market valuation of convertible securities of u.s. airlines
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Theses - Daytona Beach Dissertations and Theses
11-2006
Market Valuation of Convertible Securities of U.S. Airlines Market Valuation of Convertible Securities of U.S. Airlines
Kseniya P. Beltsova Embry-Riddle Aeronautical University - Daytona Beach
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MARKET VALUATION OF CONVERTIBLE SECURITIES OF U.S. AIRLINES
By
Kseniya P. Beltsova
A Thesis Submitted to the College of Business in Partial Fulfillment of the Requirements
for the Degree of Master of Business Administration in Aviation
Embry-Riddle Aeronautical University
Daytona Beach, Florida
November 2006
UMI Number: EP32106
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MARKET VALUATION OF CONVERTIBLE SECURITIES OF U.S. AIRLINES
By
Kseniya P. Beltsova
This research paper is prepared under the direction of the candidate's thesis committee chair, Dr. Vitaly Guzhva, College of Business and has been approved by the members of the thesis committee. It was submitted to the College of Business and was accepted in partial fulfillment of the requirements for the degree of Master of Business Administration in Aviation.
THESIS COMMI
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Dr. V Member
MBA/A Graduate P r W W <JW
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ACKNOWLEDGEMENTS
I would like to thank Dr. Guzhva and Dr. Golubev for their guidance, patience
and support during the time this thesis was prepared.
I would also like to thank my family and friends who gave me the courage and
strength to face this project.
ABSTRACT
Author: Kseniya P. Beltsova
Title: Market Valuation of Convertible Securities of U.S. Airlines
Institution: Embry-Riddle Aeronautical University
Degree: Master of Business Administration in Aviation
Year: 2006
The airlines have enormous needs for capital. Historically, capital spending was
accountable for about 15 percent of annual airline revenues, more than double the
average for manufacturing companies (Arpey, 1995). Access to capital is essential to the
long-term viability and growth of the airline industry especially due to the capital-
intensive nature of its business. However, highly cyclical nature of the airline business
and its severe dependence on general economic condition make investments in the
industry risky and uncertain. The airline's junk bond credit rating and enormous amounts
of debt result in extremely high costs of capital. In addition, the airlines find very difficult
to raise funds on equity markets since investors are not impressed with poorly performing
airline stocks. To satisfy their needs for capital the airlines have turned towards
convertible securities. The important feature of convertibles is the relative insensitivity of
their value to the risk of the issuing company (Brennan and Schwartz, 1988). This
separation is achieved by selecting appropriate convertible contract parameters.
Pricing of interest rate derivatives and instruments with embedded options, such
as callable convertible bonds and preferred stocks, is typically performed utilizing models
of the term structure of interest rates. Ramanlal, Mann, and Moore (1998) test several
contingent claims valuation models adapted to callable convertible preferred stocks.
Based on their large scale testing, the best performing valuation model produced mean
pricing errors of about -0.18%. In this study this model is utilized to assess market
valuation of airline convertible preferred stocks.
The sample consists of 11 convertible preferred stocks issued by U.S. airlines in
1980 - 1991. For each convertible daily model prices are estimated for two years after
issuance and compared with market prices by calculating pricing errors. It turns out that
mean pricing error for our sample is 2.63 %, indicating that market undervalues airline
convertible preferred stocks by about 2.63 %. In addition, a panel data analysis of pricing
errors suggests that market undervaluation in much more severe immediately after
issuance and persists for approximately 6 months. The mean pricing error for a sub-
sample containing first six months of daily prices is 8.01 %, while for a sub-sample of
convertible daily prices for 7-24 months after issuance the mean pricing error is 0.10 %.
There are two potential explanations of observed discrepancy between market and
model pricing of airline convertibles shortly after issuance: model mispricing or market
undervaluation. Since utilized model was extensively tested and found to be superior in
pricing convertible preferred stocks market undervaluation seems to be a plausible
explanation. Pricing model cannot capture investor sentiment towards traded securities.
vi
Probably, market perception of airlines as higher risk companies, influences prices of
newly issued convertibles. However, in about six months of trading, the insensitivity of
properly designed convertibles to the risks of issuing companies becomes obvious and the
market and theoretical values of convertibles converge. Market undervaluation of airline
convertibles at issuance suggests that, probably due to their reputation, airlines cannot
efficiently raise capital even with convertibles.
vn
TABLE OF CONTENTS
ABSTRACT v
TABLE OF CONTENTS viii
LIST OF FIGURES ix
LIST OF TABLES xiv
Chapter
1. INTRODUCTION 1
2. AIRLINE INDUSTRY NEED FOR THE CAPITAL 4
3. CONVERTIBLE SECURITIES CHARACTERISTICS 8
4. VALUATION MODELS OF CONVERTIBLES 14
5. RESEARCH DESIGN AND METHODOLOGY 18
6. DATA ANALASYS 24
7. CONCLUSION 66
8. REFERENCES
Vll l
LIST OF FIGURES
2.1. Historical Stock Performances - Major Airlines vs. S&P 500 6
6.1. Valuation of Air Florida Systems Inc. Convertible Preferred Stock on a Given
Trading Day 28
6.2. 450-Day Performance of the Market and Predicted Air Florida Systems Inc.
Convertible Preferred Stock Values 28
6.3. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 29
6.4. 450-Day History of the Firm Value, Market and Predicted Air Florida
Systems Inc 29
6.5. Relative Error of Predicted vs. Market Preferred Stock Value 29
6.6. Valuation of Piedmont Aviation Inc. Convertible Preferred Stock on a Given Trading
Day 31
6.7. 450-Day Performance of the Market and Predicted Piedmont Aviation Inc.
6.8. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 32
6.9. 450-Day History of the Firm Value, Market and Predicted Air Florida Systems Inc.
Convertible Preferred Stock Values 32
6.10. Relative Error of Predicted vs. Market Preferred Stock Value 32
6.11. Valuation of UAL Inc. Convertible Preferred Stock on a Given Trading
Day 34
ix
6.12. 450-Day Performance of the Market and Predicted UAL Inc. Convertible Preferred
Stock Values 34
6.13. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 35
6.14. 450-Day History of the Firm Value, Market and Predicted Air Florida Systems Inc.
Convertible Preferred Stock Values 35
6.15. Relative Error of Predicted vs. Market Preferred Stock Value 35
6.16. Valuation of Trans World Airlines Inc. Convertible Preferred Stock on a Given
Trading Day 37
6.17. 450-Day Performance of the Market and Predicted Trans World Airlines Inc.
Convertible Preferred Stock Values 37
6.18. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 38
6.19. 450-Day History of the Firm Value, Market and Predicted Trans World Airlines
Inc. Convertible Preferred Stock Values 38
6.20. Relative Error of Predicted vs. Market Preferred Stock Value 38
6.21. Valuation of Western Airlines Inc. Convertible Preferred Stock on a Given Trading
Day 40
6.22. 450-Day Performance of the Market and Predicted Western Airlines Inc.
Convertible Preferred Stock Values 40
6.23. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 41
6.24. 450-Day History of the Firm Value, Market and Predicted Western Airlines Inc.
Convertible Preferred Stock Values 41
6.25. Relative Error of Predicted vs. Market Preferred Stock Value 41
x
6.26. Valuation of Horizon Air Industries Inc. Convertible Preferred Stock on a Given
Trading Day 43
6.27. 450-Day Performance of the Market and Predicted Horizon Air Industries Inc.
Convertible Preferred Stock Values 43
6.28. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 44
6.29. 450-Day History of the Firm Value, Market and Predicted Western Airlines Inc.
Convertible Preferred Stock Values 44
6.30. Relative Error of Predicted vs. Market Preferred Stock Value 44
6.31. Valuation of Midway Airlines Inc. Convertible Preferred Stock on a Given Trading
Day 46
6.32. 450-Day Performance of the Market and Predicted Midway Airlines Inc.
Convertible Preferred Stock Values 46
6.33. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 47
6.34. 450-Day History of the Firm Value, Market and Predicted Midway Airlines Inc.
Convertible Preferred Stock Values 47
6.35. Relative Error of Predicted vs. Market Preferred Stock Value 47
6.36. Valuation of Piedmont Aviation Inc. Convertible Preferred Stock on a Given
Trading Day 49
6.37. 450-Day Performance of the Market and Predicted Piedmont Aviation Inc.
Convertible Preferred Stock Values 49
XI
6.38. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 50
6.39. 450-Day History of the Firm Value, Market and Predicted Piedmont Aviation Inc.
Convertible Preferred Stock Values 50
6.40. Relative Error of Predicted vs. Market Preferred Stock Value 50
6.41. Valuation of U.S. Air Group Inc. Convertible Preferred Stock on a Given Trading
Day 52
6.42. 450-Day Performance of the Market and Predicted U.S. Air Group Inc. Convertible
Preferred Stock Values 52
6.43. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 53
6.44. 450-Day History of the Firm Value, Market and Predicted U.S. Air Group Inc.
