Volume 33, Issue 1: Paper 4
A New Look at IPO Secondary Market Returns[1]
Jackson T.L Powell, Belmont University
Initial Public Offerings (IPOs) represent pivotal moments, serving as significant milestones in the life cycle of companies as they enter the stage of public trading. While the limelight often focuses on the IPO launch, the secondary market, occurring on the first day of trading, is where some of the most interesting post-IPO information is gathered. By uncovering underwriters strategic pricing maneuvers and safeguarding retail traders against losses, the research sheds light on the significance of underpricing, revealing its true impact on investors.
This study undertakes a thorough examination of IPO secondary market returns, aiming to illuminate the dynamics that unfold after the inaugural opening bell. Covering IPOs during the period of January 1st, 2004, to December 31st, 2023, this study rigorously analyzes the offer-to-open (15.59 percent), open-to-close (1.02 percent), and offer-to-close (16.77 percent) returns of 1671 IPOs. Utilizing industry-specific controls, measures of underpricing, and measures of market volatility, this study seeks to unveil whether there are predictable secondary market returns, thus contributing to the literature surrounding the Efficient Market Hypothesis. The Efficient Market Hypothesis proposes that financial markets reflect all available information and efficiently price securities, making it impossible for investors to consistently outperform the market.
In seminal work in this area, Bradley and Gonas (2009) explore secondary market returns during specific intraday time intervals for 2351 IPOs in U.S. markets spanning January 1st, 1993, to December 31st, 2003. Their work revealed an economically and statistically significant first day return of 2.3 percent. The main finding of their study is that almost all returns occurred within the first 15 minutes of trading, suggesting that there is a small window of time for the market to adjust post-IPO information. Distinguishing the current study from theirs is the unavailability of access to intraday trading information, thus limiting my ability to scrutinize peak returns comprehensively.
The study delves into the gray area that persists in the literature surrounding IPO secondary market returns. By discerning the industries that yield the highest returns, examining the impact of underpricing on returns, assessing the influence of market volatility, and identifying the primary beneficiaries, I contribute to the literature by offering nuanced insights into IPOs of the post Early 2000s Recession and 2008 Great Recession eras once they begin trading. In doing so, my study distinguishes itself as one of the few with such insights.
The subsequent sections of this paper are organized as follows: Section 2 provides a comprehensive review of previous literature, Section 3 details the data and descriptive statistics, Section 4 presents empirical results, and Section 5 draws conclusions, consolidating the findings of this study.
II. Related Literature
The literature underpinning my research draws from three specific papers that explore underpricing, market volatility, and the beneficiaries of IPO returns. Bradley and Gonas (2009) conduct comprehensive analysis of 2351 IPOs spanning from January 1st, 1993, to December 31st, 2003. Their investigation reveals that intraday returns, on average, experience a gain of 2.3 percent during this period. Notably, they observe that the market does not reach equilibrium pricing on the first day of trading until approximately 2 hours into the session. Documenting the influence of underwriters on the pricing of “cold” IPOs—defined as IPOs with an offer-to-open return of less than 2.67 percent—however, the study is unable to directly test the implications of laddering, which refers to the allocation of IPOs to clients who commit to buy additional shares of the offering company’s stock in the secondary market. Their findings include a positive relationship between the proportion of small trades and open-to-close returns, consistent with the notion that retail demand and sentiment can drive IPO prices higher. Lastly, they identify that open-to-close returns exhibit a negative correlation with firm size, and a positive correlation with market volatility and beta.
In a study by Barry and Jennings (1993), which examines a sample of 229 operating companies and closed-end funds from 1988 to 1990, the focus shifts to offer-to-open returns. Their research reveals an impressive return of over 8 percent. Interestingly, their findings indicate that the median first day’s open-to-close return is around 60 basis points, and fewer than half of all IPOs have positive returns on the first day after the opening transaction. Consequently, only the initial purchasers of securities in the IPO itself benefit from underpricing.
Meanwhile, Hunt-McCool, Koh, and Francis (1996) examine 1035 IPOs from 1975 to 1984. Their emphasis was on IPO underpricing sensitivity to specific market periods, particularly short bear and bull cycles creating ‘hot’ and ‘cold’ markets. Their results indicate that a ‘hot’ market exhibits both higher abnormal returns and more underpricing in the premarket. Furthermore, their study confirms that premarket underpricing could clarify most abnormalities in aftermarket returns. However, they encountered challenges in fully unraveling the impact of underwriter reputation, consumer confidence or fads, and market power on the part of the underwriter.
