Summary
Given the importance of Dividend Protection for convertibles
in today’s financial markets, we continue to improve and elaborate on the Kynex
valuation model. In the new release, we have implemented a probability-weighted calculation of the conversion ratios (at the
grid nodes in the finite-difference grid). This new algorithm is implemented to
better capture the path-dependence of the conversion ratio when dividends are
paid. As is well-known to investors, the conversion ratio adjustment on an
ex-dividend date depends on the stock price level immediately prior to the
ex-dividend date. This fact necessarily means that the conversion ratio, on a
given future date, will depend on the precise path followed by the stock price
up to that date. As an example, we construct a simple binomial tree. The
initial stock price is
, after one period the stock price goes up to 
or down to
. A dividend of 
is paid at this time.
In the next period the stock price goes back to. See the diagram below.
Suppose the initial conversion ratio is
. The usual
ratio-adjustment formula for dividend protection (assuming a dividend anchor of
zero) is
(1) 
At the “up” node the new ratio is
(2a) 
However, at the “down” node the new ratio is
(2b) 
Hence, at the final node, where, the conversion ratio can be either 10.08065 or 10.12658,
depending on the path followed by the stock price. The stock price can follow
multiple paths to reach any given node in the future. Therefore, all future
nodes in the grid do not have a pre-known unique conversion ratio. The new
probability-weighted algorithm is designed to capture this path-dependence more
accurately.
We continue to investigate whether dividend protection, via conversion ratio adjustments, fully compensates investors against future dividends that are in excess of the anchor dividend amount. The formula for the conversion ratio adjustment is structured so that the parity will be unchanged by the payment of the dividend. The formula in equation (1) clearly shows that
(3) (New ratio) x (new stock price) = (old ratio) x (old stock price)
I.e. the parity is unaffected by the drop in the stock price.
Our research and analysis reveals that the ratio adjustments can either under-compensate or over-compensate investors. There is no simple formula or pattern as to how the fair value will be affected. If future dividend estimates are in excess of the anchor dividend amount, the impact on the fair value of the convertible security today depends on expected life of the convertible, magnitude of the dividend increase, current parity level, stock price level in the market in response to the dividend increase announcement (new information) in addition to volatility and credit spread assumptions.
The modifications to the probability-weighted algorithm also affect the valuation of convertibles with Japanese-style conversion-ratio resets. Note that such bonds may or may not have dividend protection. The reset feature is independent of dividend protection.