Convertible Preferred Stock Values 53
6.45. Relative Error of Predicted vs. Market Preferred Stock Value 53
6.46. Valuation of People Express Airlines Inc. Convertible Preferred Stock on a Given
Trading Day 55
6.47. 450-Day Performance of the Market and Predicted People Express Airlines Inc.
Convertible Preferred Stock Values 55
6.48. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 56
6.59. 450-Day History of the Firm Value, Market and Predicted People Express Airlines
Inc. Convertible Preferred Stock Values 56
6.50. Relative Error of Predicted vs. Market Preferred Stock Value 56
6.51. Valuation of Conquest Airlines Inc. Convertible Preferred Stock on a Given
Trading Day 58
xii
6.52. 450-Day Performance of the Market and Predicted Conquest Airlines Inc.
Convertible Preferred Stock Values 58
6.53. 450-Day Fluctuations of the Total Firm and Preferred Stock Variances 59
6.54. 450-Day History of the Firm Value, Market and Predicted Conquest Airlines Inc.
Convertible Preferred Stock Values 59
6.55. Relative Error of Predicted vs. Market Preferred Stock Value 59
6.56. Frequency Distribution of the Errors (1-480 Days Following Issuance) 62
6.57. Frequency Distribution of the Errors (1-120 Days Following Issuance) 62
6.58. Frequency Distribution of the Errors (121-480 Days Following Issuance) 62
xin
LIST OF TABLES
2.1. Major U. S. Airlines Bond Ratings 5
3.1. Return and standard deviation for various asset classes, 1973-2000 10
6.1. Convertible Preferred Stocks in the Sample 25
6.2. Convertible Preferred of Air Florida Systems Inc 27
6.3. Convertible Preferred of Piedmont Aviation Inc 30
6.4. Convertible Preferred of UAL Inc 33
6.6. Convertible Preferred of Western Airlines Inc 39
6.7. Convertible Preferred of Horizon Air Industries Inc 42
6.8. Convertible Preferred of Midway Airlines Inc 45
6.9. Convertible Preferred of Piedmont Aviation Inc 48
6.10. Convertible Preferred of U.S. Air Group Inc 51
6.11. Convertible Preferred of People Express Airlines Inc 54
6.12. Convertible Preferred of Conquest Airlines Inc 57
6.13. Mean and Median Pricing Errors 60
6.14. Issue, market, and model prices of convertible preferred stock on the first trading
day 63
6.15. Pricing Error of Convertible Preferred Stock Panel Estimate 65
xiv
1
1. INTRODUCTION
Ever since two brothers operating a bicycle shop in Dayton, Ohio, devised a plan
to tests at Kitty Hawk - tests designed to demonstrate that man could fly - financing has
been the dynamic intergradient in the survival and growth of the airline industry. From
the barnstormers who took on passengers to fund their passion to today's frequent flyer
programs; from the flight of Lindbergh to contemporary supersavers and fare wars,
financing has always been central to marketing, growth, and operational decisions in the
airline industry (Johnson, 1999).
The airline industry has an enormous need for capital. Historically, capital
spending has consumed about 15 percent of annual airline revenues, more than double the
average for manufacturing companies.
Although airlines, including bankrupt and financially distressed carriers, have
been able to secure financing for their current, reduced capital requirements, the
industry's ability to attract investors for future and more extensive capital needs is far
from certain. Airline business has been plagued with chronic, and often, unique problems.
Nevertheless, access to capital will be essential to the long-term viability and growth of
the airline industry, as it is for any industry (Arpey, 1995).
To understand the challenges of airline finance, it is important to review the
sector's unsatisfactory financial history. Although the U.S. airline industry is a major
2
contributor to the U.S. economy and a catalyst in economic development, it has long been
in week financial condition.
After a relatively profitable decade during the 1980s, the airline industry returned
to sustained heavy losses beginning in 1990. September 11 terrorist attack has shaken the
air transportation world. In four years, from 2001 to 2005, U.S. airline industry
collectively lost $42 billion.
Two of the largest carrier - Delta and Northwest - are operating under bankruptcy
protection, and two others - United Airlines and US Airways, have flown in and out of
bankruptcy court, with US Air making the trip twice before it was purchased by a smaller
rival. John Heimlich, chief economist for the Air Transport Association, says the six
major legacy carriers have reduced their employment by 38 percent since before the 9/11
attack, or the equivalent of 169,000 full-time jobs, as they trimmed their fleets by more
than 800 planes, or about 23 percent (Isidore, 2006).
Cyclical factors such as high fuel prices and the cost of heightened security
measures in a post-September 11, 2001, context have played havoc with air carriers'
attempts to return to stability.
The capital needs of the industry are enormous. Airbus and Boeing predict it will
need between $40 and $50 billion for new aircraft each year over the next decade.
Moreover, according to International Civil Aviation Organization (ICAO), the world will
need between $250 billion and $350 in new airport infrastructure by the year 2010.
Admittedly, some of that infrastructure will come from taxpayers, concessions, parking
and such. But the bulk of it must come from the airlines, directly or indirectly, in the form
3
of landing and air traffic control fees, gate, counter and hanger leases, passenger facility
charges, fuel and other taxes, and ground services fee.
Major global alliances, low-cost carriers, and regional jet service will continue to
threaten every airline's market share and thus challenge profitable revenue growth.
Corporate travel managers are taking control of expenditures and leveraging that control
to bring about an overall lowering of the cost of the travel.
The airline industry suffers from severe business risk in the form of high fixed
costs, highly cyclical demand, and intensive competition; it suffers severe financial risk
in the form of high debt-to-equity ratios, which increases the variability of earnings and
the chances of insolvency. Because of the level and intensity of the business and financial
risk in the industry, investors discount airlines security, making it even harder for them to
raise adequate capital.
Below, in Chapter 2,1 discuss the airlines' need for capital and the ways to raise
it, in Chapter 3 I examine characteristics of convertible securities, I also introduce
valuation models of convertibles in Chapter 4; in Chapter 5 I present research design and
methodology, in Chapter 6 I address data analysis, and finish with Conclusion.
4
2. NEED FOR THE CAPITAL
WANTED: Airline industry seeks investors willing to finance billions of dollars aircraft deliveries and other capital improvements. Will offer choice of junk bonds, stocks consistently underperforming the S&P 500, and uncertain aircraft residual values to those who apply. (Arpey, 1995)
Access to the capital is essential to the long-term viability and growth of the
airline industry especially due to the capital-intensive nature of its business. Since the
majority of the U.S. airlines have failed to generate adequate or sustained earnings, the
only way for them to obtain required capital is to reach out to the capital markets.
Because of the difficult conditions in the air transportation industry, securities issued by
U.S. airlines can be perceived as very risky and would be demanded to generate higher
returns for investors.
Air fares continue to fall, and oil prices continue to rise. Airlines continuously
post losses, so investors see air transportation industry as predisposed to higher levels of
risk and the consistent way of loosing money.
In total debt of six major U.S. airlines reached $89.5 billon that represented more
than 100 percent of their assets (JP Morgan, 2004). As a result of poor performance, most
of the industry's bonds are now non-investment or "junk" (defined by Standard and
Poor's as any rating below BBB). The enormous amount of debt and the airlines
speculative grade credit rating result in extremely high cost of capital.
B-B B-B+ D B-
B-B
CC B D D
Table 2.1 shows 2002-2004 bonds rating of major U.S. Airlines (American,
Continental, Delta, Northwest, United and U.S. Airways).
Table 2.1 Major U. S. Airlines Bond Ratings
Company 2002 2003 2004 AMR Corporation BB-Continental Airlines Inc. B+ Delta Airlines Inc. BB Northwest Airlines Corp. BB-UAL Inc. CCC-US Airways Group Inc. NA
Source - Bloomberg
Unfortunately, the bond market is not the only place where airlines securities have
suffered. Equities have performed poorly, both recently and historically. Even during the
relatively profitable 1980s, returns for the publicly traded airlines included in the
Standard and Poor's Airline Index - AMR, Delta, UAL and US Air - lagged behind those
of the S&P 500 in all but three years (Arpey, 1995).
Figure 2.1 compares the performance major airlines stocks (American,
Continental, Delta, Northwest, United and U.S. Airways) with S&P 500.
Not surprisingly, that in their quest for capital, the airlines have recently turned
towards convertible securities. In 2003 the U.S. airlines issued $2,761 billion of
convertible preferred stock and convertible bond offerings, which is almost 9 times 2003
equity and 3 times straight (non-convertible) debt offerings. The current work thus
focuses on the detailed analysis of this type of security in the airline industry.
Figure 2.1 Historical Stock Performances Major Airlines vs. S&P 500
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8
3. CONVERTIBLE SECURITIES
Convertible securities are both appealing and unusual in that they have both fixed-
income and equity characteristics. They provide their holders with the option to exchange
a convertible for a predetermined number of common shares at a specified price.
