328 A.H.Y. Chen et al. International Review of Economics and Finance 8 1999 327–338
synthetic equity products.
1
For instance, PERCS Preferred Equity Redemption Cumu- lative Stock, first issued in 1988, are redeemable convertible preferred stocks designed
to provide the holders with an enhanced dividend rate in exchange for a limited potential for capital appreciation, usually in the 30–40 range. During the early 1990s,
PERCS were used to rescue more than a dozen of companies that attempted to restructure their balance sheets in the wake of junk bond market crash.
2
However, demand for PERCS has tailed off since 1993 because certain PERCS investors, notably in growth and income funds, do not like the total cap on the upside.
To plug a gap in the convertibles market, Salomon Brothers designed another equity- like convertible security called DECS Dividend Enhanced Convertible Stock in 1993.
DECS are like PERCS as both are redeemable convertible preferred stocks. But unlike PERCS that cap their upside at 30–40, DECS offer an upside capital appreciation
potential when the underlying common stock rises above the conversion price.
Since 1993, several DECS variations have been developed. But rather than use a generic name, each investment bank has invented its own acronym: ACES Automati-
cally Convertible Equity Securities by Goldman Sachs; PRIDES Preferred Redeem- able Increased-Dividend Equity Securities; STRYPES STRuctured Yield Product
Exchangeable for Stock by Merrill Lynch; and SAILS Stock Appreciation Income- Linked Securities by Credit Suisse. The common characteristics of the above acronyms
are as follows: 1 they are high-income exchangeable securities which convert into common stock, either in the issuing company or its subsidiary; 2 conversion is
mandatory at maturity three to five years, with each instrument held usually con- verting into a minimum of around 0.8 and a maximum of one share; and 3 they pay
higher yields than the underlying, normally between 6 and 9 and have a 2 to 3 yield advantage over comparable convertible preferred stock. Nicholls 1996 reported
that there had been 35 issues since the introduction of the instruments in 1993, representing around 25 of U.S. domestic convertible issuance.
Currently, convertibles are no longer considered the financing tool of last resort and, in fact, they have become far more complicated by being associated with a myriad
of specially structured products labeled with an alphabet soup of acronyms. Follow- ing the remarkable success of the aforementioned equity-like convertible securities,
the purpose of this article is to examine the first DECS issued by Masco Tech Inc. in 1993, which was later cloned by ACES, PRIDES, SAILS, and STRYPES. The
remainder of the article is organized as follows: the characteristics of DECS and the theoretical valuation of DECS are discussed in Section 2; the empirical test results
on the DECS pricing model are presented in Section 3; and a brief summary is provided in Section 4.
2. Valuation of DECS
On July 1, 1993, Masco Tech Inc. issue 10 million shares of DECS to the public at 20 per share, which is the closing price of the Masco Tech common stock on June
30, 1993. The holders of DECS are entitled to receive enhanced preferential dividends
A.H.Y. Chen et al. International Review of Economics and Finance 8 1999 327–338 329
payable quarterly at the annual rate of 1.2 per share versus the current annual rate of 0.08 per share of common stock.
Specifically, DECS are redeemable convertible preferred stocks. On July 1, 1997, the mandatory conversion date, each of the outstanding DECS automatically converts
into one share of Masco Tech common stock. However, prior to the mandatory conversion date, the holders of DECS may elect to convert into 0.806 of a share of
common stock for each DECS. The equivalent conversion price is 24.81 with a 24.05 conversion premium above the initial offering price. DECS are also redeemable at
the option of Masco Tech on or after July 1, 1996, the initial redemption date, for fractions of common shares having a market value equal to 20 plus all accrued and
unpaid dividends.