We give a list of the convertibles which display the largest differences in fair value as a result of the modifications to the probability-weighted algorithm. We give two lists, one for continuous dividends (Appendix A) and one for discrete dividends for life (Appendix B).
Convertible Securities expected to show meaningful difference from previous versions of our calculator (using continuous dividends).
|
Ticker |
Issuer |
Coupon |
Maturity |
|
Ticker |
Issuer |
Coupon |
Maturity |
|
|
|
|
|
|
|
|
||
|
ABX |
Placer Dome Inc/Barrick
Gold |
2.75 |
10/15/2023 |
|
RYI |
Ryerson Tull Inc. |
3.5 |
11/1/2024 |
|
AFR |
American Financial Realty Trust |
4.375 |
7/15/2024 |
|
SAH |
Sonic Automotive Inc |
4.25 |
11/30/2015 |
|
AHL |
Aspen Insurance Holdings |
5.625 |
NULL |
|
SOV |
Sovereign Bancorp |
4.375 |
3/1/2034 |
|
AIN |
|
2.25 |
3/15/2026 |
|
SPG |
Simon Property Grp |
6 |
NULL |
|
ARM |
ArvinMeritor
Inc |
4.625 |
3/1/2026 |
|
TARR |
Tarragon Corp |
8 |
9/16/2009 |
|
|
|
|
|
|
|
|
|
|
|
B |
Barnes Group Inc |
3.75 |
8/1/2025 |
|
TEVA |
Teva
Pharmaceuticals - D |
1.75 |
2/1/2026 |
|
BDC |
Cable Design Technologies |
4 |
7/15/2023 |
|
TRN |
Trinity Industries |
3.875 |
6/1/2036 |
|
BLK |
Blackrock
Inc |
2.625 |
2/15/2035 |
|
UAG |
United Auto Group Inc |
3.5 |
4/1/2026 |
|
BMY |
Bristol-Myers Squibb Co |
4.82938 |
9/15/2023 |
|
UDR |
United Dominion Realty |
4 |
12/15/2035 |
|
BOL |
Bausch Lomb Inc |
5.3112502 |
8/1/2023 |
|
UNS |
Unisource
Energy Corp |
4.5 |
3/1/2035 |
|
|
|
|
|
|
|
|
|
|
|
BPFH |
Boston Private Finl Hldgs |
4.875 |
10/1/2034 |
|
URI |
United Rentals |
1.875 |
10/15/2023 |
|
BXP |
Boston Properties Inc |
3.75 |
5/15/2036 |
|
UVV |
Universal Corp Va |
6.75 |
NULL |
|
CARS |
Capital Automotive Reit |
6 |
5/15/2024 |
|
VNO |
Vornado
Realty |
3.875 |
4/15/2025 |
|
CE |
Celanese Corp |
4.25 |
NULL |
|
XL |
XL Capital Ltd |
7 |
2/15/2009 |
|
|
|
|
|
|
|
|
|
|
|
CHK |
Chesapeake Energy Corp. |
2.75 |
11/15/2035 |
|
|
|
|
|
|
CHK |
Chesapeake Energy Corp. |
4.5 |
NULL |
|
DVC AU |
DCA Group |
7 |
6/15/2011 |
|
CHK |
Chesapeake Energy Corp. (3) |
5 |
NULL |
|
ELSC IN |
Electrosteel
Castings Ltd |
0 |
5/26/2011 |
|
CHK |
Chesapeake Energy Corp. (2) |
5 |
NULL |
|
GNC IN |
Gujarat NRE Coke Limited |
0 |
4/12/2011 |
|
CHP |
C&D Technologies Inc |
5.25 |
11/1/2025 |
|
KPLD SP |
Keppel Land Limited |
2.5 |
6/23/2013 |
|
|
|
|
|
|
|
|
|
|
|
CLF |
Cleveland-Cliffs Inc |
3.25 |
NULL |
|
NTPWR IN |
Tata
Power Company Limited |
1 |
2/25/2010 |
|
CTS |
CTS Corp |
2.125 |
5/1/2024 |
|
OXR AU |
Oxiana
Limited |
5.25 |
4/15/2012 |
|
|
EDO Corp. |
4 |
11/15/2025 |
|
TEL PM |
First Pacific/Philippine Long Distance |
0 |
1/18/2010 |
|
EK |
Eastman Kodak |
3.375 |
10/15/2033 |
|
|
Sonata Securities/Adecco |
1.5 |
12/9/2010 |
|
EOP |
Equity Office Prop |
4 |
7/15/2026 |
|
|
Energias
De |
2.6900001 |
12/9/2010 |
|
|
|
|
|
|
|
|
|
|
|
EP |
|
4.9899998 |
NULL |