Investors familiar with stocks for growth and bonds for income and safety will find the
convertible's hybrid features very attractive as an investment alternative. In a single
security, investors can obtain the safety of a bond and the capital gains opportunity of
common stocks. These hybrid features have provided over the years to be beneficial to
holders of these unique securities.
Investors have overlooked convertible securities for many years, partly because
they are less widely discussed in the financial press than stocks and bonds and partly
because they are very complex. At one time, the relatively small size of the public
convertible market kept it from attaining the depth necessary to develop complete
investment strategies. Those individual investors who were knowledgeable in convertible
evaluation have used convertibles investments for many years. The private convertible
market, which uses convertible securities to structure venture capital investments, has
been in widespread use for decades.
The current interest in convertibles can be tracked back to the increased volatility
of the stock and bond markets of the early 1970s.The great bull market of the 1950s and
1960s came to an end in 1969, and the economic consequences of those times threw
traditional ways of managing portfolios into disarray. Bonds became as volatile as stocks;
9
investors could not simply buy bonds for safety and stocks for growth. To achieve
financial success, investors sought ways to control volatility. The defensive
characteristics of convertibles made them increasingly attractive as a means to achieve
higher risk-adjusted returns (Calamos, 1998).
Of course, increasing interest in convertibles was not the only result of the volatile
financial markets. The demands on portfolio managers to control risk in unpredictable
times led to an increasing number of other new investment vehicles and strategies. The
opening of Chicago Board of Options Exchange (CBOE) in 1973 and the passing of the
Employees Retirement Income Security Act (ERISA) in 1974 both fostered the growth of
nontraditional investment strategies. The CBOE showed investors different ways to
reduce market volatility by using stock options, index options, and other investment
vehicles. Professors Black and Scholes developed their option price theory, which helped
provide a solid academic framework for option strategies and fostered the growth of
additional types of derivative securities.
Convertibles have performed extremely well when compared to both the equity
and fixed-income markets. Goldman Sachs research on Convertibles (Goldman Sachs,
2001) showed that convertibles achieve returns competitive with those of stocks, but with
lower volatility. Over the long term, convertibles have delivered 70 percent upside
participation with equities and only 52 percent of the downside. As shown in Table 3.1,
the compound annual returns for convertible bonds (11.89 percent) were modestly below
the S&P 500 (12.97 percent) from January 1973 to December 2000, with a significantly
lower standard deviation of 12.68 percent for convertible bonds versus 17.03 percent for
the S&P 500. Over the same period, convertibles have materially outperformed the total
10
return of long-term investment-grade bonds (8.99 percent), but with only a slightly higher
standard deviation.
Table 3.1 Return and standard deviation for various asset classes, 1973-2000
Asset Class Compound Annual Return Standard Deviation
Convertible Bonds 11.89% 12.68% S&P 500 12.97% 17.03% Long-term Corporate Bonds 8.99% 11.90%
Source - Ibbotson Associates
Table 3.2 breaks numbers out into shorter time periods. Goldman Sachs highlighted
the following in particular:
• the large deviations away from expected returns within the smaller time periods
• in the only five-year period that the S&P posted a negative return (1973-1977),
convertible bonds posted a positive return of 6.79 percent
• the total return of convertible bonds within the 1998-2000 is significantly above
the historical performance relative to both equity and fixed-income investments,
though convertibles' relative standard deviation is also higher
11
Table 3.2 Risk and Return over 5-year increments, 1973-2000
Period
1973-1977 1978-1982 1983-1987 1988-1992 1993-1997 1998-2000
Convertible Bonds
Comp. Annual Return
6.79% 16.48% 11.45% 12.49% 12.01% 12.62%
St. Deviation
10.79% 13.86% 14.81% 8.86% 8.34%
21.90%
S&P 500
Comp. Annual Return
-0.21% 14.05% 16.49% 15.89% 20.24% 12.26%
St. Deviation
17.62% 18.44% 21.08% 15.48% 12.74% 20.06%
Intermediate-Term Coroorates
Comp. Annual Return
7.81% 7.15% 14.35% 11.17% 7.73% 5.89%
St. Deviation
6.09% 9.81% 6.45% 3.89% 4.48% 3.28%
Long-Term Coroorates
Comp. Annual Return
6.29% 5.57% 14.06% 12.50% 9.08% 4.98%
St. Deviation
8.72% 15.99% 11.36% 7.01% 7.67% 5.95%
Source - Ibbotson Associates
The most plausible rationale for the popularity of convertibles lies in their
insensitivity to company risk. This allows them to be issued on terms that look fair to
management, even when the market rates the risk of the issuer higher than does
management of the issuing company.
This rationale receives strong support from the available evidence. Companies
issuing convertible bonds tend to be characterized by higher market and earning
variability, higher business and/or financial risk, stronger growth-orientation, and shorter
corporate histories than their straight debt counterparts. Such companies stand to benefit
most from convertible financing (Brennan and Schwartz, 1988).
The capital market's growth over the years has produced a convertible market that is
now significant in size and global in breadth. Like the patterns seen in the stock and bond
markets, this growth has been sporadic. There are highly developed convertible markets
in the United States and Japan. There are also advanced convertible markets in England,
France, Australia, Canada, Sweden, and Switzerland. The convertible markets in many
12
other countries are developing rapidly, with the emerging markets showing notable
growth. The convertible market includes convertibles from companies in 38 different
countries (Calamos, 1998).
The U.S. domestic convertible market is one of the most important in the world. The
size of the convertible market has kept place with the growth of capital markets
worldwide. It is a diverse market representing a broad spectrum of industries and
companies within the United States. It is primarily an institutional market where many
plan sponsors and consultants consider convertibles as a separate asset class. Some
pension funds - both public and corporate - make specific convertible allocations with
dedicated convertible portfolios.
There are many different types of convertible securities outstanding in the U.S.
market, including:
• convertible bonds
• convertible preferred stock
• convertible with put features
• zero-coupon convertible bonds
• third-party convertible notes
• mandatory convertibles
The primary types are convertible bonds, convertible preferred stocks, zero-
coupon convertibles, and mandatory convertibles.
In the United States, growth and income mutual funds often use convertibles. U.S.
total convertible offerings from 1970 to 2006 were over 7,000 issues in excess of $800
13
billion, while the proceedings from airline industry convertibles were over $2 billion
(Securities Data Corporation, 2006).
14
4. VALUATION MODELS OF CONVERTIBLES
Pricing of interest rate derivatives and instruments with embedded options, such
as callable convertible bonds and preferred stocks, is typically performed utilizing models
of the term structure of interest rates.
Two main approaches to the modeling of the term structure of interest rates in
continuous time are the equilibrium, and no arbitrage (or arbitrage-free) approaches. In
the equilibrium model, the initial term structure is an output of the model, although the
model's parameters can be chosen, so that the generated yield curve closely matches the
actual yield curves (Ramanlal, 2005).
Two groups of equilibrium models that can be distinguished are single factor and
two-factor models. Rendleman and Bartter (1980) model is a two-parameter model where
interest rates follow geometric browning motion, which is assumed to be similar to stock
prices movement. Vasicek (1977) model is a single factor three-parameter model, which
introduces mean reversion, and allows interest rates to be negative. Cox, Ingersoll and
Ross (1985) model is a single factor three-parameter model, which keeps mean reversion
and introduces a square root process to eliminate the possibility of negative interest rates.
Two-factor models are represented by Brennan and Schwartz (JFQA, 1982) and
Longstaff and Schwartz (1992) models. Brennan and Schwartz introduce a four-
parameter model where both short and long rates are stochastic, and short rates exhibit
mean reverting to long rates. The main innovation of Longstaff and Schwartz model is
stochastic volatility.
15
The questionable feature of the equilibrium models is that current bonds are not
priced correctly, and even small mispricing can result in large errors when pricing
derivatives.
No-arbitrage (or arbitrage-free) approach starts from assumptions about the
stochastic evolution of one or more interest rates and derives the prices of all contingent
claims by involving the condition that there are no arbitrage opportunities in the
economy. These models replicate the current yield curve exactly. Thus straight securities
are priced exactly, and accordingly, some reliance may be placed on model's prices for
derivatives.
No-arbitrage models fall into two broad categories: models of forward rates (or
bond prices directly), and models of the short rate.
Heath, Jarrow and Morton (1992) model is the main one in the first category.
Modeling either forward rates or bond prices directly can be done with this model, so that
the current yield curve is replicated exactly. The resulting process for the short rates does
not follow Markov process that eliminates the opportunity of employing the tree
methodology to price derivatives. Markov models for the short rate fit the yield curve
exactly. The advantages of these types of models are numerical tractability, and no-
arbitrage, when the cost of employing is that the model's parameters become time
dependent.
The first model in this category is Ho and Lee (1986) model. The model is
arithmetic Brownian motion where the drift term is time dependent to ensure the exact
matching of the current yield curve. There is no mean reversion, both short and forward
rates have the same volatility and interest rates can be negative in this model. Hull and
16
White (JFQA, 1990) introduce mean reversion.
