Convertible bonds as an asset class

Combination of bonds and equities – bond plus conversion option

• Bondholder has the right to convert the bond into common shares at
some contractual price (conversion number may change over time).
• Issuer’s call and holder’s put
• Conversion premium and break-even calculations
• Decomposition of convertible value into different components
- bond plus warrant plus default risk
- put plus stock plus yield advantage
• Interest rate sensitivities – duration
• Lattice tree calculations: incorporation of default risk, call and
conversion rights

1
 Holder’s perspective: take advantage of the future potential growth of
issuer’s company
Issuer’s perspective: raise capital at a lower cost by the provision of
conversion privilege to bond holders

convertible
bond price conversion value
conversion
premium
straight bond value

stock price
2
Equity perspective on convertibles

• To take advantage of the upside potential growth of the

underlying stock (participation into equity).

• Swapping the variable stock dividends in return for fixed

coupon payments until the earlier of the maturity date and the
conversion date.

Fixed income perspective on convertibles

• Provides the “bond floor” value.
• Conversion option that allows the investor to exchange the straight
bond for fixed number of shares.
3
 Call terms
Issuer has the right to call back the bond at a pre-specified call price prior
to final maturity, usually with a notice period requirement. Upon call,
the holder can either convert the bond or redeem at the call price.

Issuer’s perspective on the call right

• To have the flexibility to call if they think they can refinance the debt
more cheaply.

• To force bondholders to convert debt into equity, which can reduce

debt levels and result a beneficial effect on the balance sheet. The issuer
has the flexibility to shift debt into equity to reduce the leverage of the
firm. In summary, it is used as a tool by issuer for possible future equity
financing – managing the debt / equity balance.
4
 Call protection
Hard (or absolute):
To protect the bond from being called for a certain period of time.
Soft (or provisional):
The issuer is allowed to call only when certain conditions are satisfied.

For example, the closing price of stock has been in excess of 150% of
the conversion price on any 20 trading days within 30 consecutive days.

Role of call protection

To preserve the value of the equity option for the bondholders. While
waiting for the stock price to increase, convertibles typically provide
more income than the stock. Without the call protection, this income
stream could be called away at any time. Hard call protection with
longer time period is more desirable for the investors.
5
 Put feature
Allows the holder to sell back the bond to the issuer in return for a fixed
sum. Usually, the put right lasts for a much shorter time period than the
maturity date of the bond.

• The holder is compensated for the lesser amount of coupons

received in case the equity portion of the convertible has low
value.

It protects the holder against rising interest rates by effectively

•
reducing the year to maturity. With smaller value of duration*,
the convertible price becomes less sensitive to interest rate.

• Duration is the weighted average of times of cash flow stream, weighted according
to the present value of the cash flow amount. Percentage change in bond price is
proportional to negative yield change, where the proportional constant is the
duration.
6
Put above par value or premium redemption at maturity

Renong Berhad (a Malaysian company) issued a 5-year bond with

a 2.5 percent coupon with yield-to-put at 7.5 percent and a put
price of 129.7. This is above the par of 100 used in the calculation
of conversion into stock. Also, this results in increased downside
protection in case the equity portion has low value.

Investors’ perspective
Even if the conversion turns out to be unprofitable, they are
guaranteed a 7.5 percent return to the time of the put.

7
 Convertible bond issued by the Bank of East Asia
US$250,000,000
2.00 percent Convertible Bonds due 2003

Issue date July 19, 1996

Issue price 100 percent of the principal amount of the Bonds,

plus accrued interest, if any, from July 19, 1996
(in denominations of US$1,000 each)

Conversion period From and including September 19, 1996 up to and

including July 7, 2003

8
 Conversion feature

Conversion price HK$31.40 per Share and with a fixed rate of

exchange on conversion of HK$7.7405 = US$1.00.

Dilution protection The Conversion Price will be subject to adjustment

clause for, among other things, subdivision or consolidation
of the Shares, bonus issues, right issues and other
dilutive events.

9
 Put feature

Redemption at the On July 19, 2001, the Bonds may be redeemed at

option of the the option of the Bondholders in US dollars at the
bondholders redemption price equal to 127.25 percent of the
principal amount of the Bonds, together with
accrued interest.

The investors are protected to have 27.25% returns on the bond

investment upon early redemption by the issuer.

10
 Call feature
Redemption at the On or after July 19, 1998, the Issuer may redeem
option of the the Bonds at any time in whole or in part at the
bondholders principal amount of each Bond, together with
accrued interest, if for each of 30 consecutive
Trading Days, the last of which Trading Days is
not less than five nor more than 30 days prior to
the day upon which the notice of redemption is
first published, the closing price of the Shares as
quoted on the Hong Kong Stock Exchange shall
have at least 130 percent of the Conversion Price
in effect on such Trading Day.

11
 Soft call protection

Parisian feature
The closing price has to be above 130 percent of the conversion price on
consecutive 30 trading days.

