Understanding Stocks

In the previous module, we focused on fixed income securities and analyzed borrowing and lending through the lenses of interest rates, cash-flow certainty, and default risk. In this module, we move away from contractual cash flows and turn our attention to risk assets, specifically equities and cryptocurrencies. Unlike bonds, these instruments do not promise fixed payments. Instead, their appeal lies in uncertain but potentially higher returns, accompanied by significantly greater volatility.

This shift marks an important conceptual transition: from securities designed to preserve capital and generate predictable income to assets intended to capture growth and upside, often at the cost of higher risk.

To understand the role of stocks, it is useful to begin with a comparison to bonds.

Bondholders benefit from contractual protections. They receive fixed coupon payments at predetermined intervals and are entitled to repayment of principal at maturity, provided the issuer does not default. In the event of default, bondholders have priority over shareholders in claims on the firm’s assets. However, these protections come with a clear limitation: bondholders do not participate in the firm’s success beyond the agreed-upon payments. Exceptional corporate performance does not translate into additional gains for lenders.

Stocks are designed to remove this limitation.

A stock represents ownership, not lending. Shareholders own a fractional claim on the firm and therefore participate directly in both its successes and failures. If the firm grows, becomes more profitable, or increases its market valuation, shareholders benefit through rising share prices and, in some cases, dividends. Conversely, if the firm performs poorly, shareholders bear the downside risk and may lose part or all of their investment.

In modern markets, stock ownership is recorded electronically rather than through physical certificates. Ownership typically comes with voting rights, allowing shareholders to participate – at least formally – in corporate governance. While individual investors usually hold too few shares to influence decisions, shareholders collectively elect a board of directors, which appoints senior management and oversees strategic direction.

Stocks are also referred to as equities, a term rooted in accounting. From the fundamental accounting identity,

we obtain, by rearrangement,

Equity therefore represents the residual claim on a firm’s assets after all obligations to creditors have been satisfied. This residual belongs to shareholders. As a firm acquires more productive assets or reduces its liabilities, the value of equity increases, at least in principle.

Firms finance their operations and growth in two broad ways: by issuing debt (liabilities) or by issuing shares (equity). The choice between debt and equity financing is a central corporate finance decision and has implications for risk, control, and long-term sustainability.

Public companies issue shares through organized stock exchanges such as the NYSE, NASDAQ, or FTSE. From the firm’s perspective, issuing equity provides capital without the obligation of fixed repayments. From the investor’s perspective, buying equity offers exposure to the firm’s future performance.

Stock prices fluctuate continuously as new information, expectations, and market sentiment are incorporated into prices. While investors hope that prices rise over time, positive outcomes are never guaranteed. Poor management, adverse economic conditions, or structural industry changes can all lead to losses, and in extreme cases, bankruptcy can render equity holdings worthless.

Not all stocks are alike. Investors often classify equities based on their risk profiles, income characteristics, and growth potential:

• Value stocks are associated with relatively stable firms whose shares appear undervalued by the market. These companies often generate steady cash flows and may pay dividends, making them attractive to investors seeking resilience rather than rapid growth.

• Growth stocks emphasize expansion and reinvestment. These firms typically exhibit higher volatility but offer the potential for substantial capital appreciation as revenues and earnings grow faster than the broader market.

• Income stocks prioritize regular dividend payments and are often used to supplement fixed income portfolios. While they tend to have limited growth prospects, they can provide relatively stable cash flows.

• Dividend aristocrats are firms, primarily within the S&P 500, that have increased dividends consistently for at least 25 consecutive years. Their rarity and track record make them attractive to investors seeking a combination of income stability and modest growth.

Each category reflects a different trade-off between risk, income, and expected return.

Investors can acquire shares through two distinct markets:

• Primary markets, where new shares are issued directly by the firm, most commonly through an initial public offering (IPO). These offerings are typically underwritten by investment banks and are often dominated by institutional investors due to scale and allocation practices.

• Secondary markets, where existing shares are traded among investors on exchanges. Most individual investors participate exclusively in secondary markets, where liquidity allows shares to be bought and sold quickly at prevailing market prices.

Active secondary markets benefit both investors and firms by enhancing liquidity and price discovery.

From an investor’s perspective, stocks offer the possibility of long-term wealth accumulation and participation in economic growth. From a firm’s perspective, issuing equity provides access to capital without fixed repayment obligations and can support expansion, innovation, or balance-sheet restructuring.