Black, Derman and Toy (1990) include another time dependent function in the
model. In addition to the replication of the current yield curve, it allows matching the
volatilities of all spot and forward rates at time zero. Also, they use geometric Brownian
process, which removes the problem of negative interest rates. Black and Karasinski
(1991) introduce the third time-dependent function which can be fitted to the yield curve,
volatility curve, and the cup curve. However, Hull and White (1994) criticize this model
for the overparameterization (too much fitting). They argue that it leads to a non-
stationary volatility structure. Further development is coming with the introduction of the
second factor into the models.
Also, Hull and White (1990) fit the three functions to the yield curve, the
volatility curve, and future local volatilities. The advantage of the former approach is that
all three are observable. In the latter, future local volatilities are unobservable at time
zero.
Ramanlal, Mann, and Moore (1998) test several contingent claims valuation
models adapted to callable convertible preferred stocks. This is the first and only one
large scale test of these models. They test Ingersoll (1977a, b), Brennan and Schwartz
(1977, 1980), Emanuel (1983) and their own extension of Brennan and Schwartz
(1977) model. Brennan and Schwartz specify a general algorithm for valuing callable
and convertible bonds which is robust to a very general set of contract provisions.
Ramanlal, Mann, and Moore modify this algorithm such that the transmuted model is
applicable to callable and convertible preferred stocks. The modified algorithm
accommodates a wide variety of realistic contract provisions including a call and/or
17
conversion profile that varies over the security's life.
18
5. RESEARCH DESIGN AND METHODOLOGY
Comparison of market prices of convertible securities issued by U.S. Airlines
against Ramanlal, Mann, and Moore (1998) modified valuation model can provide
insights on issue of perceived risk of investing in airlines. The model very closely
matches the actual market prices of convertible securities for a sample of industrial firms.
If the deviation between model and market prices for U.S. airline securities are higher
than that for the industrial firms, it will mean that perceived risk of investing in airline
results in market undervaluation, since the model already incorporates the volatility (risk)
of underlying firms into valuation.
Ramanlal, Mann, and Moore (1998) model is an extension of Merton (1974)
model, which states that any contingent claim on the firm's value can be written as a
function of the firm's value and the time f (V ,t), where: f is a contingent claim, V is the
firm value, t is the time, and f and f are the first and second derivatives of the ' ' W V
contingent claim with respect to the firm's value, and ftis the first derivative of f with
respect to time:
^<J2V2fn+(rV-C)fv-rf + c + f,=0 5.1
For their best performing model Ramanlal, Mann, and Moore (1998) adopt the
solution technique of Brennan and Schwartz (1977) in solving Equation 5.1, subject to
boundary conditions that capture call protection periods and time-dependent contractual
call prices k that account for accrued dividends. Also, Ramanlal, Mann, and Moore hold
common and preferred dividend rates constant.
19
Closely following Ramanlal, Mann, and Moore (1998), the algorithm is
constructed utilizing the results of IngersoU (1977a) and Brennan and Schwartz (1977).
For constant, time independent cash flows C and c, constant call price k, conversion
ratio 7, and ft= 0, Equation 5.1 reduces to the ordinary differential equation:
\°2V2Lr+(rV-C)fv-rf + c = 0 5.2
For periodic cash flows, time-varying call price k(r) and conversion ratio 7(7)
Equation 5.1 reduces to the partial differential equation:
-v^gw+rVgy-rg-g, =0 5 3
where: 7 is the security's time to maturity 7 and k (at which the preferred
conversion ratio and call price cease to change).
Convertible preferred stocks with time-varying call and conversion features
should satisfy both Equation 5.2 and Equation 5.3. Assuming that the periodic cash
flows are paid continuously and are time-independent, the preferred satisfies
Equation 5.2. The solution of Equation 5.2 is f(V). Next, after setting the initial
condition for Equation 5.3 g(V,0) = f(V), the solution of Equation 5.3 gives the
value of the preferred.
For mandatory callable and mandatory convertible preferred stocks, the valuation
model is simplified since the value of security at maturity is known. For such
convertibles the initial condition for Equation 5.3 is not the solution of the ordinary
differential Equation 5.2, but the estimated value of the security at maturity.
Equation 5.3 is solved using dynamic programming. Certain events, such us
common stock dividend payments or decreases in the conversion ratio or call price can
tngger conversion of the preferred. Conversion prior to an event date may maximize the
preferred value and, hence, can be optimal. Such a situation can be modeled as:
g(V,T+)=Max[g(V-D,T-ly(T+)V] 5.4
where: r+ and r indicate time to maturity immediately before and after the event, and
D is the common stock dividend.
On a preferred dividend date the preferred's value depends on the fact if the
call protection period is active or not. When the preferred is non-callable, the pre-
dividend value equals the post-dividend value plus the preferred dividends /:
g(V,T+) = g(V-I,T-) + I 5.5
When the preferred is callable, the firm may exercise its call option prior to an
event date (preferred ex-dividend date or an increase in the conversion ratio or call price)
in order to minimize the preferred's value and maximize the common stock's value:
g(V,T+)=Min[g(V-I,T-) + I,k(r+)] 5.6
Numerical techniques have to be utilized to obtain the preferred's price g(V,7).
The ordinary differential Equation 5.2 can be approximated by the difference equation:
where:
at = rhi-o2hi2 -C,b = 2rh + 2&2hi2,cl =-rhi-cr2hi2 +C,d = 2ch,
and
f(V) = f(ih) = fv
The cash flows C and c can depend on the firm's value V, which in turn depends
on i. h is the step size for changes in the firm value V and n is the number of steps
corresponding to the maximum value of V. Equation 5.7 represents (n 1) linear
21
equations with (n + 1) unknown f , i = 0,1,...,n that can be solved subject to the boundary
conditions fQ =0, f <k , and f >rih . The partial differential Equation 3 can be
approximated by the difference equation:
a,gt-i +bSi,j +c>gl+\ =d9i = l,...9n-VJ = l,...,m 5.8
Equation 5.8 represents (n - 1) linear equations with (n + 1) unknowns g , i = 0,
1, ..., n for each value of j that can be solved subject to the boundary conditions
gn =0, and, when non-callable, (g - g , 7 h = 7 , or g < k and g >7 ih when 0,j ' ' ' v o n , j ° n - l , j ) 'j ' ° i , j j ° i , j ' j
callable. Setting the initial condition g n = f , g can be solved with iterations for all j 0 °i,0 1 ' ° i j J
starting with j = 1. The effects of periodic cash flows, changing conversion terms and
call price are accounted for using Equations 5.4, 5.5, and 5.6.
The estimation of the model value of the preferred stock g(V,7) requires the
following data:
V(r) the aggregate market value at time to maturity 7 of the firm's
outstanding equity securities (common and all preferred stocks including the issue to
be valued).
D - the aggregate dividend payment of common stock and all preferred
stock issues excluding the issue to be valued
I the aggregate dividend payment of the preferred stock to be valued
C - the annualized value of D + /
c - the annualized value of/
k(7) the call price plus accrued dividends at time to maturity (the aggregate
outlay that would be necessary if the entire issue were called).
7(7) - the conversion ratio at time to maturity (the fraction of aggregate equity that
22
would be held by the convertible issue's owner if the entire issue were converted).
7=n /(n +N), where N is the number of shares of common stock outstanding and n
is the aggregate number of shares that the convertible issue can be exchanged in.
2
o - the variance of the instantaneous return dV/V (estimated as the sample
variance of ln(Vt /V )) .
r - the estimated rate of a 30-year zero-coupon Treasury bond.
As noted by Ramanlal, Mann, and Moore (1998), the preferred's model value is a
function of the market value of equity, which in turn depends on the preferred's market
value. To avoid potential bias, the value of equity is calculated as the market value of all
equity and the model value of the preferred.
Since the Ramanlal, Mann, and Moore model was extensively tested and resulted
in superior pricing performance, it was assumed that the model is unbiased predictor of
market prices. Accordingly, the estimated pricing error for issue i on date t as:
{Model Pr icelt - Market Pricelf)
ERROR = 5.9 Model Fr ice lt
Thus a positive value for ERROR in 5.9 indicates market underpricing.
To further assess the underpricing the pricing errors were examined using panel
data analysis. There are several advantages to panel data analysis: it helps avoid
"aggregation bias" that may occur when means are compared; it can measure effects
generally overlooked by a pure cross-section or pure time-series analysis; and it can
control for unobserved heterogeneity.
Daily pricing errors are examined to see if convertibles display underpricing
(relative to prices over the two-year period) in the first five days, the first four weeks,
23
and the first six months following issuance, respectively.
The following models are estimated:
ERRORIJ=a + fib.DIIJ+e„ 5.10 n=\
ERROR„=a + fibHWIIJ+e,J 5.11 n = \
ERROR„=a + fibmMIIJI+eIJ 5.12
where:
D1-D5: Dummy variables corresponding to first to fifth trading days after issuance;
W1-W2: Dummy variables corresponding to first to fourth weeks after issuance;
M1-M6: Dummy variables corresponding to first to sixth months after issuance.