My assertions that the principal recipients of IPO secondary market returns are initial purchasers and that returns are influenced by market volatility are validated in existing literature. However, there is a noticeable gap as no literature explicitly addresses whether certain sectors yield the highest returns on the launch day. Consequently, I rely on my own findings to document which sectors demonstrate the highest returns during the period from 2004 to 2023.
III. Data
The sample of IPOs sourced from the Bloomberg Database, covers the period from January 1st, 2004, to December 31st, 2023. In alignment with established research methodologies, notably those employed by Bradley and Gonas (2009), I systematically excluded depository shares, spin-offs, real estate investment trusts (REITs), reverse leveraged buyouts, and closed-end funds. Further refinement involved filtering out IPOs with an offer price below $5.00, resulting in a finalized sample size of 1671.
To avoid the potentially confounding effects of foreign markets, I focus on IPOs within the U.S. markets. The selected companies were required to be actively traded, listed on either the Nasdaq or NYSE, and exclusively issuing pure common stock. The data reveals an average market cap of approximately $905.45 million, a mean offer size of roughly $237 million, and an average offer price of $18.31/share.
Table I contains summary statistics for all variables used in the analysis. The data is split into market capitalization categories of small cap, mid cap, and large cap. A small market cap is defined as greater than $250 million, but less than $2 billion. A mid cap company falls within the $2 billion to $10 billion range. And a large cap company exceeds $10 billion market cap. The natural log of market cap is used to capture the potential size impact of the firm. The study also strategically focuses on four primary sectors—consumer-cyclical, financial, technology, and healthcare—accounting for a significant 67.56 percent of IPOs during the specified period, with healthcare alone constituting 27.83 percent. The volatility metrics, sourced from Federal Reserve Economic Data Base – CBOE Volatility Index: VIX, were assessed using the S&P 500 as the market index and VIX as the volatility index. The market variables include S&P daily returns over the 20-year period and average return from the 20 trading sessions prior. Volatility variables consist of the volatility index, VIX, and average volatility from the previous 20 trading sessions. These variables are indicators of how volatility and market conditions affect returns at any given time.
In contrast to preceding literature, my common variable of open-to-close returns (intraday) registers at 1.02 percent. This figure surpasses Barry and Jennings (1993) sample return of merely 60 basis points, while slightly falling short by just under 140 basis points when compared to Bradley and Gonas (2009) samples of intraday returns.
Aligned with my objective of identifying predictable IPO secondary market returns, assessing the impact of volatility, and discerning industries experiencing significant returns, I conduct four distinct regressions. These regressions are systematically categorized based on various fixed effects, including industry, time, market, and volatility. Each regression is executed independently for offer-to-open returns, intraday returns, and offer-to-close returns.
IV. Results
The table presents key descriptive statistics. The Offer Price denotes the initial valuation of a stock before its introduction to the secondary market. Offer Size represents the total value of securities offered by a company to investors during the IPO, reflecting the capital the firm aims to raise. Market Cap serves as a measure of the IPOs’ market valuation, categorized into small, mid, and large cap firms based on their market capitalization. Small caps range from $250 million to $2 billion, mid-caps from $2 billion to $10 billion, and large caps exceeding $10 billion. The natural log of market cap is employed to account for potential size impacts. The Volatility Index (VIX) and 20-Day Volatility Average gauge market volatility, with higher VIX values indicating greater volatility. Previous Day S&P captures the market return from the preceding day, while 20-Day S&P Return calculates the mean return over the prior 20 trading days. Offer-to-Open signifies the percentage change from the IPO offer price to the first trade, Open-to-Close denotes the percentage change from the first trade price to the closing price, and Offer-to-Close represents total underpricing, indicating the percentage change from the offer price to the closing price on the first day.