Understanding these motivations sets the stage for analyzing expected returns, volatility, and risk, topics that become even more pronounced when we extend the discussion to cryptocurrencies in the next section.

From an investor’s perspective, stocks offer several advantages that distinguish them sharply from fixed income securities.

• Capital Appreciation

The primary attraction of equities is the potential for capital appreciation, an increase in the market value of the shares over time. If an investor purchases a stock at one price and later sells it at a higher price, the difference represents a capital gain. This mechanism underlies many equity investment strategies.

Some investors focus on identifying firms that appear undervalued relative to their fundamentals and expect prices to adjust upward over time. Others invest in firms that already command high valuations but are expected to grow even further. In both cases, capital appreciation reflects the market’s reassessment of the firm’s future prospects while the investor holds the asset.

• Dividend Income

In addition to price appreciation, stocks may generate income through dividends. When firms earn profits, management can either distribute a portion of those earnings to shareholders or retain them to fund expansion, acquisitions, or research and development.

Dividend payments provide a recurring cash flow to investors, though they are neither guaranteed nor fixed. Unlike bond coupons, dividends depend on profitability and corporate policy, and firms may increase, reduce, or suspend them at any time.

• Ownership and Voting Rights

Shareholders are legal owners of the firm and typically receive voting rights proportional to the number of shares they hold. These votes are primarily exercised in the election of the board of directors, which oversees management and sets strategic direction.

While individual investors rarely exert meaningful influence, voting rights become economically significant for large shareholders or activist investors who accumulate substantial ownership stakes in order to influence corporate decisions.

• Liquidity and Price Transparency

Stocks trade on centralized exchanges, which provide continuous price discovery during market hours. Investors can observe market prices in real time and convert their holdings into cash with relatively low transaction costs.

This liquidity and transparency sharply distinguish equities from assets such as real estate or collectibles, which are difficult to value precisely and costly to trade.

• Securities Lending Income

Equity ownership may also generate indirect income through securities lending. Investors who hold shares can allow their broker to lend those shares to short sellers in exchange for a lending fee.

During the lending period, the investor typically retains economic exposure to the stock, including dividend entitlement, while earning additional income from the lending activity. This feature makes equities unique among commonly held investment assets.

• Secure Ownership Infrastructure

Equity ownership is supported by a highly centralized and robust infrastructure of exchanges, clearinghouses, custodians, and depositories. This system ensures accurate recordkeeping and minimizes disputes over ownership.

Compared to assets such as real estate – where title disputes are possible and title insurance is required – stocks benefit from standardized settlement and centralized registries, significantly reducing legal and administrative risk.

Firms issue stock as a means of raising capital without incurring fixed repayment obligations.

• Debt Financing vs. Equity Financing

When a company issues bonds, it commits to periodic interest payments and eventual repayment of principal. These obligations exist regardless of whether the firm’s projects generate immediate cash flows. A mismatch between investment horizons and debt servicing requirements can lead to early financial distress or default.

By contrast, issuing equity allows a firm to raise capital by selling ownership stakes. Equity does not require repayment and imposes no mandatory cash-flow commitments. For firms with long development cycles, uncertain revenues, or high growth potential, equity financing is often more sustainable than debt financing.

• Going Public and Ownership Dilution

When a firm goes public, it exchanges a portion of ownership for capital provided by outside investors. Existing owners experience dilution, their percentage ownership declines – but the firm gains resources to expand operations, invest in innovation, or strengthen its balance sheet.

Investors who purchase shares in young or rapidly growing firms often accept the absence of dividends, expecting returns primarily through long-term appreciation.

The advantages of equity ownership are inseparable from significant risks:

• Price Volatility and Capital Loss

Stock prices fluctuate continuously and can decline sharply. If an investor sells shares at a price below the purchase price, the loss becomes realized. Even unrealized losses can materially affect portfolio value and investor behavior. Unlike fixed income securities held to maturity, stocks offer no principal protection.

• Uncertain Income

Dividend payments are discretionary. Firms may reduce or eliminate dividends due to financial stress or strategic reinvestment decisions. Investors relying on dividend income face uncertainty that does not exist with contractual bond coupons.

• Limited Control for Small Investors

Although shareholders have voting rights, most investors hold too few shares to influence outcomes. Corporate control may be concentrated among founders, families, institutions, or activist investors. Activist involvement, while sometimes value-enhancing, can also introduce instability and short-term pressure on management.