Including period dummies permits identifying underpricing over varying
periods: short (indicated by coefficients of D1-D5), intermediate (coefficients of Wl-
W4), or over a longer period up to six months (coefficients of M1-M6).
6. DATA ANALYSIS
In this work I examine a sample of convertible preferred stocks: 11 U.S. airline
securities, issued between March 1980 and May 1991.
Daily prices for collected securities are available in the "NYSE Daily Stock Price
Record", "Daily Stock Price Record. American Stock Exchange," and "Daily Stock
Price Record. Over the Counter." Price records up to two years following issuance are
examined. The sample is screened for appropriateness of the security\y and data
sufficiency.
The selection criteria yielded 11 convertible preferred stock issues. Information
including the convertible contract features, offer price, and issue size were obtained from
Moody's Transportation Manual. The sample of securities with summary statistics is
listed in Table 6.1.
25
Table 6.1 Convertible Preferred Stocks in the Sample
Issuer Security Issue Date # of CV Price Conv Rat Div
Air Florida Systems
Piedmont Aviation
UAL
Trans World Airlines
Western Airlines
People Express Airlines
Horizon Air Industries
Midway Airlines
Piedmont Aviation
US Air Group
Conquest Airlines
$2 40ser B cum cvt pfd ,
par $0 50 $2 375 cvt pfd, no par $2 40 ser B cum cvt pfd,
no par $2 25 cum cvt
pfd, par $0 001
$2 1375 ser B cum cvt pfd,
no par $2 50 ser B cum cv pfr, par $0 01
$1 20 cum cvt exch pfd, par
$0 02 $1 85 ser B cvt ech pfd, par $0 01 $3 25 cvt
exch pfd, no par
$4 375 ser B cum cvt pfd,
no par 12% ser A
cum cvt pfd, par$0 10
3/25/1980 800,000 $20 00 2 3810 $2 40
12/5/1980 1,000,000 $25 00 16217 $2 38
1/13/1983 4,000,000 $24 00 0 5854 $2 40
7/29/1983 4,000,000 $23 79 15000 $2 25
4/11/1984 1,000,000 $15 00 3 0000 $2 14
4/12/1985 1,200,000 $25 00 2 5000 $2 50
12/31/1985 1,100,000 $1000 12987 $120
12/31/1985 1,000,000 $20 00 2 2222 $ 1 8 5
5/15/1986 2,400,000 $50 00 10000 $3 25
5/21/1991 4,263,050 $50 00 2 4900 $2 38
7/15/1991 400,000 $9 25 8 0000 $111
The sample includes convertible preferred issues listed in the New York Stock Exchange (NYSE) and Over the Counter (OTC) at some point during 1980-1997, based on entries in Standard and Poor's NYSE Daily Stock Price Record, and Daily Stock Pi ice Record Ovei the Counter All issues meet the following cntena (1) convertible into common stock of the issuing firm only (not a subsidiary or another firm), accordingly, all exchangeable issues and issues associated with mergers and acquisitions were omitted, (2) not exchangeable for debt or any other security, (3) have all significant contingent claims traded on the NYSE m order to determine firm value in the model, (4) be an industrial firm wit clearly stated call and conversion provisions described in Moody's Industrial Manuals, (5) have a fixed dividend rate, and (6) have sufficient daily trading volume, defined as a minrmum of 30 data points per quarter in order to estimate the return vanance Market values of convertible preferreds are based on offer pnce, market values of common stocks are based on first-day trading pnces
Tables 6 2 to 6 12 present issue characteristics withm the convertible preferred
stocks sample description of the convertible preferred stock, short description of the
26
equity securities issued by the same company, firm size, offer size, annualized dividend
payment of the preferred stock, sum of annualized dividend payment of common and all
preferred stock issues, call schedule, call prices, conversion ratio at time to maturity, the
variance of the instantaneous return, and 30-year zero-coupon Treasury bond interest
rate.
For each convertible preferred stock issue five figures are provided. First figure is
a snapshot of the convertible preferred stock in time. All characteristics of the security
are embedded into boundary and initial conditions.
Second figure shows the predicted and market value for preferred stock over a
450-day period, and demonstrates how accurate the model prediction. The volatility of
the firm influence the level of divergence between predicted and market value of the
preferred stock. Our sample shows constant underpricing of convertible security, mostly
in the 1-120 day period after issuance.
Third figure is a 450-day variance history, based on the calculation of total market
value, and predicted preferred stock value. Graph supports the theory that volatility of the
firm value is much higher then the volatility of the convertible security.
Fourth figure is a 450-day history of the firm value, market and predicted
preferred stock value. Market convertible stock value rarely follows the firm value trend,
and does not show as much volatility as total company value.
Figure five shows the relative error of predicted and market values of the
preferred stock. It also suggests that preferred stock is undervalued for 120 trading days
after issuance.
27
Table 6.2 Convertible Preferred of Air Florida Systems Inc.
Air Florida Systems Inc Convertible Preferred Stock $2.40 ser. B cum conv. pfd.; par $0.50 Issue Date Number of Preferred Stock Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convertion Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock - G Variance - (a)A2 30-year zero-coupon T-bond r Conversion Ratio- Y(T)
3/25/1980 800,000 $20.00 $19.75 2.381 $2.40
$2,812,800 $86,688,000
0.00198 12.56% 0.2022
Call Schedule: Date Price - k(T) 3/31/1981 3/31/1982 3/31/1983 3/31/1984 3/31/1985 3/31/1986 3/31/1987 3/31/1988 3/31/1989 3/31/1990 3/31/1991 Called
$22.4000 $22.1600 $21.9200 $21.6800 $21.4400 $21.2000 $20.9600 $20.7200 $20.4800 $20.2400 $20.0000 6/19/1981
Other Securities
Common Stock Number of Shares Annual Total Dividend Payment
common; par $0.50 11,008,000 $2,812,800
28
Figure 6.1 Valuation of Air Florida Systems Inc. Convertible Preferred Stock on a Given Trading Day
Figure 6.2 450-Day Performance of the Market and Predicted Air Florida Systems Inc. Convertible Preferred Stock Values
50
45
^ 40
> o ° 35
n2 30
25 F
20
" 1 — 1 • 1 •
~" — — g(V) - Market — — " " 900 - Predicted
•
L iML# j \ l ^ n l lw W
r 1 1 1 _ L 1 1
V*f
1
J *
- " 7
i i i
50 100 150 200 250 300 350 400 450 500 Day
Figure 6.3 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
50 100 150 200 250 300 350 400 450 Day
Figure 6.4 450-Day History of the Firm Value, Market and Predicted Air Florida Systems Inc. Convertible Preferred Stock Values
Day
Figure 6.5 Relative Error of Predicted vs. Market Preferred Stock Value
"020 50 100 150 200 250 300 350 400 450 500 Day
30
Table 6.3 Convertible Preferred of Piedmont Aviation Inc.
Piedmont Aviation Inc Convertible Preferred Stock $2.375 cvt pfd; no par Issue Date 12/5/1980 Number of Preferred Stock Shares 1,000,000 Convertible Preferred Stock Issue Price $25.00 Convertible Preferred Stock Market Price $23.75 Conversion Ratio 1.62168 Preferred Stock Dividend $1.62 Annual Convertible Dividend Payment - c $1,203,750 Market Value Convertible Preferred Stock - G $23,750,000 Variance - (a)A2 0.00110 30-year zero-coupon T-bond r 11.75% Conversion Ratio- Y(T) 0.2948
Call Schedule: Date 12/15/1981 12/15/1981 Called
Price - k(T) $27.38 $25.00
6/6/1981
Other Securities
Common Stock common; par $1.00 Number of Shares 4,698,371 Annual Total Dividend Payment - C $1,705,725
31
Figure 6.6 Valuation of Piedmont Aviation Inc. Convertible Preferred Stock on a Given Trading Day
8
200 250 300 Total Firm Value
Figure 6.7 450-Day Performance of the Market and Predicted Piedmont Aviation Inc. Convertible Preferred Stock Values
8 35
35
• g(V) - Market • g(V) - Predicted
80 Day
32
Figure 6.8 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
4
3 5
3
2 5
2
1 5
1
n <;
x 10
" VarCV) - | Var(g)
: XJ
^ r
^^r — — — — — — — — — -».—
90 100 110 120 130 140 150 160 Day
Figure 6.9 450-Day History of the Firm Value, Market and Predicted Air Florida Systems Inc. Convertible Preferred Stock Values
> 200
V - Market • — — g(V) - Market • — g(V) - Predicted
20 40 60 80 100 120 140 Day
Figure 6.10 Relative Error of Predicted vs. Market Preferred Stock Value
33
Table 6.4 Convertible Preferred of UAL Inc.
