Stocks

Bonds & Stocks Fundamentals

Lecture Overview

• Bond Markets: Discussion on bond ratings, tax status, the yield curve, and term structure.

• Stock Markets: History and features of common stock, definition of various stock market indices.

• Stock Market Dynamics: Analysis of supply, demand, and equilibrium in the stock market.

• Valuation & Theories: Determination of fundamental stock value, exploration of the Efficient Market Hypothesis, long-run investing, and the equity premium puzzle.

Bond Ratings

Bond ratings indicate the creditworthiness and default risk of a bond issuer. They are categorized into Investment Grade and Noninvestment (Speculative) Grade.

Investment Grade Ratings (Lower Risk)

• Aaa (Moody's) / AAA (Standard & Poor's): Bonds of the best quality with the smallest risk of default. Issuers are exceptionally stable and dependable. Examples in $2016$: Johnson & Johnson, Microsoft.

• Aa (Moody's) / AA (Standard & Poor's): Highest quality with a slightly higher degree of long-term risk. Examples: Google/Alphabet, Canada.

• A (Moody's) / A (Standard & Poor's): High-medium quality, with many strong attributes but somewhat vulnerable to changing economic conditions. Examples: Procter & Gamble, South Korea, JPMorgan Chase, Wells Fargo.

• Baa (Moody's) / BBB (Standard & Poor's): Medium quality, currently adequate but perhaps unreliable over the long term. Examples: China, Hewlett Packard, Italy, Portugal.

Noninvestment, Speculative Grade Ratings (Higher Risk)

• Ba (Moody's) / BB (Standard & Poor's): Some speculative element, with moderate security but not well safeguarded. Examples: Goodyear Tire, Nokia, Brazil.

• B (Moody's) / B (Standard & Poor's): Able to pay now but at risk of default in the future. Examples: Hertz, Greece.

• Caa (Moody's) / CCC (Standard & Poor's): Poor quality, clear danger of default. Examples: Kenya, Ferrellgas Partners.

• Ca (Moody's) / CC (Standard & Poor's): Highly speculative quality, often in default. Example: Sable Permian Resources.

• C (Moody's) / C (Standard & Poor's): Lowest-rated, poor prospects of repayment though may still be paying. Example: Venezuela.

• D (Moody's) / D (Standard & Poor's): In default. No specific examples given, but represents bonds currently not meeting their obligations.

Impact of Ratings Downgrade

When a bond's rating is downgraded, it implies more risk relative to other assets. This leads to:

• Demand Shift: The demand for the bond shifts inward (to the left) on a supply-demand graph.

• Price and Interest Rate Impact: The bond price ( $P<em>B$ ) decreases ( $P</em>B <br>ightarrow ext{ } ext{all down arrow}$ ), which causes the bond's interest rate ( $i$ ) to increase ( $i <br>ightarrow ext{ } ext{all up arrow}$ ).

• Quantity and Risk Premium: The quantity ( $Q<em>B$ ) decreases ( $Q</em>B <br>ightarrow ext{ } ext{all down arrow}$ ), and the risk premium ( $rp$ ) increases ( $rp <br>ightarrow ext{ } ext{all up arrow}$ ) because investors demand higher compensation for the increased risk.

Bond Tax Status

• Tax-Exempt Bonds: Do not incur taxes on the interest earned.

• Normal (Taxable) Bonds: Interest earned is subject to taxation.

Arbitrage Condition

Investors engage in arbitrage to ensure that the after-tax returns from tax-exempt bonds and normal bonds are equivalent. The relationship between the interest rate on a tax-exempt bond ( $i<em>E$ ) and a taxable bond ( $i</em>T$ ) is given by:

• $i<em>E = i</em>T imes (1 - au)$ where $au$ is the marginal tax rate.

Impact of Granted Tax-Exempt Status

If a bond is granted tax-exempt status, it becomes more attractive relative to other assets due to the higher after-tax return (or lower effective cost for issuers).

• Demand Shift: Demand for the bond shifts outward (to the right).

• Price and Interest Rate Impact: The bond price ( $P<em>B$ ) increases ( $P</em>B <br>ightarrow ext{ } ext{all up arrow}$ ), leading to a decrease in its interest rate ( $i_E <br>ightarrow ext{ } ext{all down arrow}$ ).

• Quantity Impact: The quantity ( $Q<em>B$ ) increases ( $Q</em>B <br>ightarrow ext{ } ext{all up arrow}$ ).

Yield Curve and Term Structure

Yield Curve Definition

The yield curve plots the interest rates (or yields) of bonds of equal credit quality but differing maturities against their time to maturity.