• On the date of issuance of the notice of redemption (treated as day 0),

the Issuer looks back 5 to 30 days (corresponds to [-30,-5] time
interval) to check whether the history of the stock price path
satisfies the Parisian constraint. That is, the last of the 30 trading days
(with closing price above 130% of the conversion price) falls in [-30,-5]
time interval.

• From Issuer’s perspective, when the Parisian constraint has been

satisfied, the Issuer has 5 to 30 days to make the decision on
redemption or not.
12
 Reset feature in convertible bonds

In most cases, the reset on conversion price is downward and this makes
the bond more valuable. For example, the conversion number is reset
by dividing the par by the prevailing stock price.

Floor limit
The extent of downward reset cannot be below a certain multiplier of
the first conversion price.

13
Hong Kong example - market manipulation on conversion

China Travel
China Travel (a red chip company in Hong Kong) issued a convertible
bond with coupon rate 4.25% per annum in Nov., 1993, near the peak of
1993 bull market, with maturity date in Nov., 1998. The conversion price
is HK$3.66.

• Market background

Stock price jumped from HK$1.24 at the beginning of 1996 to HK$6.1 on

11 Aug., 1997 (historical high). The share price was seen to be
overvalued. The management would like to convert the debt into equity.

14
• Possible market manipulation
China Travel owned more than 30% of its company’s total shares, and
the red chip stocks were widely held by other red chip companies.
Therefore, it was relatively easy to push up the share prices in bull
market situation.

• Constraint on calling
The daily closing stock price had to stay over HK$5.49 (call price =
150% x conversion price) for more than 20 of the 30 consecutive
trading days. This provision makes market manipulation more difficult
and easily detectable.

15
Failed attempt of conversion
• On 6 Aug., 1997, the share price went above the call price for the
first time and managed to stay above for 17 trading days.

• In Sept., 1997, the share price stayed above the call price for two
more days (only one day short of the call requirement).

• Unfortunately, the share price went down under the general market’s
big drop.

• Within two months after the failed attempt, the share price dropped
below HK$3.66, and within one year, it fell below HK$1.0.

• The share price of China Travel fell much faster than the general
stock market, suggesting a strongly inflated price before the market
crash.
16
 Premium for conversion right

• An investor who purchases a convertible bond

rather than the underlying stock typically pays a
premium over the current market price of the stock.

• Why would someone be willing to pay a premium

to buy this stock? The market conversion premium
per share is related to the price of a call option –
limit the downside risk of the convertible bond.

17
Analytics of convertible bonds

stock price $30.00 per share

stock dividend $0.50 per share
convertible market price $1,000
coupon rate 7.00%
maturity 20 years
conversion price $36.37

Stock dividend yield = annual dividend rate

/ current stock price
= $0.50 / $30.00 = 1.67%
18
 Conversion ratio
= number of shares for which one bond may be
exchanged
= par / conversion price
= $1,000 / $36.37 = 27.50 shares

Conversion value
= equity value or stock value of the convertible
= stock price x conversion ratio
= $30.00 x 27.50 = $825.00

19
 Conversion premium
= (convertible price – conversion value)
/ conversion value
= ($1,000 – $825) / $825.00 = 21.21%

Dollar premium
= convertible price – conversion value (expressed
in points)
= ($1,000 – $825) / $1,000 x 100%
= 17.50 points

20
 Break even calculations
Break even (years)
= conversion premium / (convertible yield – stock yield)
= 21.21 / (7.00 – 1.67) = 3.98 (years)

Number of years necessary for the stock investor to recover

the conversion premium from the convertible’s higher
income relative to an instrument of an equivalent amount in
the stock.

After 3.98 years, the convertible has made up, in income

alone, the amount of the conversion premium.
21
 Break-even calculations (cont’d)

Dollar maintenance
market price – conversion value
=
coupon − market price stock dividend
stock price

The time it takes for the convertible yield advantage to

pay for its premium compared to an equivalent dollar
amount purchased of the underlying stock.
• May use conversion ratio instead of market
price/ stock price.
22
 Weaknesses of break-even analysis

• It ignores the main advantage of convertible:

protection on downside risk on the underlying
equity.
• It ignores the margin of safety offered by the
convertible with the payment of principal at
maturity.

23
 Convertible = bond + warrant

Factors that affect the bond component

• Interest rates
• Credit rating/spreads
• Coupon
• Duration

Factors that affect the warrant component

Stock performance
• Embedded strike price
• Common dividend yield and dividend growth rate
• Stock volatility
• Life of warrant / call protection

24
 Put plus stock plus yield advantage

Applying the put-call parity:

call + bond = put + stock.
Here, put is the right to sell the stock for bond

One may treat a convertible bond as yield-enhanced stock

plus a put option.

• The put option represents the bond floor protection.

The strike price is the bond investment value.