|
FORA NA |
ABN/Fortis |
1.875 |
10/27/2010 |
|
ESS |
Essex Ppty Tr Inc |
3.625 |
11/1/2025 |
|
LLB SW |
Liechtensteinische
Landesbank |
1.65 |
4/12/2011 |
|
ETR |
Entergy Corp |
7.625 |
2/17/2009 |
|
NUM NA |
Royal Numico |
3 |
7/11/2010 |
|
FCX |
FreeportMcmoran |
5.5 |
NULL |
|
PARG SW |
Pargesa
Holdings SA |
1.7 |
4/27/2013 |
|
GBX |
Greenbrier Cos Inc |
2.375 |
5/15/2026 |
|
PUB LN |
Punch Taverns Plc |
5 |
12/14/2010 |
|
|
|
|
|
|
|
|
|
|
|
GM |
General Motors |
6.25 |
7/15/2033 |
|
RICHT HB |
Hungary/Gedeon Richter |
1 |
9/28/2009 |
|
GPI |
Group 1 Automotive Inc |
2.25 |
6/15/2036 |
|
TUI1 GR |
TUI AG |
4 |
12/1/2008 |
|
HCR |
Manor Care Inc. |
2.125 |
8/1/2035 |
|
WHA NA |
|
2.5 |
3/23/2011 |
|
HCR |
Manor Care Inc. |
2 |
6/1/2036 |
|
WPPGY |
Grey Global Group |
5 |
10/15/2033 |
|
INTC |
Intel Corp |
2.95 |
12/15/2035 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
IPCR |
Ipc
Hldgs Ltd |
7.25 |
11/15/2008 |
|
|
|
|
|
|
KWD |
Kellwood Co. |
3.5 |
6/15/2034 |
|
6423 JP |
Abilit
Corp |
0 |
9/24/2010 |
|
LCUT |
Lifetime Brands Inc |
4.75 |
7/15/2011 |
|
6504 JP |
Fuji Electric Holdings Co |
0 |
6/1/2016 |
|
LFG |
Landamerica
Financial |
3.125 |
11/15/2033 |
|
7911 JP |
Toppan Printing Co Tranche
1 |
0 |
6/12/2018 |
|
LFG |
Landamerica
Financial |
3.25 |
5/15/2034 |
|
7911 JP |
Toppan Printing Co Tranche
2 |
0 |
6/12/2026 |
|
LXP |
Lexington Corp |
6.5 |
NULL |
|
9104 JP |
Mitsui OSK Lines |
0 |
3/29/2011 |
|
|
|
|
|
|
|
|
|
|
|
MDT |
Medtronic Inc Tranche 1 |
1.5 |
4/15/2011 |
|
Asia/Pac
Rim |
|
|
|
|
MDT |
Medtronic Inc Tranche 2 |
1.625 |
4/15/2013 |
|
1114 HK |
Brilliance |
0 |
6/7/2011 |
|
MEE |
Massey Energy Co. |
2.25 |
4/1/2024 |
|
2314 HK |
Lee & Man Paper Manufacturing |
0 |
1/13/2011 |
|
MET |
MetLife Inc. |
6.375 |
11/15/2008 |
|
392 HK |
|
0 |
12/21/2010 |
|
MLS |
Mills Corp |
6.75 |
NULL |
|
450 HK |
Hung Hing Printing
Group |
0 |
3/29/2011 |
|
|
|
|
|
|
|
|
|
|
|
MNT |
Mentor Corp |
2.75 |
1/1/2024 |
|
5346 TT |
Powerchip
Semiconductor |
0 |
6/30/2011 |
|
MSPD |
Mindspeed
Technologies Inc |
3.75 |
11/18/2009 |
|
641 HK |
Fongs
Industries Co Ltd |
0 |
5/10/2011 |
|
NAFC |
Nash Finch Co |
1.631375 |
3/15/2035 |
|
683 HK |
Kerry Properties Limited |
0 |
4/8/2010 |
|
NHP |
Nationwide Health Properties |
7.75 |
NULL |
|
|
|
|
|
|
NLY |
Annaly
Mortgage Management |
6 |
NULL |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
NPO |
Enpro
Inds Inc |
3.9375 |
10/15/2015 |
|
|
|
|
|
|
NX |
Quanex
Corp |
2.5 |
5/15/2034 |
|
|
|
|
|
|
OCR |
Omnicare |
3.25 |
12/15/2035 |
|
|
|
|
|
|
OMM |
Omi Corp |
2.875 |
12/1/2024 |
|
|
|
|
|
|
PIR |
Pier 1 Imports |
6.375 |
2/15/2036 |
|
|
|
|
|
|
RA |
Reckson
Associates |
4 |
6/15/2025 |
|
|
|
|
|
Appendix – B.
Convertible
Securities expected to show meaningful difference from previous versions of our
calculator (using discrete dividends for life).
|
Ticker |
Issuer |
Coupon |
Maturity |
|
Ticker |
Issuer |
Coupon |
Maturity |
|
|
|
|
|
|
|
|
|
|