Table I: Descriptive Statistics
| N | Mean | Standard Dev. | Minimum | Maximum | |
|---|---|---|---|---|---|
| Offer Price ($) | 1671 | 18.31 | 50.91 | 5.00 | 1800.00 |
| Offer Size ($m) | 1671 | 236.56 | 434.13 | 0.439 | 8100.00 |
| Market Cap ($m) | 1671 | 905.45 | 2848.91 | 0.00 | 75713.4 |
| Natural Log of Market Cap (%) | 1523 | 6.10 | 1.20 | 2.57 | 11.24 |
| Small Cap | 1671 | 0.53 | 0.50 | 0 | 1 |
| Mid Cap | 1671 | 0.10 | 0.30 | 0 | 1 |
| Large Cap | 1671 | 0.01 | 0.08 | 0 | 1 |
| Volatility Index | 1663 | 17.13 | 5.73 | 9.14 | 57.08 |
| 20-Day VIX Average | 1663 | 17.24 | 5.40 | 9.78 | 33.26 |
| Previous Day S&P Return (%) | 1663 | -0.03 | 0.86 | -3.18 | 4.62 |
| 20-Day S&P Return (%) | 1663 | -0.79 | 3.51 | -15.17 | 33.26 |
| Offer-to-Open Return (%) | 1671 | 15.59 | 33.96 | -100.00 | 533.33 |
| Open-to-Close Return (%) | 1668 | 1.02 | 14.17 | -79.53 | 217.37 |
| Offer-to-Close Return (%) | 1671 | 16.77 | 40.34 | -100.00 | 689.40 |
A. Offer-to-Open Returns
Table II presents offer-to-open statistics, revealing an average return of 15.59 percent. The model to calculate offer-to-open returns is as follows:
$$\displaylines{OpenReturn=\ \beta_0+\beta_1{LNSIZE}_i+\beta_2{SMALLCAP}_i+\beta_3{MIDCAP}_i+\beta_4{LARGECAP}_i\\+\beta_5{CONSUMERCYCLICAL}_i+\beta_6{FINANCIAL}_i+\beta_7{TECHNOLOGY}_i\\+\beta_8{HEALTHCARE}_i+\delta_i+\epsilon}$$
Notably, an increase in market capitalization, as indicated by lnsize, corresponds to a rise in offer-to-open returns, with a 5.52 percent increase for every 1 percent increment in market cap. This suggests that larger companies tend to yield greater returns. However, despite the seemingly significant increase, large cap returns hover around -23 percent when considering the most saturated model. Similarly, mid-cap returns also show negative returns of 9 percent. Thus, while the natural log of market cap, lnsize, is significant, relying solely on market cap for returns results in negative returns across all sizes of issuing firms.
Table II: Offer-to-Open Returns
| (Industry) Returns |
(Time) Returns |
(Market) Returns |
(Volatility) Returns |
|
|---|---|---|---|---|
| Natural Log of Market Cap | 5.464*** (1.279) |
5.637*** (1.233) |
5.526*** (1.241) |
5.517*** (1.248) |
| Small Cap (%) | 0.147 (2.491) |
-0.0998 (2.568) |
-0.0224 (2.572) |
-0.0153 (2.585) |
| Mid Cap (%) | -7.631* (4.585) |
-9.554** (4.476) |
-9.088** (4.460) |
-9.061** (4.476) |
| Large Cap (%) | -21.79** (10.82) |
-23.13** (10.88) |
-23.06** (10.89) |
-23.08** (10.87) |
| Consumer-Cyclical (%) | -39.35*** (12.19) |
-36.12*** (13.77) |
-35.80*** (13.51) |
-35.96*** (13.69) |
| Financial (%) | -12.71 (16.47) |
-16.73 (16.31) |
-16.82 (16.27) |
-16.76 (16.32) |
| Technology (%) | -10.15 (12.29) |
-15.06 (11.15) |
-14.97 (11.08) |
-14.89 (11.16) |
| Healthcare (%) | -15.95 (12.74) |
-22.29* (11.59) |
-22.39* (11.51) |
-22.36* (11.59) |
| N | 1523 | 1523 | 1515 | 1515 |
| r2 | 0.119 | 0.166 | 0.166 | 0.166 |
| Industry FE | Yes | Yes | Yes | Yes |
| Time FE | Yes | Yes | Yes | |
| Market FE | Yes | Yes | ||
| Volatility FE | Yes |
When examining the four main sectors, consumer-cyclical, which is comprised of firms with ties to the business cycle – retail, automotive, restaurants, entertainment, and lodging, offer notably poor returns, posting almost a -35.96 percent return, almost 14 percent worse than other sectors. Financial, healthcare, and technology sectors also show significant negative returns; healthcare, particularly experiences a sharp drop due to factors like market conditions and volatility.