25
 Casino operator brings ringgit convertible
• Malaysia's only casino operator, Resorts World,
has raised M$1.1 billion ($300 million) from a
convertible bond that was well received despite
offering a negative yield.
• Issuing the zero-coupon bonds at par and setting the
redemption price at 99%, which results in a yield to
maturity of -0.5%. Desire to see bonds convert
prompts Resorts World to use rare negative yield
structure.
• The conversion price was fixed at launch at 10%
over yesterday's (September 7, 2006) volume
weighted average price of M$11.593, giving an initial
26
conversion price of M$12.75.
• There is an issuer call after one year, subject to a 120%
hurdle, to force conversion in case investors drag their
feet.
• The reset mechanism has a floor at 90.9% of the original
conversion price, which is high compared with the
typical reset floor at 80-85%. The floor is equal to
yesterday's volume weighted average price.
• The bonds were priced assuming a credit spread of 40
basis points over the Malaysian interest rate curve, a
dividend yield of 2.2% = 120% of the previous year's,
and a stock borrow cost of 5%. Note that the issuer is
essentially shorting stock.
27
Issuer’s perspectives
• While common a few years back when interest rates were
much lower, negative yields are rarely seen on CBs
nowadays but highlights the issuer's desire to have the
bonds convert in order to get equity on its balance sheet.
• The bonds have a short maturity of only two years, a
conversion premium of only 10% and two conversion
price resets - after the first year and 60 days before
maturity - making it all but inevitable that the bonds will
convert.
• The issuer is essentially saying that it is happy to sell
equity at today's market price, but not lower. The
expected appreciation of the ringgit makes the bonds a
reasonable proposition. 28
Investor’s perspectives

• The bond floor was set at 90.7%, which one observer

says is "reasonably attractive" given the strong focus
on conversion and the implied volatility is 24%. This
would mean if no conversion occurs at maturity, the
loss in value is about 10%.
• Analysts are, however, optimistic that the company's
casino operations will drive earnings growth, and of
the 19 analysts that cover the company, according to
Bloomberg data, 16 have a "buy" or "overweight"
recommendation.

29
• The share price is up a modest 4.5% this year to
Thursday's closing price of M$11.70, which
compares with a 6.2% gain in the Kuala Lumpur
Composite Index.
• There is no stock lending available at the moment,
although Resorts World, which is a subsidiary of
conglomerate Genting, is among a group of stocks
that is qualified for short-selling once this becomes
available.

30
 Intrinsic value of convertibles
The intrinsic value of a convertible bond is the greater of
1. Conversion value
2. Bond investment value – value as a corporate bond
without the conversion option (based on the convertible
bond’s cash flow if not converted).

• To estimate the bond investment value, one has to

determine the required yield on a non-convertible bond
with the same quality rating and similar investment
characteristics.
• If the convertible bond does not sell for the greater of
these two values, arbitrage profits could be realized.
31
 Bond investment value
• Present value of the interest and principal payments discounted at the
straight (non-convertible) bond interest rate
n
C P
bond interest value = ∑
t =1 (1 + r ) t
+
(1 + r ) n

where P = par value, r = discount rate, C = coupon rate,

n = number of periods to maturity.

present present
value value
Years payment factor
1 - 20 $80 8.514 $681.12
20 $1,000 0.149 $149.00
$830.12
take r = 10%
32
 Estimation of the discount rate

Use the yield-to-maturity of a similar non-

convertible bond as a proxy.

• The apparent deterioration of the creditworthiness

of an issue will not be reflected in the convertible
price because the common stock may be rising
due to higher share price volatility.

33
 Valuation of convertible debts
List of parameters
Coupon rate
Creditworthiness of the issuer
Maturity date
Conversion premium
Ratio of conversion price to current stock price
Volatility of the stock price
Dividend yield of the stock price
Presence of other embedded option features, like callability
and puttability
Prevailing risk free interest rate and volatility of interest rate
Correlation of the stock price with the interest rate
34
 Duration
Duration is the weighted average of the times that the
principal and interest payments are made.
n

∑ t
tC
t =1
/(1 + i ) t

duration = n

∑ t
C
t =1
/(1 + i ) t

where t is the time of payment

Ct is the coupon and/or principal payment
i is the market yield.

Duration analysis provides a measure how bond

values change with changing interest rates.
35
Duration analysis applied to convertibles
The approximation for the convertible bond’s interest
rate sensitivity
⎛ C/I ⎞
D = Dadj ⎜1 −
cv
⎟
⎝ 2 ⎠
where C = conversion value and I = investment value.
• The equity component of the convertible bond may
dampen the convertible’s interest rate sensitivity,
depending on the bond’s equity participation.
Hence, convertibles trading high above their
investment value will be less sensitive to interest
rates. 36
 Duration and coupon
For non-convertible bonds, the duration decreases
as their coupon increases. This is because higher
coupon bonds deliver more cash flows near the
start of bond’s life.
With convertible feature, the higher coupon rate
may lead to lower propensity to convert. The CB
then has a longer life, so this leads to higher
duration.

