual coupon is guaranteed at 6.5
  (very juicy), payable semi-annually.

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• The remaining coupon rate of 1 will be based on
  the LIBOR movement. The inverse floater formula
  is
• However, the total coupon received will not
  shoot beyond the target rate of 7.5. If the
  coupon payment accrued during the deposit period
  is less than the target rate, then the remaining
  amount will be paid at maturity.

max7 - 2 6-month LIBOR (in arrears), 0
Early termination
Once the accumulated coupon payment reached the
target rate, the deposit will be terminated
automatically.
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Worst scenario
The deposit is held for 5 years until maturity so
that the annual return for the deposit is only
1.5 per annum.
Market background
The US Fed policy makers voted unanimously to
keep the Fed Fund Rate unchanged at 1 on 28
October 2003, the lowest level in the past 45
years. They had indicated that the interest rate
would remain at a low level for a considerable
period.
Potential risk
If the 6-month LIBOR rises beyond 3.5 one year
afterwards and never come down again. The deposit
is then held for 5 years until maturity.
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Equity target redemption notes
SG Product

• 10-year fund that is 100 capital guaranteed
• Pay a juicy fixed coupon of 10 in the first year
  
• For Year Two, the coupon payment is referenced to
  the average performance of the 6 worst stocks in
  a basket of 24 blue-chip stocks.
• From Year Three onwards, the investor gets the
  better of the previous years coupon or the
  payout formula.
• Once the aggregate coupon payments reaches or
  exceeds 20, the fund terminates with full
  payment of the coupon for that year.

max0,10 0.5 average performance of the 6
worst stocks
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Worst scenario 10-year fund with total coupon of
20
Blending equity and rates

• Design products that have both equity and
  fixed-income risk.
• The equity and fixed-income markets typically
  offset each other during economic downturns,
  therefore hedging the investor against excessive
  downside in one market.

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Guaranteed equity bonds (GEBs)

• The issuer (usually an insurance company)
  guarantees a stated interest rate and some
  protection from loss of initial capital, and
  provides an opportunity to earn additional
  interest based on the performance of an equity
  market index (say, Standard and Poors 500
  Composite Stock Price Index).
• GEBs credit interest using a formula based on
  changes in the index to which it is linked. It
  enables investors to achieve potential capital
  appreciation by participating in the positive
  performance of the index but also provide
  investors with a guaranteed minimum return of
  their investment at maturity.

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Term
The index term is the period over which
index-linked interest is calculated. Interest is
credited to the investor at the end of a term.
Participation Rate
The participation rate decides how much of the
increase in the index will be used to calculate
index-linked interest. For example, if the
calculated change in the index is 9 and the
participation rate is 70, the index-linked
interest rate for the contract will be 6.3 (9 ?
706.3).

• The company usually guarantees the participation
  rate for a specific period, from one year to the
  entire term.
• When that period is over, the company sets a new
  participation rate for the next period.
• Some contracts guarantee that the participation
  rate will never be set lower than a specified
  minimum or higher than a specified maximum.

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Cap Rate
Some contracts may put an upper limit, or cap, on
the index-linked interest rate. This is the
maximum rate of interest the contract will earn.
Floor
The floor is the minimum index-linked interest
rate that will be paid. The most common floor is
0. A 0 floor assures that even if the index
decreases in value, the index-linked interest
that can earn will be zero and not negative.
Guaranteed interest compounding
Some contracts pay simple interest during an
index term. That means index-linked interest is
added to the original premium amount but does not
compound during the term. Others pay compound
interest during a term, which means that
index-linked interest that has already been
credited also earns interest in the future.
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Dividends
Depending on the index used, stock dividends
usually are not included in the index value. For
example, the S P 500 is a tock price index and
only considers the prices of stocks. It does not
recognize any dividends paid on those stocks.
Early withdrawal
In most cases, investors cannot take all or part
of the money out of contract at any time during
the term. There will be a cost and the
index-linked interest on the amount withdrawn
will not be paid.
Indexing method
The approach used to measure the amount of
change, if any, in the index.
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Point-to-Point
The contingent claim C(t) in year t for one unit
of GEB can be represented as followed

• While subject to the maximum cap rate z that can
  be earned under this design, the first random
  term allows the investors to have a participation
  rate a in any potential upside gain in the equity
  market.
• In the event of an adverse market environment,
  the downside risk is constrained to the minimum
  guarantee floor component, that is, (1 g)t.
• The presence of the cap rate, although placing an
  upper bound on the rate of return of the
  contract, could reduce the cost of such design
  substantially.

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The payoff in year t for one unit of GEB is given
by
where the random variable RS again measures the
appreciation of the referenced index fund in year
s.

• RS is solely determined by the index levels at
  the beginning and the end of year s

• The interest is credited each year for the annual
  reset GEBs. The credited interest cannot be lost
  even if the index subsequently goes down.
• The index level used to determine the
  appreciation of the index is reset annually.
  This lock in feature can be extremely valuable,
  particularly in a more volatile market.

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High Water Mark (Lookback)
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Point-to-Point with Barrier
To increase the participation rate, we apply an
up-and-in barrier option to the point-to-point
GEBs. An up- and-in barrier GEB provides
purchasers with the greater of the index return
times the participation rate and a minimum
guaranteed return if the index rises above a
barrier for the monitoring period and offers the
minimum guaranteed return otherwise.
where
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Annual Reset with Barrier
In each period, the GEBs will provide customers
with the greater of either the annual index
return times the participation rate or a minimum
guaranteed rate if the index value for the
monitoring period rises above a barrier.
Otherwise, the GEBs will credit to the
policyholder the minimum guaranteed rate as
annual return.
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Average
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Cap rate 1.3
Guaranteed annual return 1.03
Number of simulation 100
Initial index level 5800
Barrier level 9000
Initial interest rate 0.045
Initial volatility 0.15
In general, we can see that the change of
participation rate does not place great effect to
the point-to-point, lookback, and average
contracts until 50.
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Impact of cap rate Participation rate 0.8

• The decreasing cap rate will lower the price of
  the contract.
• For the average design, the price does not change
  so much when the cap rate decrease.
• For ratchet design, the price also does not
  change so much when the cap rate decrease until
  10.

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Annual Guaranteed Interest
Some contracts pay guarantee interest during an
index term if the index-linked return is less
than the guarantee return or negative.
The increasing guarantee interest will increase
the price of the contracts.
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Source Structured Retail Products (April 2006)
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Guaranteed annuity options

• In the United Kingdom, the GAO guarantees a
  minimum conversion rate of lump sum of annuity.
  Typically, guarantees of 111 annual annuity per
  1,000 maturity lump sum have been offered for
  male policyholders, and around 91 annuity per
  1,000 maturity lump sum for females. The
  conversion rate is known as the guaranteed
  annuity rate of GAR.
• Let g be the guaranteed annuity rate (e.g., g
  1/9 for a rate of 111 annuity per 1000 lump sum),
  and let ax(t) be the market price at t of a
  whole-life annuity of 1 per year payable
  immediately to a life aged x. The value of
  separate fund at t FT.
• The payoff under the GAO at the maturity of the
  separate fund account, say t n (which is the
  annuity vesting date), for a life age 65 at
  vesting, is

This option is in-the-money when a65(t) is
greater than 1/g and out-of-the-money otherwise.