UAL Inc Convertible Preferred Stock $2 40 ser B cum cvt pfd, no par Issue Date Number of Preferred Stock Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convention Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock Variance - (a)A2 30-year zero-coupon T-bond - r Conversion Ratio- Y(T)
1/13/1983 4,000,000
$24 00 $25 75 0 5854 $2 40
$10,000,000 $103,000,000
0 00110 10 99% 0 0669
Call Schedule Date Price - k(T) 1/1/1986 1/1/1987 1/1/1988 1/1/1989 1/1/1990 1/1/1991 1/1/1992 1/1/1993
$26 05 $25 90 $25 75 $25 60 $25 45 $25 30 $25 15 $25 00
Other Securities
Common Stock Number of Shares Annual Total Dividend Payment
common, par $5 00 2,500,000
$10,028,800 Conv Pref Stock Number of Shares
$ 40 cum conv ser A pfd, no par 72,161
34
Figure 6.11 Valuation of UAL Inc. Convertible Preferred Stock on a Given Trading Day
200 400 600 800 1000 1200 1400 1600 1800 2000 Total Firm Value
Figure 6.12 450-Day Performance of the Market and Predicted UAL Inc. Convertible Preferred Stock Values
190
180
170
co 160 a>
5 150
m 140
fe 130
110
• g(V) - Market •g(V) - Predicted
120 - I
90 100 200 300 400
Day 500 600 700 800
35
Figure 6.13 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
Var(V) Var(g)
300 400 500 600 700 Day
Figure 6.14 450-Day History of the Firm Value, Market and Predicted Air Florida Systems Inc. Convertible Preferred Stock Values
1800
V - Market ~" 9(V) - Market
g(V) - Predicted
,_II*I H I P II j * l i » *" "***"
100 200 300 400 Day
500 600 700 800
Figure 6.15 Relative Error of Predicted vs. Market Preferred Stock Value
I £ -0 1
S /ssV% v^ 100 200 300 400 500 600 700 600
Day
36
Table 6.5 Convertible Preferred of Trans World Airlines Inc.
Trans World Airlines Inc Security $2.25 cum cvt pfd; par $0.001 Issue Date Number of Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convertion Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock • Variance - (a)A2 30-year zero-coupon T-bond - r Conversion Ratio- Y(T)
7/29/1983 4,000,000
$23.79 $21.75
1.5 $2.25
$9,000,000 $87,000,000
0.00070 11.73% 0.1368
Call Schedule: Date Price - k(T) 8/29/1985 8/29/1986 8/29/1987 8/29/1988 8/29/1989 8/29/1990 8/29/1991 8/29/1992 8/29/1993 8/29/1994
$26.80 $26.58 $26.35 $26.13 $25.90 $25.68 $25.45 $25.23 $25.00
Other Securities
Common Stock Number of Shares Annual Total Dividend Payment - C
common; par $0.01 31,250,000
$23,850,000 Conv. Pref. Stock Number of Shares
cum pfd. $2.25, par $0,001 6,000,000
Figure 6.16 Valuation of Trans World Airlines Inc. Convertible Preferred Stock on a Given Trading Day
Total Firm Value
Figure 6.17 450-Day Performance of the Market and Predicted Trans World Airlines Inc. Convertible Preferred Stock Values
^ 90 Q_
80
70
60 100 200 300 400 Day
500 600 700 800
38
Figure 6.18 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
0 9
0 8
0 . 7
0 6
0 5
0 .4
0 3
0 . 2
0 1
x 10 J
----
" _.#«. « ™ . . —
Var(V) I Var(g)| _
r~-'
400 Day
Figure 6.19 450-Day History of the Firm Value, Market and Predicted Trans World Airlines Inc. Convertible Preferred Stock Values
1200
1000
800
600
400
200
— — V - Market — — — g(V) - Market
gfV) - Predicted
» A ' S i * w ' > ^ " 1 1 ' ^ 1 +*vmm m*"*mi
400 Day
500 600
Figure 6.20 Relative Error of Predicted vs. Market Preferred Stock Value
39
Table 6.6 Convertible Preferred of Western Airlines Inc.
Western Airlines Inc Security $2.1375 ser B cum cvt pfd; no par Issue Date Number of Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convertion Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock Variance - (a)A2 30-year zero-coupon T-bond - r Conversion Ratio- Y(T)
4/11/1984 $1,000,000.00
$15.00 $12.75
3 $2.14
$2,137,000 $12,750,000
0.00066 13.46% 0.1107
Call Schedule: Date Price - k(T) 3/1/1987 3/1/1988 3/1/1989 3/1/1990 3/1/1991 3/1/1992 3/1/1993 3/1/1994 3/1/1995 Called
$16.71 $16.50 $16.28 $16.07 $15.86 $15.64 $15.43 $15.21 $15.00
8/30/1985
Other Securities Common Stock Number of Shares Annual Total Dividend Payment - C
common; par $1 24,086,000 $4,529,000
Conv. Pref. Stock Number of Shares
$2.00 ser A cum cvt pfd, no par 1,200,000
40
Figure 6.21 Valuation of Western Airlines Inc. Convertible Preferred Stock on a Given Trading Day
,u
35
30
£ 25
8 Zo 20
? «S? £ 15
10
5
-
j
/
/ /
/
i i i - •
^^^ ^+*
1—
— — — Day 1 ----• Day 450 '
-^S^ ^
•
•
100 150 Total Firm Value
Figure 6.22 450-Day Performance of the Market and Predicted Western Airlines Inc. Convertible Preferred Stock Values
30
• " • g C V ) - Market — — 9(Y) - Predicted
50 100 150 200 250 300 350 400 450 500 Day
41
Figure 6.23 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
I
SO 100 150 20© 250 300 Day
350 400 450 500
Figure 6.24 450-Day History of the Firm Value, Market and Predicted Western Airlines Inc. Convertible Preferred Stock Values
250
V - Market "~ "" ™ 9(Y) - Market
g(V) - Predicted
l —< • — — m i TT. i w w i mixi S rfr.-etf 'urJS'A, ~ *
0 50 100 150 200 250 300 350 400 450 500 Day-
Figure 6.25 Relative Error of Predicted vs. Market Preferred Stock Value
50 100 150 200 250 300 350 400 450 500
42
Table 6.7 Convertible Preferred of Horizon Air Industries Inc.
Horizon Air Industries Inc Security $1.20 cum cvt exch pfd; par $0.02 Issue Date Number of Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convertion Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock Variance - (a)A2 30-year zero-coupon T-bond r Conversion Ratio- Y(T)
12/31/1985 $1,100,000.00
$10.00 $10.25
1.298701299 $1.20
$1,320,000 $11,275,000
0.00103 10.39% 0.2205
Call Schedule: Date Price - k(T) 7/1/1986 7/1/1987 7/1/1988 7/1/1989 7/1/1990 7/1/1991 7/1/1992 7/1/1993 7/1/1994 7/1/1995 7/1/1996
ICalled
$11.20 $11.08 $10.96 $10.84 $10.72 $10.60 $10.48 $10.36 $10.24 $10.12 $10.00
1/30/1987
Other Securities Common Stock Number of Shares Annual Total Dividend Payment
common; par $1.00 5,067,000
$1,320,000
43
Figure 6.26 Valuation of Horizon Air Industries Inc. Convertible Preferred Stock on a Given Trading Day
* t 3
40
35
J 30
> -S 25 o
6o
Pre
ferr
ed
en
o
10
5
n
i i
Day 400
/ .
• • i
i i i
i i i i
j f * -
-
i i i i
20 40 60 80 100 120 140 160 180 200 Total Firm Value
Figure 6.27 450-Day Performance of the Market and Predicted Horizon Air Industries Inc. Convertible Preferred Stock Values
145
14
135
CD
5 12 5
J 11 5 CD
CL ^
1 0 5
10
9 5
" • " —9(Y) - Market — — g(V) - Predicted
<fK/ !
H I
ifd 100 200 300 400
Day 500 600 700
44
Figure 6.28 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
1 8
£ 1 6
:> I 1 4
05
i 1 2
§ -g 0 8
| 06
5 0 4
0 2
°C
" -
)
rt A \ /
100
/
/ i
V \r
200
w I \ JV V\ 1
300 400 Day
jj
Var(V) Var(g)
' \
- ——* 500 600 7C
Figure 6.29 450-Day History of the Firm Value, Market and Predicted Western Airlines Inc. Convertible Preferred Stock Values
70
60
•1 50
c/5 40
£ 30
IB 20
10 h
— — V - Market g(V) - Market 9(Y) • Predicted
H W . - * *
100 2 0 0 300 400 Day
5 0 0 6 0 0 7 0 0
Figure 6.30 Relative Error of Predicted vs. Market Preferred Stock Value
45
Table 6.8 Convertible Preferred of Midway Airlines Inc.