Although dissecting the exact timing of poor performance in an IPOs first day is challenging, macro-events provide insight into return assumptions. During the period of the 2008 Financial Crisis, King and Banderet (2014) found that IPOs underperformed by 26 percent, highlighting the influence of timing, market factors, and significant volatility.
An industry fixed effect corresponds to an industry dummy variable utilized within the model. This dummy variable encompasses industries spanning the four primary sectors to assess their impact on returns. Time denotes the specific month and year when the IPO began trading. The market fixed effect comprises variables such as the previous day S&P return and 20-Day S&P. The previous day S&P captures the market’s return from the day prior, while the 20-Day S&P return calculates the average return over the preceding 20 trading days. Additionally, the Volatility Index (VIX) and 20-Day Volatility Average serve as metrics for measuring market volatility, where higher VIX values signify increased volatility. Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01
B. Offer-to-Close Returns
Offer-to-Close, as shown in Table III, explores similar variables with slightly different outcomes. Underpricing, a term often associated with offer-to-close returns, is evident, with IPOs underpriced by an average of 16.77 percent on the first day of trading, enabling initial purchasers and secondary market investors to seek profit on select investments. The model to determine underpricing results follows:
Examining the natural log of market cap reveals that for every 1 percent change in market cap, there is nearly a 6 percent change in offer-to-close returns. Although small-cap has no significant impact on returns, mid-cap and large-cap firms exhibit substantial effects, with mid-cap firms returning -10.54 percent and large-cap firms experiencing a considerable loss of 27.51 percent. Moreover, returns worsen throughout the day, suggesting potential increased losses for holders of mid and large-cap stocks.
The four primary sectors examined – consumer-cyclical, financial, healthcare, and technology – all show improvements compared to offer-to-open sector returns. Notably, consumer-cyclical sees a significant reduction in losses, dropping from nearly -36 percent to just -7.40 percent by the end of the first trading day. Although the other sectors show modest rebounds, they are overshadowed by the remarkable 28 percent rebound in consumer-cyclical returns. Further examination of yearly trends from Baig and Chen (2022) reveals that in 2020, amidst the Covid-19 pandemic, IPOs witnessed an average return of roughly 23 percent, underscoring the enduring impact of market conditions, volatility, and timing on IPO trends.
Table III: Offer-to-Close Returns
| (Industry) Returns |
(Time) Returns |
(Market) Returns |
(Volatility) Returns |
|
|---|---|---|---|---|
| Natural Log of Market Cap | 6.701*** (1.554) |
6.112*** (1.498) |
6.001*** (1.510) |
5.996*** (1.517) |
| Small Cap (%) | 0.512 (2.639) |
0.292 (2.656) |
0.279 (2.690) |
0.293 (2.693) |
| Mid Cap (%) | -10.40** (5.271) |
-10.71** (5.176) |
-10.46** (5.182) |
-10.54** (5.203) |
| Large Cap (%) | -28.54** (11.49) |
-27.28** (11.62) |
-27.29** (11.73) |
-27.51** (11.78) |
| Consumer-Cyclical (%) | -17.83 (14.38) |
-9.990 (14.89) |
-7.806 (15.11) |
-7.397 (14.70) |
| Financial (%) | -9.113 (18.80) |
-13.60 (18.54) |
-12.82 (18.85) |
-12.65 (18.37) |
| Technology (%) | -9.886 (14.49) |
-14.41 (13.60) |
-13.19 (13.83) |
-13.48 (13.40) |
| Healthcare (%) | -16.24 (14.81) |
-22.30 (14.03) |
-21.44 (14.25) |
-21.97 (13.82) |
| N | 1523 | 1523 | 1515 | 1515 |
| r2 | 0.0911 | 0.127 | 0.128 | 0.129 |
| Industry FE | Yes | Yes | Yes | Yes |
| Time FE | Yes | Yes | Yes | |
| Market FE | Yes | Yes | ||
| Volatility FE | Yes |
An industry fixed effect corresponds to an industry dummy variable utilized within the model. This dummy variable encompasses industries spanning the four primary sectors to assess their impact on returns. Time denotes the specific month and year when the IPO began trading. The market fixed effect comprises variables such as the previous day S&P return and 20-Day S&P. The previous day S&P captures the market’s return from the day prior, while the 20-Day S&P return calculates the average return over the preceding 20 trading days. Additionally, the Volatility Index (VIX) and 20-Day Volatility Average serve as metrics for measuring market volatility, where higher VIX values signify increased volatility. Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01
Offer-to-Close returns underscore the underpricing of IPOs by 16.77 percent. However, with variables indicating negative returns across all market capitalizations and sectors, it’s essential to note significant losses recover throughout the day. Once again, initial purchasers benefit compared to secondary market traders.