3
To simplify the analysis, we first assume that the initial redemption date coincides with the mandatory conversion date. The payoff for a DECS at maturity can be
expressed as follows:
V
T
5
5
F S
T
2 X
2
1 X
1
if S
T
. X
2
; X
1
if X
1
S
T
X
2
S
T
if S
T
, X
1
. 1
where V
T
5 payoff for a DECS at maturity T; F 5
0.806; S
T
5 the prevailing stock price at maturity; X
1
5 exercise price of 20.00; and X
2
5 exercise price of 24.81. Eq. 1 can be interpreted as follows. At maturity, if Masco Tech’s common stock
price exceeds the equivalent conversion price of 24.81, the DECS holder may elect to convert into 0.806 of a share of common stock, or FS
T
, for each DECS. It can be shown easily that FS
T
5 FS
T
2 X
2
1 X
1
because X
2
5 X
1
F. If the stock price drops below the DECS’ initial offering price of 20, Masco Tech neither will redeem the
outstanding DECS early, nor will the DECS holders exercise their conversion option. Consequently, DECS will automatically convert on the mandatory conversion date
into one share of common stock per DECS share. However, if the stock price falls between 20.00 and 24.81, it is optimal for Masco Tech to redeem DECS and each
DECS holder will receive a fraction of a share between 0.806 and 1.0 worth 20.
The theoretical payoff for a DECS is also presented in Table 1. Column 5 shows the payoff for a bull call spread, that is, buying a call option on Masco Tech common
stock with exercise price equal to X
1
and simultaneously selling Fcall options on the same stock with exercise price equal to X
2
. Column 6 presents the payoff for holding a covered bull call spread, that is, holding a long position in Masco Tech common
stock and a short position in a bull call spread. As shown, the payoff in column 6 is identical to that of holding a DECS presented in column 7. Thus, Eq. 1 can be
further rearranged as follows:
→
A.H.Y. Chen
et al.
International
Review of
Economics
and Finance
8 1999
327–338 Table 1
Payoff for holding a DECS at maturity 1
3 4
5 5 3 1 4 6 5 2 2 5
7 Stock Price
2 Long
Short Bull Call Spread 5
Long Stock 2 Long DECS
S
T
Long Stock C
X
1
F CX
2
C X
1
2 FCX
2
Bull Call Spread V
T
S
T
, X
1
S
T
S
T
S
T
X
1
S
T
5 X
1
X
1
X
1
X
1
, S
T
, X
2
S
T
S
T
2 X
1
S
T
2 X
1
X
1
X
1
X
2
S
T
5 X
2
X
2
2 X
1
X
2
2 X
1
X
1
X
1
X
2
, S
T
S
T
S
T
2 X
1
2FS
T
2 X
2
S
T
2 X
1
2 FS
T
2 X
2
X
1
1 FS
T
2 X
2
X
1
1 FS
T
2 X
2
V
T
5 payoff for a DECS; X
1
5 exercise price of 20.00; X
2
5 exercise price of 24.81; F 5 0.806; and C. 5 call option.
A.H.Y. Chen et al. International Review of Economics and Finance 8 1999 327–338 331
Fig. 1. Maturity payoffs for long stock and short bull call spread a. Maturity payoff for holding a DECS b.
V
T
5 S
T
2 Bull Call Spread 5 S
T
2 {Max[0, S
T
2 X
1
] 2 FMax[0, S
T
2 X
2
]}. 2
The graphical counterpart of Table 1 is depicted in Fig. 1. The maturity payoff for a long position in common stock and a short position in a bull call spread is shown at
the top of Fig. 1, and the maturity payoff for holding a DECS is shown at the bottom of Fig. 1. As shown in Fig. 1, the opportunity for equity appreciation by holding a
DECS is not capped on the upside as PERCS, but it is less substantial than the opportunity for equity appreciation afforded by an investment in the common stock.