Midway Airlines Inc Security $1.85 ser B cvt ech pfd; par $0.01 Issue Date Number of Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convertion Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock - G Variance - (a)A2 30-year zero-coupon T-bond r Conversion Ratio- Y(T)
12/31/1985 $1,000,000.00
$20.00 $20.00
2.222222222 $1.85
$1,850,000 $20,000,000
0.00097 9.28% 0.2268
Call Schedule: Date Price - k(T) 2/5/1989 2/5/1996 Called
$21.85 $20.00
2/13/1987
Other Securities Common Stock Number of Shares Annual Total Dividend Payment - C
common; par $0.50 7,574,000 $1,850,000
46
Figure 6.31 Valuation of Midway Airlines Inc. Convertible Preferred Stock on a Given Trading Day
70
60
3 50
2
t V) 40 • o
1 £ 30
20
10
n /
** " " " " " " ^
/
i
• i i i
— Day 1 - - - - • Day 400
~
^ ^ ^+"*
^/^ ^+*
^^^ "*
.^^ * » * * ^*r ^++*
-
150 Total Firm Value
200 250
Figure 6.32 450-Day Performance of the Market and Predicted Midway Airlines Inc. Convertible Preferred Stock Values
40
35
£ 30
CO
5 25
20
15
1 1 1
— g(V) - Market
• i LV>^
1 1 — 1
V?
i
$*P • 1 -#
-*//
i i i •
50 100 150 200 250 Day
300 350 400 450
47
Figure 6.33 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
3
2 5
2
1 5
1
0 5
0 5
x icr
•
0
' ~ ~
Var(g)
100 150 200
0-.r~~*
250
-r*
•
•
1 I t
^ f
300 350 400 46 Day
Figure 6.34 450-Day History of the Firm Value, Market and Predicted Midway Airlines Inc. Convertible Preferred Stock Values
200
180
160
^ 140
V - Market — — — g(V) - Market
g(V) - Predicted
4 5 0
Figure 6.35 Relative Error of Predicted vs. Market Preferred Stock Value
200 250 Day
48
Table 6.9 Convertible Preferred of Piedmont Aviation Inc.
Piedmont Aviation Inc Security $3.25 cvt exch pfd; no par Issue Date 5/15/1986 Number of Shares 2,400,000 Convertible Preferred Stock Issue Price $50.00 Convertible Preferred Stock Market Price $51.25 Convertion Ratio 1 Preferred Stock Dividend $3.25 Annual Convertible Dividend Payment - c $7,800,000 Market Value Convertible Preferred Stock - G $123,000,000
Variance - (a)A2 0.00023 30-year zero-coupon T-bond - r 7.41 % Conversion Ratio- Y(T) 0.1149
Call Schedule: Date Price - k(T) 3/14/1987 $53.25 3/14/1988 $52.93 3/14/1989 $52.60 3/14/1990 $52.28 3/14/1991 $51.95 3/14/1992 $51.63 3/14/1993 $51.30 3/14/1994 $50.98 3/14/1995 $50.65 3/14/1996 $50.33 3/15/1996 $50.00 Called 11/4/1987
Other Securities Common Stock Number of Shares Annual Total Dividend Payment - C
common; par $1.00 18,480,000
$12,252,240
Figure 6.36 Valuation of Piedmont Aviation Inc. Convertible Preferred Stock on a Given Trading Day
200 400 600 800 1000 1200 1400 1600 1800 2000 Total Firm Value
Figure 6.37 450-Day Performance of the Market and Predicted Piedmont Aviation Inc. Convertible Preferred Stock Values
240
220
200
> 180
120
100
•g(V) - Market
'g(V) - Predicted
100 200 300 Day
400 500 600
50
Figure 6.38 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
i 1 5
J o s
- Var(V) • Var(g) |
50 100 150 200 250 300 350 400 450 500 550 Day
Figure 6.39 450-Day History of the Firm Value, Market and Predicted Piedmont Aviation Inc. Convertible Preferred Stock Values
1400
800
600
400
200
O
g(V) - Market g(V) - Predicted
200 300 Day
500
Figure 6.40 Relative Error of Predicted vs. Market Preferred Stock Value
51
Table 6.10 Convertible Preferred of U.S. Air Group Inc.
US Air Group Inc Security $4.375 ser B cum cvt pfd; no par Issue Date Number of Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convertion Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock Variance - (a)A2 30-year zero-coupon T-bond - r Conversion Ratio- Y(T)
5/21/1991 4,263,050
$50.00 $52.50
2.49 $2.38
$9,500,000 $210,000,000
0.00107 8.31% 0.1792
Call Schedule: Date 4/1/1994 4/1/2001
I
Price - k(T) $53.06 $50.00
Other Securities Common Stock Number of Shares Annual Total Dividend Payment - C
common; par $1.00 45,624,000 $9,500,000
52
Figure 6.41 Valuation of U.S. Air Group Inc. Convertible Preferred Stock on a Given Trading Day
1500 Total Firm Value
Figure 6.42 450-Day Performance of the Market and Predicted U.S. Air Group Inc. Convertible Preferred Stock Values
280
260
240
220 [fi
~ —™ 90>0 - Market — — g(V) - Predicted
800
53
Figure 6.43 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
O 03S
g O 03
Figure 6.44 450-Day History of the Firm Value, Market and Predicted U.S. Air Group Inc. Convertible Preferred Stock Values
1500
> 1000
V - Market — — — g(V) - Market
g(V) - Predicted
•xy-*-^
1 0 0 400 Day
Figure 6.45 Relative Error of Predicted vs. Market Preferred Stock Value
54
Table 6.11 Convertible Preferred of People Express Airlines Inc.
People Express Airlines Inc Security $2.50 ser B cum cv pfr; par $0.01 Issue Date Number of Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convention Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c
Market Value Convertible Preferred Stock Variance - (o)A2 30-year zero-coupon T-bond - r Conversion Ratio- Y(T)
4/12/1985 $1,200,000.00
$25.00 $26.00
2.5 $2.50
$3,000,000 $31,200,000
0.00089 11.37% 0.1080
Call Schedule: Date Price - k(T) 4/21/1986 4/21/1987 4/21/1988 4/21/1989 4/21/1990 4/21/1991 4/21/1992 4/21/1993 4/21/1994 4/21/1995 4/21/1996 Acquired by Texas Air group on
$13.08 $12.97 $12.86 $12.76 $12.65 $12.54 $12.43 $12.32 $12.22 $12.11 $12.00
12/30/1986
Other Securities Common Stock Number of Shares Annual Total Dividend Payment
common; par $1 22,000,000 $2,500,000
Conv. Pref. Stock Number of Shares
$2.64 ser A cum cv pfd; par $0.01 3,450,000
55
Figure 6.46 Valuation of People Express Airlines Inc. Convertible Preferred Stock on a Given Trading Day
<-JU
70
60
CD
£ 50
_*: o
m 40 CD
•S 30 Q>
20
10
n
-
/
— —
/
i i
— Day 1 - Day 350
i i i i
^0T -
. ^ ^ . • # •
^r **
s^-'' .sT *+ _-X **
SZ'' v ^ ^ > ^ '
- _ ^ >
1 1 1 I 1 1
100 200 300 400 Total Firm Value
500 600 700
Figure 6.47 450-Day Performance of the Market and Predicted People Express Airlines Inc. Convertible Preferred Stock Values
50
45
40
35
8 to
30
20-
15 -
10
~
fchj •1
-
'
~
p*
i i i i
g ( V ) - Market g(V) - Predicted
* \ *
i i
- A
l • m \ • m \ * n i i 11
i i i 100 200 300 400
Day 500 600 700
Figure 6.48 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
Figure 6.49 450-Day History of the Firm Value, Market and Predicted People Express Airlines Inc. Convertible Preferred Stock Values
- V - Market - 9(V) - Market • g(V) - Predicted
Figure 6.50 Relative Error of Predicted vs. Market Preferred Stock Value
57
Table 6.12 Convertible Preferred of Conquest Airlines Inc.