• Subordination in Bankruptcy

In the event of bankruptcy, equity holders are residual claimants. Secured creditors are paid first, followed by unsecured creditors and other priority claims. Shareholders receive payment only if assets remain after all obligations have been satisfied – an outcome that is often unlikely.

• Market Access Constraints

Equity markets do not operate continuously. Stocks trade only during exchange hours, and significant price adjustments can occur between sessions in response to new information. This gap risk can prevent timely exit during adverse events.

• Loss of Control for Issuing Firms

From the firm’s perspective, issuing stock dilutes ownership and may reduce control over strategic decisions. Large outside shareholders or activist investors can influence board composition and management, potentially altering the firm’s original vision. In some cases, debt financing may preserve control more effectively than equity issuance.

A central motivation for investing in equities is the expectation of capital appreciation. Assessing whether such appreciation is likely requires forming a view about a stock's intrinsic value, an estimate of what the stock should be worth based on its expected future cash flows and risk profile.

Stock valuation is not an exact science. Even professional analysts produce widely differing estimates for the same firm. Nevertheless, valuation models provide a disciplined framework for thinking about prices, expectations, and risk. Most valuation techniques are grounded in corporate finance and the time value of money.

At one end of the spectrum are discounted cash flow (DCF) models, which attempt to value the entire firm based on detailed forecasts of operating cash flows. These models are powerful but require extensive firm-specific knowledge and are typically used by professional analysts.

At the other end are dividend-based and relative valuation models, which are more accessible and rely on fewer inputs. Among these, the Gordon Growth Model (GGM) and its extensions offer a simple yet insightful approach to equity valuation, particularly for mature, dividend-paying firms.

The Gordon Growth Model is a special case of the dividend discount model. It is based on a straightforward idea: the value of a stock today equals the present value of all future dividends the stock is expected to pay.

Under the GGM, dividends are assumed to grow at a constant rate forever. The resulting value is often referred to as the stock’s fair value or intrinsic value. Investors compare this estimate to the observed market price to guide their decisions.

The model requires only two economic inputs:

1. Dividend expectations - Let $D_1$ denote the expected dividend per share in the next period, and let $g$ denote the constant dividend growth rate. Dividends are assumed to grow at rate $g$ in perpetuity.

2. Required return on equity - Let $r$ represent the firm’s cost of equity capital – the return investors require as compensation for the risk of holding the stock. This rate reflects both time value and risk and must satisfy $r$ > $g$.

Under these assumptions, the GGM formula is:

Interpretation

• If the intrinsic value $P_0$ exceeds the market price, the stock appears undervalued.
• If the intrinsic value $P_0$ is less than the market price, the stock appears overvalued.

Suppose company ABC is expected to pay a dividend of $1.50 next year. Dividends are expected to grow at 2% per year, and the firm's cost of equity is 8%.

If ABC currently trades at $30, the stock appears overvalued relative to the GGM estimate, suggesting that an investor should consider selling or avoiding the stock.

Suppose ABC just paid a dividend of $1.40, and dividends are expected to grow at 2.2% per year. The cost of equity remains 8%.

First compute the next dividend:

Then apply the model:

If ABC currently trades at $30, the stock appears overvalued relative to the GGM estimate, suggesting that an investor should consider selling or avoiding the stock.

While intuitive and easy to implement, the GGM has important limitations:

• It applies only to dividend-paying firms, making it unsuitable for many growth companies and startups.
• The assumption of constant growth is most plausible for mature firms with stable earnings.
• The firm is assumed to exist indefinitely and sustain dividend growth forever.
• The model requires $r$ > $g$; otherwise, the valuation is undefined.
• Broader market conditions and short-term dynamics are ignored.

These limitations motivate extensions of the model.

The multistage GGM relaxes the constant-growth assumption by allowing dividends to grow at different rates over time. A common structure includes:

• An initial high-growth phase lasting $N$ years,
• Followed by a stable growth phase that continues indefinitely.

To implement this model, we need:

• Current or next dividend ($D_0$ or $D_1$),
• High-growth rate ($g_1$),
• Stable growth rate ($g_2$),
• Duration of high-growth phase ($N$),
• Cost of equity ($r$).

The valuation involves discounting dividends during the high-growth period and adding the present value of a terminal price computed using the GGM with growth rate $g_2$. While the formula is more complex, it is easily implemented using a spreadsheet and can be extended to multiple stages if necessary.