This is because Masco Tech may, at its discretion, redeem the DECS if the market price of common stock exceeds the conversion price, thus lowering the potential equity
332 A.H.Y. Chen et al. International Review of Economics and Finance 8 1999 327–338
appreciation. In such event, the DECS holder will receive less than one 0.806 share of common stock for each DECS. The dotted area at the bottom of Fig. 1, therefore,
represents the lost opportunity for equity appreciation. To compensate for the foregone partial equity appreciation potential, the DECS holder will receive for four years a
higher annual preferred dividend rate of 1.20 per share as opposed to the current annual dividend rate of 0.08 on common stock.
Finally, the value of a DECS at time zero is simply the sum of the present value of Eq. 2 and the present value of the incremental dividend stream:
V 5 S 2 {C[S,X
1
5 20,T] 2 FC[S,X
2
5 24.81,T]} 1 I, 3
where V 5
current DECS value; S 5
current common stock price; C
. 5 call option; X 5
exercise price; T 5
time to maturity; and I 5
present value of the incremental dividend stream. The expression in Eq. 3 shows that a DECS can be decomposed into a package
analogous to: 1 a long position in Masco Tech common stock; 2 a short position in a bull call spread; and 3 the incremental dividend stream. Specifically, the DECS
holder writes a four-year bull call spread and sells it to Masco Tech in exchange for a stream of enhanced dividend rate.
Valuation of a DECS is further complicated since dilution in stock price upon DECS conversion or redemption is inevitable. Given that each DECS will be converted into
a fraction of a share of common stock between 0.806 and 1.0, the outstanding shares of common stock upon conversion or redemption will increase between 16.26 and
20.18.
4
Thus, the call options embedded in DECS are unequivocally warrants in nature and the conventional Black and Scholes 1973 option pricing model cannot be directly
employed here without some adjustments for the impact of dilution as follows:
5
W 5 [NNQ 1 M]{[S 2 Se
2
rT
D 1 MNW]Nd
1
2 e
2
rT
XN d
2
}, 4
where W 5
current warrant price; N 5
the number of outstanding shares of common stock; Q 5
the number of shares that can be purchased by each warrant; M 5
the number of warrants; D 5
the dollar amount of dividend per share; X 5
exercise price; d
1
5 {ln[S 2 Se
2
rT
D 1 MNWX] 1 r 1
1
⁄
2
s
2
T}sT
1⁄2
; d
2
5 d
1
2 sT
1⁄2
; s 5 the standard deviation of the return of S 1 MNW per unit time; and
N . 5 cumulative normal density function.
A.H.Y. Chen et al. International Review of Economics and Finance 8 1999 327–338 333
As shown in Eq. 4, three modifications to the conventional Black and Scholes option pricing model are necessary. First, S 1 MNW must be substituted for the
stock price, which represents the equity per share of stock. Second, the standard deviation used in Eq. 4 is the standard deviation of equity, i.e., S 1 MNW, rather
than the stock volatility. Finally, the entire conventional Black and Scholes model is multiplied by NNQ 1 M. Furthermore, a direct solution in Eq. 4 for the warrant
price is not possible as W appears on both sides of the equation. Hence, the solution must be solved through an iterative process.
Substituting the dilution-adjusted Black and Scholes option pricing model in Eq. 4 into Eq. 3 for C yields:
V 5 S 2 {W[S,Q
1
5 1,X
1
5 20,T] 2 FW[S,Q
2
5 0.806,X
2
5 24.81,T]} 1 I, 5
Where W[.] 5 current warrant price as a function of current stock price, the number of shares that can be purchased by each warrant, exercise price, and time to maturity.
Furthermore, since DECS are also redeemable at the discretion of Masco Tech on or after July 1, 1996, we follow Finnerty 1993 in handling early redemption and
conversion issues. Specifically, each DECS share is valued using Eq. 5 based on six alternative redemption dates, i.e., the initial redemption date, the four dates when
the redemption price steps down, and the maturity date. Since Masco Tech controls the optional redemption provision and will rationally choose the exercise date that
minimizes the value of the outstanding DECS, the lower of the six estimated values outlined above is used as the predicted DECS value.
3. Application of DECS