These two effects are counteracting.

37
 Interest rate sensitivity
1. The exercise price is a function of the investment
value. An increase in interest rates will lower the
investment value.

2. However, the exercise price of the embedded call

is reduced. A lower exercise price will increase the
value of the warrant.

38
 Interest rate sensitivity (cont’d)
Basic Int rate Change Int rate Change
price + 1% -1%
_______________________________________________________
Investment value $847.84 $812.75 -$35.09 884.74 $36.90

Warrant value $337.66 $362.58 +24.92 $312.72 -$24.94

Total $1185.50 $1175.33 -$10.17 $1197.47 +$11.92

Percent change -1.02% 1.19%

39
 Correlation with interest rates
Consider the impact of an increase on interest rate
The future share price is expected to be higher because of
higher drift rate.
Due to negative correlation between interest rate and share
price (say, the S&P 500-stock index has a correlation of about
minus 0.5), the share price drops first.

Negative correlations normally lower CB value;

positive correlations make the CB worth more.

In some situation, CBs may have price differences in the range

of 10-15% when correlation moves from 1.0 to –1.0.
40
Pricing of risky convertible bonds
One-factor binomial model
* stock price process follows binomial random walk
* interest rates to be deterministic
Two discount rates
1. If the convertible is certain to remain a bond, it is appropriate
to use a discount rate corresponding to the creditworthiness
of the issuer − risky rate.
2. Suppose the bond is certain to be converted, it is then
appropriate to use the riskfree rate.
At maturity, the holder will choose the maximum between
the par value and the value of stocks received upon
conversion. 41
How to account for the creditworthiness of the issuer?

The discount rate to be used when we roll back is given by

pwu + (1 − p)wd.

Here, p is the probability to a node where the discount rate is

wu and (1 − p) is probability to a node with wd. The appropriate
discount rate is the weighted average of the discounted rates
at the nodes in the next time step.

42
 conv = value of stocks received if conversion takes place
call = call price
roll = value given by the rollback
(neither converted nor recalled)

At each node, the optimal strategy of the holder is exemplified

by taking the maximum of min(roll, call) and conv.
• The maximum reflects the conversion right, which persists
with or without recall by the issuer.
• min(roll, call) means the bond value can never shoot beyond
the call price.

Dynamic programming procedure:

max(min(roll, call), conv)
43
Alternative dynamic programming procedure:

min(max(roll, conv), max(call, conv))

• The term max(roll, conv) represents the optimal strategy of

the holder.

• Upon recall, the holder chooses to accept the call price or

convert into shares. This can be represented by
max(call, conv).

The issuer chooses to recall or to abstain from recalling in

order to minimize the option value.
44
Third dynamic programming procedure:

min(max(roll, conv), call)

• The term max(roll, conv) represents the optimal strategy of

the holder.

• Even under the optimal strategy adopted by the holder,

the bond value is always bounded above by the call price.

45
Example
A 9-month discount bond issued XYZ company with a face
value of $100. Assume that it can be exchanged for 2 shares
of company’s stock at any time during the 9 months.
* It is callable for $115 at any time.
* Initial stock price = $50, σ = 30% per annum and no
dividend; risk-free yield curve to be flat at 10% per annum.
* Yield curve corresponding to bonds issued by the company
to be flat at 15%.
* Tree parameters are: u = 1.1618, d = 0.8607, p = 0.5467,
R = e0.1Δt = 1.0253.
* At maturity, the convertible is worth max (100, 2ST).

46
Binomial tree for pricing a risky convertible bond
equity 78.42
8 10%
67.49 156.84
10%
D
8
58.09 134.98
8
11.03% equity 58.09
B 11%
8116.18 50.00 116.18
50.00 812.27%
11.59% A E
104.85 43.04 8
105.56
8 13.51% 8 bond
43.04
C 15%
98.00 37.04 8 100.00
8 15%
F
96.32
upper figure: stock price
bond 31.88
middle figure: discount rate
lower figure: value of convertible
8 15%
47
100.00
At node D
Roll back gives the bond value
(0.5467 × 156.84 + 0.4533 × 116.18)e-0.1 × 0.25 = 134.98.
The bondholder is indifferent to conversion or hold, also the
issuer is also indifferent as to whether the bond is called;
the correct discount rate at node D is 10%.
At node F
The correct discount rate is 15% since the convertible is
contain not to be converted if node E is reached.
At node E
The correct discount rate is
0.5467 × 10% + 0.4533 × 15% = 12.27%.
The value of convertible at E
(0.5467 × 116.18 + 0.4533 × 100)e-0.1227 × 0.25 = 105.56.
The bond should be neither converted nor called. 48
At node B
The discount rate is
0.5467 × 10% + 0.4533 × 12.27% = 11.03%
and value of convertible is
(0.5467 × 134.99 + 0.4533 × 105.56)e-0.1103 × 0.25 = 118.34.
It is optimal to call the bond at node B so that it causes
immediate conversion and leads to $116.18. The discount
rate at node B should be taken to be 10%, since conversion
takes place at this node.
At node A
The discount rate is
0.5467 × 10% + 0.4533 × 13.51% = 11.59%.
The convertible value at node A is
(0.5467 × 116.18 + 0.4533 × 98.00)e-0.1159 × 0.25 = 104.85.
If the bond has no conversion option, its value is
e-0.75 × 0.15 = 89.36. 49
The value of conversion option = 104.85 − 89.36 = 15.49.
Structured convertibles