|
ABX |
Placer Dome Inc/Barrick
Gold |
2.75 |
10/15/2023 |
|
ABBN VX |
ABB Ltd. |
3.5 |
9/10/2010 |
|
AHL |
Aspen Insurance Holdings |
5.625 |
NULL |
|
AEG SJ |
Aveng
Ltd |
6.125 |
3/17/2012 |
|
ARM |
ArvinMeritor
Inc |
4.625 |
3/1/2026 |
|
BAY GR |
Bayer AG |
6.625 |
6/1/2009 |
|
AXL |
American Axle |
2 |
2/15/2024 |
|
BIN IM |
Banca
Intesa |
6.1 |
9/29/2010 |
|
BDC |
Cable Design Technologies |
4 |
7/15/2023 |
|
BMPS IM |
JP Morgan / Banca Monte |
3.911 |
12/30/2040 |
|
|
|
|
|
|
|
|
|
|
|
CARS |
Capital Automotive Reit |
6 |
5/15/2024 |
|
BMPS IM |
Banca
Monte dei Paschi |
3.941 |
12/30/2049 |
|
CEI |
Crescent Real Estate |
6.75 |
NULL |
|
BNP FP |
BNP Paribas |
0 |
1/7/2010 |
|
CHK |
Chesapeake Energy Corp. |
4.5 |
NULL |
|
BUHR NA |
|
2 |
12/18/2010 |
|
CHK |
Chesapeake Energy Corp. (2) |
5 |
NULL |
|
CON GR |
Continental AG |
1.625 |
5/19/2011 |
|
CHK |
Chesapeake Energy Corp. (3) |
5 |
NULL |
|
DCX GR |
UBS/DaimlerChrysler |
4.35 |
2/18/2010 |
|
|
|
|
|
|
|
|
|
|
|
CKR |
CKE Restaurants Inc |
4 |
10/1/2023 |
|
|
Man Group Plc |
3.75 |
11/12/2009 |
|
CNP |
CenterPoint
Energy |
3.75 |
5/15/2023 |
|
|
EMI Group |
5.25 |
10/2/2010 |
|
CNP |
Centerpoint
Energy Inc |
2.875 |
1/15/2024 |
|
FORB BB |
Fortis |
4.205 |
11/7/2049 |
|
CTCO |
Commonwealth Telephone Enter. |
3.25 |
7/15/2023 |
|
FTE FP |
France Telecom SA |
1.6 |
1/1/2009 |
|
EP |
|
4.99 |
NULL |
|
FTE FP |
Sonata Sec/France Telecom |
4.263 |
5/5/2036 |
|
|
|
|
|
|
|
|
|
|
|
ETR |
Entergy Corp |
7.625 |
2/17/2009 |
|
FTE FP |
France Telecom SA |
5.75 |
1/29/2049 |
|
F |
Ford Motor Co. |
6.5 |
1/15/2032 |
|
FUGR NA |
|
2.375 |
4/27/2010 |
|
FCH |
Felcor
Lodging Trust |
7.8 |
NULL |
|
GEBN SW |
Geberit
AG |
1 |
6/14/2010 |
|
FCX |
Freeport-McMoRan |
7 |
2/11/2011 |
|
HDD GR |
Heidelberger Druckmaschinen |
0.875 |
2/9/2012 |
|
FCX |
FreeportMcmoran |
5.5 |
NULL |
|
|
International Power |
3.75 |
8/22/2023 |
|
|
|
|
|
|
|
|
|
|
|
FIF |
Financial Federal Corp |
2 |
4/15/2034 |
|
|
Liberty International PLC |
3.95 |
9/30/2010 |
|
FNM |
Fannie Mae |
5.375 |
NULL |
|
LLB SW |
Liechtensteinische
Landesbank |
1.65 |
4/12/2011 |
|
GLB |
Glenborough Realty |
7.75 |
NULL |
|
MOL HB |
Magnolia Finance Ltd. |
4 |
NULL |
|
GM |
General Motors |
6.25 |
7/15/2033 |
|
NEX FP |
Nexans
SA |
3.125 |
1/1/2010 |
|
GMT |
GATX Corp |
5 |
8/15/2023 |
|
NUM NA |
Royal Numico |
3 |
7/11/2010 |
|
|
|
|
|
|
|
|
|
|
|
HET |
Caesars Entertainment |
5.06825 |
4/15/2024 |
|
PUB LN |
Punch Taverns Plc |
5 |
12/14/2010 |
|
HST |
Host Marriott |
3.25 |
3/15/2024 |
|
REP SM |
Repcon
Lux/Repsol YPF SA |
4.5 |
1/26/2011 |
|
INTC |
Intel Corp |
2.95 |
12/15/2035 |
|
RUKN VX |
Swiss Re |
6 |
12/15/2008 |
|
IPCR |
Ipc
Hldgs Ltd |
7.25 |
11/15/2008 |
|
SIE GR |
Siemens AG |
1.375 |
6/4/2010 |
|
LAD |
Lithia Motors Inc |
2.875 |
5/1/2014 |
|
SIS IM |
Societa
Iniziative Autostradali |
2.625 |
6/30/2017 |
|
|
|
|
|
|
|
|
|
|
|
LFG |
Landamerica
Financial |
3.25 |
5/15/2034 |
|
SLHN VX |