The H-model is a refinement of the multistage framework. Instead of assuming an abrupt shift from high growth to stable growth, it allows the growth rate to decline linearly over time.

The structure consists of three stages:

1. A short initial phase at the high growth rate,
2. A transition period during which growth declines linearly,
3. A stable-growth phase that continues in perpetuity.

Under these assumptions, the H-model admits a closed-form valuation formula, making it both flexible and computationally efficient.

Example

Suppose company STU has the following characteristics:

• Current stock price: $34 -Cost of equity: 9.5%
• Last dividend: $1.85
• Initial growth rate: 7%
• Long-run growth rate: 3%
• Transition period: 10 years

Using the H-model, the estimated intrinsic value is $35.01. Since this exceeds the market price, the stock appears mildly undervalued.

The most general version of the H-model allows:

• A sustained high-growth period,
• A gradual transition phase with declining growth,
• A perpetual stable-growth phase.

In this case, closed-form solutions become unwieldy, and valuation is best performed using a spreadsheet. The logic remains unchanged: forecast dividends under the assumed growth structure, discount them at the cost of equity, and sum their present values.

Example

Company PQR trades at $27.14 per share and just paid a dividend of $0.55. Dividends are expected to grow at 10% for five years, then decline linearly to 5% over the next ten years. The required return on equity, estimated using CAPM, is 8.5%.

A spreadsheet-based valuation yields an intrinsic value of $24.75 per share, indicating that PQR is overvalued by approximately 9.6%.

Stocks and bonds are both instruments through which firms raise capital, but they differ fundamentally in the nature of the claim they grant to investors.

When a corporation issues a bond, the investor is lending money to the firm. The bond contract specifies a maturity date, periodic interest payments, and the repayment of principal. As long as the firm remains solvent, these payments are legally enforceable.

When a corporation issues stock, the investor is not lending but purchasing an ownership stake. Equity financing has no maturity date and no contractual obligation to repay the initial investment. Instead, shareholders receive residual claims on the firm’s cash flows and assets.

This distinction drives nearly all differences between stocks and bonds.

Bondholders are creditors. They are entitled to fixed payments and are paid before shareholders in the event of liquidation. As long as the firm can meet its obligations, bondholders receive interest and principal regardless of how profitable the firm becomes.

Shareholders, by contrast, are residual claimants. They receive dividends only if the firm is solvent, profitable, and chooses to distribute earnings rather than reinvest them. In bankruptcy, shareholders are paid only after all creditors have been satisfied, which often leaves equity holders with nothing.

Because bond cash flows are contractual and senior in priority, bonds are generally less risky than stocks. This lower risk is reflected in lower expected returns.

For a bondholder to receive promised cash flows, the firm merely needs to remain solvent. For a shareholder to earn dividends, the firm must also be profitable and willing to distribute earnings. For a shareholder to earn capital gains, the market must reassess the firm’s future prospects more favorably.

These additional layers of uncertainty make equity prices far more volatile than bond prices. Stock prices respond strongly to changes in expectations, sentiment, and growth opportunities, whereas bond prices are primarily driven by interest rates and credit risk.

Because equities expose investors to greater risk, uncertain dividends, price volatility, and subordination in bankruptcy, they tend to offer higher expected returns than bonds over long horizons. This risk–return trade-off is a central theme in finance and will be explored further in later modules.

Suppose Cindy purchases 100 shares of company ABC at $12.44 per share. She holds the stock for one year, during which ABC pays four quarterly dividends of $0.60 per share. Immediately after receiving the fourth dividend, Cindy sells all 100 shares at $15.13 per share. Assume dividends are not reinvested.

Cash Flows

• Initial investment: $1,244 (outflow)
• Dividends received: $240 (inflow)
• Sale proceeds: $1,513 (inflow)

Total Return Calculation

Total return = (Dividends + Sale Proceeds - Initial Investment) / Initial Investment

Total return = $(240 + 1,513 - 1,244) / 1,244 \approx 0.409 \ \text{or} \ 40.9\%$

This return can be decomposed into two components:

• Dividend yield = Dividends / Initial Investment = $240 / 1244 \approx 19.3 \%$
• Capital gain = (Sale Price - Purchase Price) / Purchase Price = $(15.13 - 12.44) / 12.44 \approx 21.6$

The example illustrates how equity returns arise from both income and price appreciation, in contrast to bonds, where returns are largely driven by contractual interest payments and principal repayment.