Stylized Facts About the Yield Curve

1. Co-movement of Rates: Interest rates of bonds with different maturities tend to move together over time.

2. Short-term Volatility: Short-term yields are generally more volatile than long-term yields.

3. Long-term Yields Higher: Long-term yields are typically higher than short-term yields.

Theories Explaining the Term Structure

• Expectations Hypothesis: This theory suggests that long-term interest rates are an average of expected future short-term interest rates. It explains the first two stylized facts.

  • Formula for $2$-year bond: $i<em>{2,t} = rac{(i</em>{1,t} + i<em>{1,t+1}^e)}{2}$ where $i</em>{2,t}$ is the current $2$-year rate, $i<em>{1,t}$ is the current $1$-year rate, and $i</em>{1,t+1}^e$ is the expected $1$-year rate next period.

  • Example $1$: If current $1$-year rate ( $i<em>{1,t}$ ) is 1 ext{%} and expected future $1$-year rate ( $i</em>{1,t+1}^e$ ) is 5 ext{%}, then the current $2$-year rate ( $i_{2,t}$ ) is 3 ext{%}.

  • Example $2$: If current $1$-year rate ( $i<em>{1,t}$ ) is 3 ext{%} and expected future $1$-year rate ( $i</em>{1,t+1}^e$ ) is 5 ext{%}, then the current $2$-year rate ( $i_{2,t}$ ) is 4 ext{%}.

• Liquidity Premium Theory (Term Premium): This theory explains the third stylized fact (long-term yields are generally higher). It states that investors demand a higher yield (a liquidity/term premium) for holding longer-maturity bonds due to increased interest rate risk and inflation risk.

  • Example: The Silicon Valley Bank (SVB) collapse highlighted how rapid changes in interest rates can negatively impact institutions holding long-duration bonds.

History of Stocks

• Innovation and Growth: Stocks facilitate capital formation, enabling innovation and growth that inherently involve taking risk.

• Risk Compensation: Investors demand compensation for taking on this risk.

• Dutch East India Company: An early example of a company that issued shares, allowing for the spreading of risk across multiple ventures (e.g., more ships to reduce idiosyncratic risk).

• Major Stock Market Crashes:

  • Black Tuesday (October $1929$): The NYSE lost 25 ext{%} of its value in one week, contributing to the Great Depression.

  • Black Monday (October $1987$): The NYSE experienced a 20 ext{%} loss in value in a single day.

  • Dot-Com Bubble ( $2000$-$2001$): The Nasdaq Composite lost 70 ext{%} of its value as speculative technology companies failed.

  • China (Summer $2015$): The Shanghai Composite index fell by 38 ext{%}, reflecting concerns about the Chinese economy.

Common Stock (Equity) Features

Common stock represents ownership in a corporation and typically has these features:

• Large Number of Shares: Corporations often issue many shares to a broad range of investors.

• Low Share Price: Relative to the company's total valuation, individual shares can have a low price.

• Transferable: Shares can be bought and sold freely on exchanges, providing liquidity to investors.

• Residual Claimant: Stockholders are the last claimants on a company's assets and earnings in case of liquidation, after bondholders and other creditors are paid.

• Limited Liability: Stockholders are only liable for the amount of their initial investment; their personal assets are protected from the company's debts.

• Voting Rights: Common stockholders typically have the right to vote on corporate matters, such as electing the board of directors.

Stock Market Indices

Stock market indices are statistical measures that track the performance of a basket of stocks, providing a snapshot of market or sector health.

• Dow Jones Industrial Average (DJIA):

  • Comprises $30$ large, well-established companies.

  • Price-weighted: Heavier influence from stocks with higher share prices.

• Standard & Poor’s $500$ (S&P $500$):

  • Includes $500$ of the largest companies by market capitalization in the U.S.

  • Value-weighted (or market-capitalization weighted): Companies with larger market caps have a greater impact on the index's value.

• Nasdaq Composite:

  • Primarily includes technology and growth companies listed on the Nasdaq exchange.

  • Value-weighted.

• Wilshire $5000$:

  • Used to include virtually all publicly traded companies in the U.S.

  • Value-weighted. (Note: The index itself exists but was removed from FRED at the time of the lecture's example).

Fundamental Stock Value

The fundamental value of a stock is the present value of its expected future dividends. The infinite sum of discounted future dividends is expressed by:

• $P<em>0 = ext{sum from } t=1 ext{ to } ext{infinity} ext{ of } rac{D</em>t}{(1+i)^t}$ where $P<em>0$ is the current stock price, $D</em>t$ is the dividend at time $t$, and $i$ is the discount rate.