- Mandatory convertibles
(performance based conversion premium, parallel debts)
- LYON (Liquid Yield Option Note)
- Exchangeables
- convertible stock notes
- Debt exchangeable for common stock

50
 Mandatory convertible securities
Product nature

• Mandatory convertible into common stock at maturity.

• They are effectively yield-enhanced common stock, and

offer no downside protection to the investor apart from
their higher yield.

• MCS have grown to constitute about 14% of the total US

convertible market.

51
52
 Mandatory convertible securities (cont’d)

• Issue price – lower strike price: The same as the common stock
price at the time of issue.

• Conversion price – upper strike price: This is the price at which the
MCS are convertible into common stock at a premium to the issue
price.

• The conversion ratio at maturity changes depending on the price

of the stock.

• At issue, the MCS is priced with a so-called conversion premium,

which determines the level of the strike price for the long call in
the call spread (the upper strike).
53
54
An MCS consists of the following pieces
MCS = underlying common stock (stock price × lower
conversion ratio)

+ (out-of-the-money call option on the

underlying common stock struck at the upper
strike price) × upper conversion ratio

− at-the-money call option on the underlying

common stock struck at the lower conversion
ratio

55
56
 Perspective of the investor

• MCS involves the forward sale of equity at a price

higher than the current stock price, but without the
traditional downside support of investment value of
a normal convertible.
• In return, the investor receives a higher dividend.
• Less interest rate sensitive but more equity sensitive
compared to convertibles.

57
Numerical example
Stock price at issue $27.875
Upper strike $30.750
Lower strike $25.000

Valuation
Long stock value $27.875
Long 0.8130 calls struck at $30.750 $5.411
Short 1 call struck at $25 -$9.228
Present value of net cash flow +$4.391
_______
Fair value $28.450

58
Performance based conversion premium
1. If the stock goes up from the issue price, the participation is
at first delayed until the point of the upper strike, and then
rises at a reduced rate equal to the upper conversion
number.
2. On the downside, participation is one-for-one with the
stock.

Why it is called performance based premium

The investor does not actually pay the conversion premium up

front. The declining ratio represents the conversion premium
paid by the investor – paid only when the stock performs well.

Both issuer’s and investors’ interests are aligned.

59
60
 Parallel debt MCS
The higher dividend paid by the issuer is not tax deductible.
To get around the problem: pairing of the equity MCS with a
debt security.

• All the proceeds from the sale of the MCS are invested in
US Treasuries with maturities same as that of the MCS.
• The yield from the Treasuries is supplemented with an
additional fee from the issuer to arrive at the stated yield on
the MCS.

Parallel debt
• The issuer enters the public debt market to issue an interest
bearing note with a maturity and face amount similar to the
terms of MCS.
61
 Parallel debt MCS (cont’d)

• At maturity, the investor delivers either cash (the settlement

fee) or the maturing Treasury note to satisfy the terms of
the purchase contract of the MCS.

• In return, at maturity, the issuer can use these proceeds to

retire the corporate debt obligation.

• The Treasuries are owned by the investor – so the investor

does not need to bear the default risk of the issuer.

• The investor also enjoys a tax benefit from this structure

since that portion of the income received from the Treasury
coupon payments is exempt from state and local taxes.
62
63
 Exchangeable convertible bonds
They are issued by one company and converted into the stock of another company.

Example
Pennzoil owned over 18,000,000 shares of Chevron common stock. Using this stock as
collateral, Pennzoil issued over $902,000,000 worth of bonds convertible into Chevron
shares.

Advantages
Received the proceeds for selling the issues at a 21% premium over Chevron’s
current stock price.
Pennzoil received $33.4 million annually in dividends from the Chevron shares.

Disadvantage
Forfeit the potential upside growth of the stock price.

64
 Liquid Yield Options Note (LYON)

- introduced by Merill Lynch in 1985

1. The bonds were created as zero coupon bonds offered at a deep discount to face
value.

2. Investors were given a put option at a price equal to the original offering price of
the LYONs plus the interest that accrues to the date of the put.

Since the put price is based on a yield-to-maturity consistent with the time frame of the
put, companies can issue what is essentially longer-term debt at rates equivalent to those
of short to intermediate maturities.