Conquest Airlines Corp Security 12% ser A cum cvt pfd; par $0.10 Issue Date Number of Shares Convertible Preferred Stock Issue Price Convertible Preferred Stock Market Price Convertion Ratio Preferred Stock Dividend Annual Convertible Dividend Payment - c Market Value Convertible Preferred Stock Variance - (a)A2 30-year zero-coupon T-bond - r Conversion Ratio- Y(T)
7/15/1991 400,000
$9.25 $9.75
8 $1.11
$444,000 $3,900,000
0.00189 8.50% 0.4382
Call Schedule: Date 7/5/1992
I
Price - k(T) $9.25
Other Securities Common Stock Number of Shares Annual Total Dividend Payment
common; par $0,001 4,103,000 $444,000
58
Figure 6.51 Valuation of Conquest Airlines Inc. Convertible Preferred Stock on a Given Trading Day
25
20
g 15
10
.
i — i r i - • — i i i I i
Day 1 Day 350
^ ^^ , > ^£> j£*
.^^ /> ^ > ^ > ^^ ^ ^ V
^ > ^y?v ^/++ ^i* ^x>
^ > ^ > ^&
^^v ^ x > ^ >
^ > >& ^2* ^ > ^ > *> ^ > st* . > ^ ^ ~ >^
i i i i i i i i i
10 15 20 25 30 Total Firm Value
35 40 45 50
Figure 6.52 450-Day Performance of the Market and Predicted Conquest Airlines Inc. Convertible Preferred Stock Values
16
14 — — - g ( V ) - Market
— — — g(V) - Predicted
> i
100 200 300 Day
400 500 600
59
Figure 6.53 450-Day Fluctuations of the Total Firm and Preferred Stock Variances
Figure 6.54 450-Day History of the Firm Value, Market and Predicted Conquest Airlines Inc. Convertible Preferred Stock Values
™ 1 0
^ v * " ^ -100 300
Day 500 600
Figure 6.55 Relative Error of Predicted vs. Market Preferred Stock Value
% 0 1
300 Day
60
Analysis of Model-Market Pricing Errors
Results for 5.9 are presented in Table 6.13. The mean pricing error for the sample
convertibles is 2.63 %. Pricing error was calculated as
{Model Pr icei t - Market Pr iceit) ERROR =
Model Pr icei(
Table 6.13 Mean and Median Pricing Errors
y f ° t1 2 ! : 4 8 0 Difference in means
All Sample t ; a d , n gf t \ r a d i n9 between 1-120 and
days after days after 1 2 1 . 4 8 0 s u b s a m p | e s issuance issuance
Mean 2.63% 8.01% 0.10% 7.91%***
(19.29%) Median 4.43% 0.85%
T-statistics presented in parentheses. *** indicate significance at the 1% level.
Data was partitioned into sub-samples according to time following issuance
(1-120 vs. 121-480 trading days). This way the underpricing in the six months following
issuance and underpricing after six months of issuance was tested.
The mean pricing errors for the 1-120 day sub-sample is 8.01%, whereas for the
121-480 day sub-sample it is 0.10 %. The difference in mean pricing errors : mean (1-120
day sub-sample) - mean (121 - 480 day sub-sample) is 7.91 % suggesting that
convertible securities are underpriced about 7.91 % on average for up to six months
following issuance compared to the following eighteen months.
Median prices errors are comparable. The median pricing errors for the 1-120
day sub-sample is 4.43 %, and 0.85 % for the 121 - 480 day sub-sample.
Frequency distributions of the errors in each of the sub-samples are depicted as
histograms in Figures 6.56 - 6.58.The horizontal axes are the same for all histograms to
61
facilitate comparison. Figure 6.56 displays data for the whole period, Figure 6.57 shows
1-120 day period, Figure 6.58 exhibits histogram for the 121-480 day period.
62
Figure 6.56 Frequency Distribution of the Errors (1-480 Days Following Issuance)
M e a n = 0 02631719731 Std Dev. =0 12776945971E N =4,096
Figure 6.57 Frequency Distribution of the Errors (1-120 Days Following Issuance)
-0.20 0.00 0.20
Error First 6 M o n t h s
Mean =0 0 8 0 0 9 6 3 2 0 4 7 Std Dev =0 1 3 5 5 6 2 1 2 2 7 2 5 N =1 .31 0
Figure 6.58 Frequency Distribution of the Errors (121-480 Days Following Issuance)
M e a n = 0 0 0 1 S t d . D e v = 0 1 1 5 3 6 N = 2 . 7 9 8
-0.20 O.OO 0.20 E r r o r 7 - 2 4 M o n t h s
63
Table 6.14 presents issue, market, and model prices of convertible preferred stock
on the first trading day. For 8 out of 11 securities model convertible preferred price is
higher then both issue and market price. It supports our conclusion, that convertibles of
U.S. airlines are underpriced at issuance, and airlines are loosing money, selling the
securities below their price.
Table 6.14 Issue, market, and model prices of convertible preferred stock on the first trading day
Issuer Issue Price Market Price Model Price
$20.00 $19.75 $21.93 Air Florida Systems
Piedmont Aviation UAL Trans World Airlines Western Airlines People Express Airlines Horizon Air $10.00 $10.25 $11.18 Industries Midway Airlines Piedmont Aviation US Air Group Conquest Airlines
$25.00
$24.00
$23.79
$15.00
$25.00
$23.75
$25.75
$21.75
$12.75
$26.00
$26.40
$26.50
$23.98
$16.70
$24.83
$20.00
$50.00
$50.00
$9.25
$20.00
$51.25
$52.50
$9.75
$21.70
$50.42
$49.25
$14.20
Analysis of Pricing Errors in Early Periods Following Issuance
Parameter estimates for models 5.10, 5.11 and 5.12 are presented in Table 6.15
for our sample of U.S. airlines convertible preferred stocks. Model 5.11 estimates
indicates significant underpricing (at the 1 percent level) for two out of the four weeks
following issuance. Underpricing is ranging from 5 % to 5.26 %. Model 5.12 yields
similar results: underpricing is significant (at the 1 percent level) for all six months
following issuance, ranging from 4.66 % to 9.95 %.Underpricing is higher in early
months then gradually tapering off. For all three models, the constant coefficient is not
significantly different from zero indicating that the model is well specified, i.e., other
than the indicated underpricing, the average pricing errors are not significantly different
from zero. This is consistent with the findings of Guzhva (2004), and Ramanlal, Mann
and Moore (1998).
65
Table 6.15 Pricing Error of Convertible Preferred Stock Panel Estimate
Model (5.10)
Model (5.11)
Model (5.12)
Constant 0.0336 (1.29)
Constant 0.0315 (1.22)
Constant 0.007 (0.26)
D1 0.0444 (1.55) W1
0.0450*** (3.51)
M1 0.0687***
(10.97)
D2 0.0451 (1.58) W2
0.0526*** (3.95)
M2 0.0706***
(11.27)
D3 0.0482 (1.69) W3
0.0358 (3.01)
M3 0.0995***
(15.89)
D4 0.0483 (1.69) W4
0.0373 (3.04)
M4 0.0841***
(13.43)
D5 0.0536 (1.88)
M5 0.0686***
(10.96)
M6 0.0466***
(7.33)
Panel-data analysis (random effect model) of pricing errors of convertible preferred stocks using equations:
n=S
ERROR.^a + b.D^+e,, 5.10
ERRORtJ=a + fibmW.J+e,JI 5.11 n=\
«=6
ERROR,, =a + YtbnMm,+eu 5.12 n=\
where: the pncing error for issue i on date t is defined as
(ModelPr ice lt - Market Vr ice lt) ERROR = 5.9
Model Fr ice l(
D1-D5 are the first through fifth day of trading dummies, W1-W4 are the first through fourth week trading dummies, and M1-M6 are the first through sixth month trading dummies. Parameter estimates are presented for two samples separately, with t-statistics in parentheses. *, **, and *** indicate significance at the 10%, 5%, and 1% levels respectively.
66
7. CONCLUSION
Using an option-based valuation model and a sample of 11 convertible preferred
stocks issued by U.S. airlines in 1980 - 1991, daily model prices for two years after
issuance estimated and compared with prices by calculating pricing errors. It turns out
that mean pricing error for the sample is 2.63 %, indicating that market undervalues
airline convertible preferred stocks by about 2.63 %. In addition, a panel data analysis of
pricing errors suggests that market undervaluation in much more severe immediately
after issuance and persists for approximately 6 months. Panel-data analysis provides
evidence of underpricing that varies approximately from 4.66 % to 9.95 % and decreases
with time following issuance. The mean pricing error for a sub-sample containing first six
months of daily prices is found to be 8.01 %, while for a sub-sample of convertible daily
prices for 7-24 months after issuance the mean pricing error is 0.10 %. The underpricing
is statistically and economically significant.
Based on model valuation, airline companies tend to issue convertible securities at
a price lower than the model calculated price. 8 out of 11 companies issued convertible
securities at a discount, which lowered the amount of money the airlines could have
raised should they issued the securities at the model calculated price.
There are two potential explanations of observed discrepancy between market and
model pricing of airline convertibles shortly after issuance: model mispricing or market
undervaluation. Since utilized model was extensively tested and found to be superior in
pricing convertible preferred stocks market undervaluation seems to be a plausible
explanation. Pricing model cannot capture investor sentiment towards traded securities.
67
Probably, market perception of airlines as higher risk companies, influences
prices of newly issued convertibles. Even the airline companies may make their securities
more attractive to buyers by offering them at a discount, they are sending the wrong
message about the well-being of the company, and missing on the opportunity to raise
more money. However, in about six months of trading, the insensitivity of properly
designed convertibles to the risks of issuing companies becomes obvious and the market
and theoretical values of convertibles converge.
Market undervaluation of airline convertibles at issuance suggests that, probably
due to their reputation, airlines cannot efficiently raise capital even with convertibles.
Airlines are leaving money on the table when they raise funds from investors.
Understanding of this issue may help U.S. airlines in their need for capital.
In conclusion, the current work suggests that the employed valuation model may
also be helpful in proposing new approaches for making the convertible offerings more
attractive to investors, based on optimized sets of contractual parameters. Such
parameters may include call protection period, and call/dividend payment schedule.
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