C. Open-to-Close Returns
Table IV: Open-to-Close Returns
| (Industry) Returns |
(Time) Returns |
(Market) Returns |
(Volatility) Returns |
|
|---|---|---|---|---|
| Natural Log of Market Cap | 0.782 (0.714) |
0.355 (0.736) |
0.377 (0.738) |
0.389 (0.743) |
| Small Cap (%) | 0.251 (1.127) |
0.196 (1.158) |
0.174 (1.164) |
0.171 (1.161) |
| Mid Cap (%) | -1.946 (2.189) |
-1.071 (2.204) |
-1.186 (2.197) |
-1.260 (2.201) |
| Large Cap (%) | -5.301 (3.728) |
-3.831 (3.787) |
-3.956 (3.799) |
-4.026 (3.775) |
| Consumer-Cyclical (%) | 26.24*** (4.398) |
31.98*** (6.142) |
33.29*** (6.215) |
33.71*** (6.133) |
| Financial (%) | 3.732 (4.408) |
4.041 (4.958) |
4.648 (5.209) |
4.641 (5.170) |
| Technology (%) | 0.706 (4.340) |
1.073 (4.659) |
1.554 (4.728) |
1.310 (4.607) |
| Healthcare (%) | 0.763 (4.416) |
1.189 (4.772) |
1.576 (4.838) |
1.297 (4.711) |
| N | 1520 | 1520 | 1512 | 1512 |
| r2 | 0.0400 | 0.0767 | 0.0811 | 0.0838 |
| Industry FE | Yes | Yes | Yes | Yes |
| Time FE | Yes | Yes | Yes | |
| Market FE | Yes | Yes | ||
| Volatility FE | Yes |
An industry fixed effect corresponds to an industry dummy variable utilized within the model. This dummy variable encompasses industries spanning the four primary sectors to assess their impact on returns. Time denotes the specific month and year when the IPO began trading. The market fixed effect comprises variables such as the previous day S&P return and 20-Day S&P. The previous day S&P captures the market’s return from the day prior, while the 20-Day S&P return calculates the average return over the preceding 20 trading days. Additionally, the Volatility Index (VIX) and 20-Day Volatility Average serve as metrics for measuring market volatility, where higher VIX values signify increased volatility. Standard errors in parentheses * p < 0.10, ** p < 0.05, *** p < 0.01
Open-to-close returns, Table IV, intuitively represent the spread between offer-to-close and offer-to-open returns. The open-to-close return, at 1.02 percent, falls short of Bradley and Gonas’ (2009) 2.3 percent. Although seemingly insignificant, these returns favor secondary market traders. Notably, a 1 percent increase in market cap yields an average return of 0.39 percent within the first trading day. Specifically, small cap remains insignificant, while mid-cap and large-cap firms exhibit slightly negative open-to-close returns. I investigate additional results with the following model:
Unlike offer-to-open and offer-to-close sector returns, open-to-close sector returns are positive across the board. Consumer-cyclical stands out with an average return of 33.71 percent during the first trading day. Moreover, the return steadily increases as control variables are factored in, suggesting consumer-cyclical’s resilience to intraday volatility. The other three sectors – financial, technology, and healthcare – offer positive returns, but remain within the 1 to 5 percent range. Returns in other sectors are not statistically significant.