65
 LYON example – Motorola Inc. 0% Due 2013
Risk/Reward Table

Time Stock price Bond price Convertible

% change % change participation

DOWNSIDE 1.00 year -32.0 -1.4 4.3%

0.50 year -23.9 -1.8 7.5%

0.50 year 31.5 15.2 48.2%

UPSIDE 1.00 year 47.3 23.4 49.4%

66
Example of LYON – Waste Management, Inc.
Issued on April 12, 1985.
Face value of $1,000 maturing on Jan. 21, 2001.
At any time prior to maturity, the investor may elect to
convert the bond into 4.36 shares of Waste
Management common stock.
Though the issuer may call the LYON immediately
after issuance, the investor does receive some call
protection since the issuer may not call the bond prior
to June 30, 1987 unless the price of the common stock
rises above $86.01.
On issue date, the stock price was $52.125.
67
LYON – Waste Management, Inc. (put prices)
Date Put Price Date Put Price
June 30, 1988 $301.87 June 30, 1995 $613.04
June 30, 1989 $333.51 June 30, 1996 $669.45
June 30, 1990 $375.58 June 30, 1997 $731.06
June 30, 1991 $431.08 June 30, 1998 $798.34
June 30, 1991 $470.75 June 30, 1999 $871.80
June 30, 1993 $514.07 June 30, 2000 $952.03
June 30, 1994 $561.38

68
LYON – Waste Management, Inc. (call prices)
Date Call Price Date Call Price
At issuance $272.50 June 30, 1994 $563.63
June 30, 1986 $297.83 June 30, 1995 $613.04
June 30, 1987 $321.13 June 30, 1996 $669.45
June 30, 1988 $346.77 June 30, 1997 $731.06
June 30, 1989 $374.99 June 30, 1998 $798.34
June 30, 1990 $406.00 June 30, 1999 $871.80
June 30, 1991 $444.08 June 30, 2000 $952.03
June 30, 1992 $477.50 At maturity $1,000.00
June 30, 1993 $518.57

The call prices are increases at a rate of 9% per year

compounded semi-annually.
69
 Stock price for optimal conversion
Date Critical Price Date Critical Price
At issuance $129.50 June 30, 1993 $273.00
June 30, 1985 $132.00 June 30, 1994 $287.00
June 30, 1986 $145.00 June 30, 1995 $301.50
June 30, 1987 $158.50 June 30, 1996 $316.00
June 30, 1988 $173.50 June 30, 1997 $329.50
June 30, 1989 $194.50 June 30, 1998 $339.00
June 30, 1990 $217.00 June 30, 1999 $340.00
June 30, 1991 $238.50 June 30, 2000 $317.50
June 30, 1992 $257.00 Jan. 21, 2001 $229.36
June 30, 1993 $518.57

70
Some properties of zero-coupon convertibles
It is most sensitive to interest rate changes since only
par is paid at maturity.

With conversion ratio fixed, as the bond value moves

toward par, the conversion price rises. Hence, in
order for it to be worthwhile for the investor to
convert, the stock price must rise at least as fast as
the bond price accrues.

Since the call option is less valuable, the zero-coupon

convertibles should be issued with a lower
conversion premium.
71
 Rationale for issuing exchangeables
The issuer wants to monetize the value of a non-strategic
asset in a tax-efficient manner. This an alternative form of
capital raising. The shares in a third company may be held
due to aborted takeover.

The issuer receives the proceeds of the sale immediately

(at a premium to the current share price and may gain
advantage from higher volatility of share price prior to
aborted takeover), but does not have to pay capital gains
tax until the bonds are actually converted several years in
the future.
72
 Asset-linked convertibles
Combined the security of fixed income with convertibility into precious metal
instead of common stock.

Example
Sunshine Mines issued a convertible bond with a 15-year maturity and an 8.5 percent
coupon, convertible into silver at $20 an ounce.

The issuer is willing to share the potential price appreciation of the underlying
commodity in exchange for a lower coupon rate and better terms in bond
indentures.

Payouts can be in either the commodity or its cash equivalent.

Investors looked to metal to preserve their capital when inflation is pronounced.

As inflation leveled its peak in the early 1980s, interest in asset-linked convertibles
also faded.

73
 CrEDITS structure
(Credit Enhanced Debt Indexed To Stock)

• Characteristic
Principal and coupon payments are guaranteed by an irrevocable letter
of credit from a highly rated financial institution.

• Issuer’s perspective
Pay a lower coupon rate. Get the credit guarantee by paying amount
less than the coupon rate differential.

- Six percent coupon rate is reduced to four percent but with

principal and income guaranteed by a high-rated third party.
This works well if the protection requires less than the 2
percent coupon rate differential.
74
 CrEDITS structure (cont’d)

Attraction to investors

1. Upside potential of an emerging market or growth stock;

2. A name with high stock volatility;

3. High-quality downside protection that is uncorrelated to the shares.

Example
Indian Petrochemicals Corporation and GVC (a Taiwanese technology
company)

75
 Convertible stock notes
• Instead of paying interest and principal in cash, these notes
pay in common stock or cash, at the issuer’s option
(designed to give issuers flexibility in managing cash
flow).