Swiss Life |
0.625 |
6/10/2010 |
|
LMT |
Lockheed Martin Corp |
4.92 |
8/15/2033 |
|
|
Scottish and Southern Energy |
3.75 |
10/29/2009 |
|
LXP |
Lexington Corp |
6.5 |
NULL |
|
USG NA |
USG People NV |
3 |
10/18/2012 |
|
LYO |
Millennium Chemical Inc |
4 |
11/15/2023 |
|
|
Vedanta Resources PLC |
4.6 |
2/21/2026 |
|
MLS |
Mills Corp |
6.75 |
NULL |
|
VOE AV |
Voestalpine
AG |
1.5 |
7/21/2010 |
|
MSPD |
Mindspeed
Technologies Inc |
3.75 |
11/18/2009 |
|
|
Glencore/Xstrata |
4.125 |
10/6/2010 |
|
|
|
|
|
|
|
|
|
|
|
NAFC |
Nash Finch Co |
1.631375 |
3/15/2035 |
|
|
|
|
|
|
NDE |
IndyMac
Bancorp Inc |
6 |
11/14/2031 |
|
5334 JP |
NGK Spark Plug |
0 |
3/31/2011 |
|
NHP |
Nationwide Health Properties |
7.75 |
NULL |
|
6141 JP |
Mori Seiki Co |
0 |
6/13/2012 |
|
NLY |
Annaly
Mortgage Management |
6 |
NULL |
|
6423 JP |
Abilit
Corp |
0 |
9/24/2010 |
|
NPO |
Enpro
Inds Inc |
3.9375 |
10/15/2015 |
|
6502 JP |
Toshiba Corporation |
0 |
7/21/2011 |
|
NYB |
New York Community Bank |
6 |
11/1/2051 |
|
8325 JP |
Hokuetsu Bank |
1.5 |
9/30/2011 |
|
OMM |
Omi Corp |
2.875 |
12/1/2024 |
|
9107 JP |
|
0 |
4/4/2013 |
|
|
|
|
|
|
|
|
|
|
|
PCG |
PG&E Corp |
9.5 |
6/30/2010 |
|
Asia/Pac
Rim |
|
|
|
|
PNM |
PNM Resources Inc |
6.75 |
5/16/2008 |
|
1101 TT |
Taiwan Cement Corp |
0 |
3/3/2009 |
|
RGC |
Regal Entertainment Group |
3.75 |
5/15/2008 |
|
1114 HK |
Brilliance |
0 |
6/7/2011 |
|
RPT |
Ramco-Gershenson
Properties |
7.95 |
NULL |
|
175 HK |
Geely
Auto Holdings |
0 |
4/10/2011 |
|
SOV |
Sovereign Bancorp |
4.375 |
3/1/2034 |
|
2324 TT |
Compal
Electronics Inc |
0 |
8/19/2010 |
|
|
|
|
|
|
|
|
|
|
|
SPG |
Simon Property Grp |
6 |
NULL |
|
2888 TT |
Shin Kong Financial |
0 |
12/15/2010 |
|
STA |
Travelers Insurance |
4.5 |
4/15/2032 |
|
2890 TT |
SinoPac
Holdings |
0 |
7/12/2007 |
|
TARR |
Tarragon Corp |
8 |
9/16/2009 |
|
5371 TT |
Coretronic
Corporation |
0 |
5/18/2010 |
|
TEVA |
Teva
Pharma - B |
0.25 |
2/1/2024 |
|
641 HK |
Fongs
Industries Co Ltd |
0 |
5/10/2011 |
|
TEVA |
Teva
Pharma - A |
0.5 |
2/1/2024 |
|
682 HK |
Chaoda
Modern Agriculture |
0 |
5/8/2011 |
|
|
|
|
|
|
|
|
|
|
|
URI |
United Rentals |
1.875 |
10/15/2023 |
|
AMTK IN |
Amtek
Auto Ltd |
0.5 |
6/3/2010 |
|
UVV |
Universal Corp Va |
6.75 |
NULL |
|
APN AU |
APN News & Media |
7.25 |
10/31/2008 |
|
VGR |
Vector Group |
3.875 |
6/15/2026 |
|
CSM AU |
Consolidated Minerals Limited |
6.5 |
6/29/2011 |
|
VNO |
Vornado
Realty |
3.875 |
4/15/2025 |
|
DVC AU |
DCA Group |
7 |
6/15/2011 |
|
WM |
|
5.375 |
5/1/2041 |
|
GNC IN |
Gujarat NRE Coke Limited |
0 |
4/12/2011 |
|
|
|
|
|
|
|
|
|
|
|
WMB |
Williams Companies |
5.5 |
6/1/2033 |
|
HKL SP |
|
2.75 |
12/21/2012 |
|
WNC |
Wabash National Corp. |
3.25 |
8/1/2008 |
|
OXR AU |
Oxiana
Limited |
5.25 |
4/15/2012 |
|
WRS |
Windrose
Med Pptys |
7.5 |
NULL |
|
SPC SP |
Singapore Petroleum Co |
1.75 |
4/28/2009 |
|
XEL |
Xcel
Energy Inc |
7.5 |
11/21/2007 |
|
|
|
|
|
|
XL |
XL Capital Ltd |
7 |
2/15/2009 |
|
|
|
|
|