While open-to-close returns barely hold over the break-even threshold, they represent a positive outcome for secondary market traders. Initial purchasers continue to be the primary beneficiaries of IPO underpricing, but there is potential for profitability in the secondary market. While no definitive trend can be established across the three returns, it’s essential to note that almost all sectors were overpriced by underwriters before correcting at the market opening, allowing some IPOs to make significant gains, and providing higher returns for both initial purchasers and secondary market traders.
V. Conclusion
The predictability of secondary market returns for IPOs remains a mystery, yet strides have been made in unraveling the many influences of IPO pricing and performance. This investigation delves into the influence of market volatility, underlying market factors, timing, and underpricing.
Offer-to-open mean returns were nearly 16 percent, yet market cap sizes, specific sector inclusion, and time present a different picture. With consistent negative returns, it’s evident that consumer-cyclical, financial, healthcare, and technology IPOs are overpriced, leading to a price correction at the market opening. Consequently, initial purchasers still have a higher probability of significant positive returns compared to secondary market traders.
Underpricing emerges as the predominant factor driving significant offer-to-close returns; however, discerning whether this phenomenon stems from strategic maneuvering by underwriters or mere luck for initial purchasers poses a challenge.
Across the range of offer-to-open, offer-to-close, or intraday returns, the timing of transactions, market conditions, and volatility emerge as pivotal factors shaping IPO secondary market returns. While I may not have the data to perfectly isolate each of these control variables, their undeniable correlation with IPO returns is evident. Moreover, macro events such as recessions, geopolitical tensions, or health crises invariably influence market, time, and volatility dynamics, thereby impacting IPO performance during the period under review.
Amidst the uncertainties, significant revelations have come to light. The intricate implications of laddering, underwriting reputation, consumer confidence, and underwriters’ market power, as highlighted in the studies of Hunt-McCool, Koh, and Francis (1996) and Bradley and Gonas (2009), remain challenging to analyze. Furthermore, it becomes evident that the primary beneficiaries of underpricing are the initial purchasers. Despite the influences of timing, market conditions, and volatility on IPO performance, there are limited insights into profitability and predictability of first day IPO returns throughout the 2004–2023 period.
The significance of comprehending the IPO secondary market has become evident. While the first day of trading offers lucrative opportunities for initial investors benefiting from underwriters strategic pricing, it is similar to stepping into a casino for retail traders. With profitability hovering around 50 percent and marginal returns barely surpassing 100 basis points, the IPO launch is hardly beneficial to achieving financial freedom for retail investors. It’s wise to seek out alternative investment strategies.
VI. References
Baig, Ahmed S., and Mengxi Chen. “Did the COVID-19 pandemic (really) positively impact the IPO Market? An Analysis of information uncertainty.” Finance Research Letters 46, Part B (2022): Accessed February 2, 2024. https://doi.org/10.1016/j.frl.2021.102372.
Barry, Christopher B., and Robert H. Jennings. “The Opening Price Performance of Initial Public Offerings of Common Stock.” Financial Management 22, no. 1 (1993): 54–63. Accessed January 27, 2024. https://doi.org/10.2307/3665965.
Bloomberg. (2012) “Historical Initial Public Offering Data”, Bloomberg Professional. [Online]. Available at: Subscription Service (Accessed: 16 February 2024)
Bradley, Daniel J., John S. Gonas, Michael J. Highfield, and Kenneth D. Roskelley. “An Examination of IPO Secondary Market Returns.” Journal of Corporate Finance 15, no. 3 (2009): 316-330. Accessed January 20, 2024
Chicago Board Options Exchange, CBOE Volatility Index: VIX [VIXCLS], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/VIXCLS, February 13, 2024.
Hunt-McCool, Janet, Samuel C. Koh, and Bill B. Francis. “Testing for Deliberate Underpricing in the IPO Premarket: A Stochastic Frontier Approach.” The Review of Financial Studies 9, no. 4 (1996): 1251–69. Accessed January 20, 2024. http://www.jstor.org/stable/2962228.
King, Emmet, and Luca Banderet. “IPO Stock Performance and the Financial Crisis.” SSRN, Accessed February 2, 2014. http://dx.doi.org/10.2139/ssrn.2456220.
S&P Dow Jones Indices LLC, S&P 500 [SP500], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/SP500, February 15, 2024.
VII. Notes
[1] Thanks to Dr. Dustin J Rumbaugh and Dr. John S. Gonas for their mentorship.