• They are typically issued by troubled companies.

Companies facing bankruptcy often ask creditors to
exchange debt for convertible stock notes (allowing for
increased equity participation but forfeiting coupon
incomes).

76
 Example
Anacomp - facing bankruptcy in the mid-1980s
• proposed to exchange the convertible 137/8
percent bonds for convertible stock notes with higher
conversion ratio (increased to 250 shares per bond
from 57.143).

As the stock price recovered to $8 (original conversion

price was $17.50) in mid-1987, the new convertible
stock notes had an intrinsic value of 200% of par.
This illustrates the advantage of being a creditor
rather than a shareholder when a company’s fortunes
77
change.
 Convertibles as a means of
cheap financing
Sweeten debt
Allow firms to borrow cheaply relative to
straight debts.
Convertibles protect companies with high and
indeterminate risk from a prohibitive cost of
straight debt.

Remark Should not ignore the liabilities

associated with the convertibility
feature.
78
Considerations for corporate treasurers

What are the costs associated with issuing equity,

debt, or convertibles. Quantify them using a
weighted cost of capital for debt and equity.

What is the probability of financial distress or

embarrassment caused by a given capital structure?

Consider the design of the corporate structure as a

marketing problem. What types of investors will be
attracted to the various pieces of the corporate pie?

79
 Financing strategies
Advantage of equity as a source of financing –
excellent insurance properties against financial
distress.

Equity will be issued by the more pessimistic firms.

Straight debt will be issued by the more optimistic
firms.
Convertible debt will be issued by medium-quality
firms.

80
Small, fast growing companies

Such companies have comparative advantage in the convertible

market versus the fixed income market.

They lack a long-term track record and have volatile capital

structures – high coupon must be offered.

They can transform the high volatility into a benefit since the
warrant is more expensive.

When the company grows, they may call the bonds. This in
turn will strengthen the company’s equity base at the moment
when it is most needed.

81
 Convertibles as backdoor
equity financing
Delayed equity
Convertibles provide a way of selling common stock
at a price above the existing market.
They are employed as deferred common stock
financing.

The call feature is important since it gives the

company the means to shift debt to equity.

Convertibles offer a means to control the

debt/equity ratio.
82
 Findings from questionnaires
Pilcher (1955) Brigham (1966) Hoffmeister (1977)

Delayed equity 82% 68% 40%

Sweeten debt 9% 27% 37%

Others 9% 5% 23%

83
 Reason(s) for Offering
Neither
Strongly Agree Nor Strongly
My firm chose convertible as its financing source … Disagree Disagree Agree
1 2 3 4 5
a. because of the lower coupon rate versus straight debt. 4.7% 4.7% 4.7% 50.6% 35.5%
b. because management felt that the stock was undervalued
16.9% 14.5% 24.1% 25.3% 19.3%
at the time.
c. because management felt that the stock was overvalued
42.7% 19.5% 31.7% 3.7% 2.4%
at the time.
d. as "delayed equity" financing, expecting that the debt
7.0% 3.5% 5.8% 46.5% 37.2%
would be converted.
e. because the conversion feature provides bondholders with
protection against unfavorable actions by stockholders or 45.1% 20.7% 28.0% 6.1% 0.0%
management.
f. because our investment banker recommended it over
10.7% 8.3% 45.2% 29.8% 6.0%
other forms of financing.
g. because other firms had recently made successful
10.8% 10.8% 33.7% 42.2% 2.4%
convertible offerings.

84
 Reasons for Offering (cont’d)
By order of importance, please rank the following factors on a scale of
1 to 6 on the extent to which it influenced your firm’s decision to issue
convertible; 1 = most influential, 2 = next most influential, etc.)

1 2 3 4 5 6
Lower coupon versus straight debt 48.3% 25.0% 13.3% 5.6% 5.6% 1.2%
stock was undervalued, so we couldn't issue equity 15.7% 22.6% 7.8% 11.3% 7.0% 28.0%
Stock was overvalued, so we took the opportunity
to lock in a favorable conversion premium 3.4% 4.8% 2.2% 7.0% 26.8% 52.4%
Firm wished to issue "delayed equity" 22.5% 31.0% 20.0% 12.7% 14.1% 2.4%
Investment banker recommended it 7.9% 4.8% 27.8% 38.0% 18.3% 7.3%
Other firms had recently issued convertible debt successfully 2.20% 11.90% 28.90% 25.40% 28.20% 8.50%

85
 Environment in which issuance occurred
1. In retrospect, my firm’s stock was _____ valued around the time
of the convertible debt offering.
under correctly over
1 2 3 Mean Median
46.4% 41.6% 12.0% 1.66 2.00
2. Around the time of the convertible debt offering, my firm’s
management expected future earning to be _____ the market was
expecting.
about the same as much higher than
2 3 4 5 Mean Median
3.6% 49.4% 35.1% 11.9% 3.55 3.00

3. At the time of the convertible debt offering, prospects for my

firm’s short-term (1-2 years) performance relative to its industry
were:
poor fair good very good excellent
1 2 3 4 5 Mean Median
2.4% 5.9% 34.1% 47.1% 10.6% 3.58 4.00

86
 Equity-like returns with less risk

Convertible securities are an appropriate investment

vehicle for long-term investors seeking a high rate of
total return but with less risk than common stock.