• Assuming Constant Exponential Growth: If dividends grow at a constant rate ( $g$ ), the formula simplifies to the Gordon Growth Model:

  • $P<em>0 = rac{D</em>0(1+g)}{i-g}$ or $P<em>0 = rac{D</em>1}{i-g}$ where $D<em>0$ is the current annual dividend and $D</em>1$ is the next year's dividend.

• Incorporating Risk: Since stocks are risky, the discount rate ( $i$ ) is replaced by the risk-free rate ( $r<em>f$ ) plus a risk premium ( $r</em>p$ ).

  • $P<em>0 = rac{D</em>0(1+g)}{r<em>f + r</em>p - g}$

• Example Calculation: What is the fundamental value of a stock with a current annual dividend of $10$, a growth rate of 3 ext{%}, and a risk premium of 5 ext{%}, when the risk-free rate is 2 ext{%}?

  • P_0 = rac{$10 imes 1.03}{0.02 + 0.05 - 0.03} = rac{$10.30}{0.04} = $257.50

• Leverage: Companies leverage by issuing bonds, but a stock portfolio itself is considered to be already leveraged, as equity is a residual claim.

Calculating Implied Risk Premium

The risk premium can be derived from the Gordon Growth Model:

• $r<em>p = ( rac{D</em>0(1+g)}{P<em>0}) - r</em>f + g$

• Example Calculation: If a stock pays a current dividend of $12$, expected to grow by 1 ext{%} annually, and the risk-free rate is 2 ext{%}, what is the implied risk premium when the stock price is $175$?

  • r_p = ( rac{$12 imes 1.01}{$175}) - 0.02 + 0.01 = 0.0693 - 0.02 + 0.01 = 0.0593 or 5.93 ext{%}.

Stock Market Dynamics: Supply and Demand

Primary Stock Supply

• Issuers: Corporations issue new shares (primary market).

• Supply Curve: Upward sloping (positive slope).

• Ceteris Paribus: Assuming future dividends are unchanged.

• Issuer's Perspective: The issuer receives the stock price ( $P_S$ ).

  • If $P<em>S$ increases ( $P</em>S <br>ightarrow ext{ } ext{all up arrow}$ ), the effective interest rate for the issuer ( $i<em>S$ ) decreases ( $i</em>S <br>ightarrow ext{ } ext{all down arrow}$ ).

  • Higher stock prices mean issuance raises more money for the company for the same ownership stake.

Primary Stock Demand

• Buyers: Investors demand new shares.

• Demand Curve: Downward sloping (negative slope).

• Ceteris Paribus: Assuming future dividends are unchanged.

• Investor's Perspective: The investor pays the stock price ( $P_S$ ).

  • If $P<em>S$ decreases ( $P</em>S <br>ightarrow ext{ } ext{all down arrow}$ ), the effective interest rate for the investor ( $i<em>S$ ) increases ( $i</em>S <br>ightarrow ext{ } ext{all up arrow}$ ).

  • A lower stock price means the investor expects a higher return on their investment.

Equilibrium in the Primary Stock Market

• Arbitrage: The equilibrium stock price ( $P<em>S$ ) determines the effective interest rate on stock ( $i</em>S$ ). This yield must roughly equal the yield available for comparable risk in the secondary market.

• Risk Premium: Stocks are considered risky assets. The risk premium ( $r_p$ ) for stocks is the difference between the stock's expected return and the risk-free rate from the bond market.

  • $r<em>p = i</em>S - r_f$

  • The bond market determines the risk-free rate ( $r<em>f$ ), while the stock market determines the stock risk premium ( $r</em>p$ ).

Impact of Increased Demand (e.g., Aversion Falls)

Suppose investor risk aversion falls, meaning investors are more willing to hold risky assets like stocks.

• Demand Shift: Demand for stocks shifts outward (to the right).

• Market Impact: The stock price ( $P<em>S$ ) increases ( $P</em>S <br>ightarrow ext{ } ext{all up arrow}$ ), the effective interest rate on stock ( $i<em>S$ ) decreases ( $i</em>S <br>ightarrow ext{ } ext{all down arrow}$ ), and consequently, the risk premium ( $r<em>p$ ) decreases ( $r</em>p <br>ightarrow ext{ } ext{all down arrow}$ ). The quantity ( $Q_S$ ) traded also increases.

Efficient Market Hypothesis (EMH)

• Core Idea: Developed by Fama and French, the EMH states that all available information is already reflected in current market prices.

• Implication: It is consistently impossible for investors to