Convertible investors hope to earn two-thirds of the

upside return with only one-third of the downside
risk.
- In bull markets, convertibles have trailed global
equity markets by only a few percentage point
- In bear markets convertibles offer considerably
more downside support. 87
 Convexity ratio
• Classic “two-thirds upside, one-third downside”

• Convexity ratio is the ratio of upside and downside

participation.

For example, suppose the convertible provides 64% of the

upside participation with only 34% of the downside
movement, then the convexity ratio is 1.85. That is, the
convertible provides 85% more upside participation than
downside risk.

88
 Risk-reward relationship
Performance of various asset classes, 1973-1995

Compound annual return standard deviation

Convertible bonds 11.70 % 12.47%

S&P 500 11.84% 17.27%

Long-term corporate bonds 9.66% 12.44%

Intermediate-term 9.91% 8.93%

corporate bonds

Source: Goldman Sachs Global Convertible Research (1996)

“Convertibles as an Asset Class.”

89
 Insulation from volatility
The price movements of convertibles are generally far less volatile.

Convertible Bond Price Changes,

August 24, 2001-September 2001
Common Stock Convertible
Closing Price Closing Price % Closing Price Closing Price %
Company 8/24/01 9/21/01 Change 8/24/01 9/21/01 Change
Avon Products 45.89 44.04 4.03 51.13 51.25 0.24
Bell Atlandtic/
17.85 14.15 -20.73 100.50 101.25 0.75
New Zealand Tel
Diamond Offshare 27.90 26.35 -5.56 83.50 84.13 0.75
Federal Realty Trust 23.62 20.32 -13.97 93.25 87.13 -6.57
INCO 17.55 12.45 -29.06 99.38 97.25 -2.14
Average -14.15 -2.78
DJIA 10423.20 8235.81 -20.99 -20.99
S& P 500 1184.90 965.80 -18.49 -18.49
NASDAQ 1916.80 1423.19 -25.75 -25.75

90
• Adding convertibles to either bonds or stocks moves the efficient
frontier lower in terms of risk and higher in terms of reward.91
 Long term convertible performance
• Over the period for which reliable long-run data are
available (since early 1970s), the total return performance
of US convertibles has virtually replicated that of the
S & P 500, but with significantly lower risk.

• Over the same period, convertibles have significantly

outperformed long-term corporate bonds while
demonstrating comparable risk.

• Total return for convertible bonds has demonstrated a

much higher correlation with the S & P 500 than with
the corporate bond market.

• Convertibles can help maximize performance in both

equity and fixed-income portfolios.
92
Possible reasons for the better performance
Inefficient company timing in calling convertible issues
If a deep-in-the-money convertible enjoys a significant yield
advantage over the common stock but it is not called, it is likely to
outperform the underlying stock. Companies may delay conversion
for a number of reasons including balance sheet and rating agency
considerations.

Attractive convertible pricing at issue

Typically, convertible securities are initially priced several
percentage points cheap to their theoretical value in order to insure
a successful launch. These securities trade higher in the
immediate after-market.
Apparently, companies are prepared to offer attractive terms in
order to assure entry to the capital markets and to enjoy the
tax benefits offered by convertibles. 93
 What is a busted convertible?

The underlying stock is far out-of-the-money – the convertible trades

on its fixed income characteristics.

Busted convertibles are characterized by low equity price sensitivity

(low delta), large conversion premium and high yield to maturity.

• delta < 4%

• conversion premium > 75%

• yield more than 10%

Average credit quality of the busted convertibles is BB- versus BB+

for the entire domestic universe. 94
95
Advantages
• In contrast to junk bonds, the upside potential is not capped – may
enjoy unlimited upside potential if the stock price recovers.

• With busted convertibles, the equity warrant (deep out-of-the-money)

is often mispriced. Investors are effectively buying high yield debt
with a free equity kicker.

• Busted convertibles are more attractive investment than high-yield

debts in a modern economy that has shifted from slow growth,
cyclical companies to more volatile growth companies.

96
Disadvantages

• Busted convertibles are often more illiquid. Traditional convertible

investors become sellers as equity sensitivity diminishes.

• Convertible securities are generally subordinate to other creditors

in the event of a liquidation or bankruptcy.

• The biggest risk is continued credit deterioration.

Analyzing busted convertibles is a research intensive process involving

both equity and credit analysis.

97