Investments Study Guide — Chapters 6, 7, 8, 10, 12

Indenture

The legal contract between the bond issuer and the bondholder. Spells out the issuer's obligations and protective covenants: restrictions on collateral, sinking funds, dividend policy, and further borrowing.

Sinking Fund

A bond indenture provision requiring the issuer to periodically repurchase a portion of outstanding bonds before maturity — spreading out repayment instead of one large balloon payment at the end.

Subordination Clause

Restricts additional borrowing. In bankruptcy, senior (existing) bondholders must be paid before subordinated (junior) debtholders. Specifies priorities of claims. PROTECTS BONDHOLDER.

Collateral (Bond)

A specific asset pledged against default. Mortgage bonds: backed by real estate. Collateral trust bonds: backed by securities. Equipment obligation bonds: backed by equipment. If the issuer defaults, bondholders may claim the pledged asset.

Debenture

A bond with NO specific collateral. Riskier than secured bonds. In default, debenture holders are simply general creditors of the firm.

Dividend Restrictions

An indenture provision that limits how much the firm can pay shareholders, preserving cash and assets that protect bondholders.

Call Provision

Lets the ISSUER repurchase the bond before maturity at a specified call price (usually during a call period, often above par). PROTECTS ISSUER, not bondholder.

Convertible Provision

Lets the BONDHOLDER exchange the bond for a fixed number of shares of common stock.

Puttable Provision

Lets the BONDHOLDER choose to redeem early at par, or extend the bond for additional years.

Bond Rating Scale

S&P / Moody's: AAA/Aaa & AA/Aa = Very High Quality. A/A & BBB/Baa = High Quality (investment grade minimum). BB/Ba & B/B = Speculative (junk). CCC/Caa & D/C = Very Poor. BBB-/Baa3 and above = investment grade. S&P uses +/- ; Moody's uses 1/2/3.

Coverage Ratios (Bond Safety)

Measures a firm's ability to meet its debt obligations. Earnings relative to fixed costs (e.g., interest payments). High coverage ratios = lower default risk.

Leverage Ratios (Bond Safety)

Measures how much debt the firm is using. Debt-to-equity. Too-high ratio means too much debt to comfortably service. Higher leverage = greater default risk.

Liquidity Ratios (Bond Safety)

Measures ability to meet short-term obligations. Current ratio = current assets / current liabilities. Quick ratio excludes inventory. Higher liquidity = lower probability of default.

Profitability Ratios (Bond Safety)

Measures a firm's ability to generate earnings. Return on assets and return on equity — overall firm performance indicators.

Cash Flow-to-Debt Ratio

Total cash flow relative to outstanding debt. Measures ability to service debt from actual cash generated by the business.

Bond Pricing Formula

Bond Price = Coupon x Annuity Factor(r, T) + Par Value x PV Factor(r, T). The price is the present value of all future cash flows: coupon payments plus par value at maturity.

Price-Yield Inverse Relationship

Bond prices FALL when market interest rates RISE, and RISE when rates fall. Interest rate moves are the primary source of bond market risk.

Maturity Sensitivity

Longer-maturity bonds are MORE sensitive to interest rate changes than shorter-maturity bonds.

Premium Bond

Sells ABOVE par value. Occurs when coupon rate is GREATER than the current market rate.

Discount Bond

Sells BELOW par value. Occurs when coupon rate is LESS than the current market rate.

Flat Price vs. Invoice Price

Flat (quoted) price excludes accrued interest since the last coupon date. Invoice Price = Flat Price + Accrued Interest. Invoice price is what a buyer actually pays.

Coupon Rate vs. Current Yield vs. YTM

Coupon rate: fixed, based on par value. Current yield: annual coupon divided by current price. YTM: accounts for time value of money over the bond's full remaining life. They are only equal when the bond sells exactly at par.

Zero-Coupon Bond

Pays NO periodic coupons. Purchased at a deep discount; pays full par value at maturity. All return comes from price appreciation. Price rises predictably toward par as maturity approaches.

Treasury STRIPS

Zero-coupon securities created by separating ('stripping') the individual coupon and principal payments of a Treasury bond into independent, tradeable securities.

Zero-Coupon Bond Taxation (Phantom Income)

The IRS taxes you EACH YEAR on the bond's built-in price appreciation even though you receive NO cash until maturity. The IRS calculates an annual price-appreciation schedule (constant yield method) and taxes that imputed interest annually. This is why zeros are often held in tax-deferred accounts like IRAs.

Imputed Interest

Each year's taxable amount on a zero-coupon bond = this year's constant-yield price minus last year's constant-yield price. If sold, any difference between sale price and constant-yield value is a capital gain or loss.

Covariance Formula

Cov(rA, rB) = Sum of p(i) x [rA(i) - E(rA)] x [rB(i) - E(rB)]. For each scenario: multiply Asset A's deviation from its expected return by Asset B's deviation from expected return, weight by probability, and sum across all scenarios.

Covariance -- Step by Step

1) Find each asset's expected return: Sum of p(i) x r(i). 2) For each scenario, compute each asset's deviation from its expected return. 3) Multiply the two deviations together. 4) Multiply by that scenario's probability. 5) Sum all probability-weighted products = covariance.

Covariance Sign Interpretation

Positive covariance: when one asset is up, the other tends to be up too. Negative covariance: when one is up, the other tends to be down -- ideal for diversification. Raw number is in percent-squared units; analysts usually convert to correlation instead.

Covariance from Correlation

Cov(rA, rB) = rho(A,B) x sigma_A x sigma_B. You can derive covariance if you know the correlation coefficient and both assets' standard deviations.

Random Walk Hypothesis

Stock price changes are random and unpredictable -- today's price move gives no information about tomorrow's. If changes were predictable, investors would trade on it, eliminating the pattern. Only new, unpredictable information should move prices.

Efficient Market Hypothesis (EMH)

Security prices already fully reflect ALL available information. The only thing left to move prices is new information -- which arrives randomly. Random walk and EMH are two sides of the same coin.

Weak-Form EMH

Prices reflect all information in PAST TRADING HISTORY. Implication: technical analysis (studying price charts) cannot add value.

Semistrong-Form EMH

Prices reflect all PUBLIC INFORMATION. Implication: fundamental analysis on public data cannot consistently add value.

Strong-Form EMH

Prices reflect ALL information, including private/inside information. Even insider trading cannot consistently generate excess returns.

Beta Formula

Beta_i = Cov(r_i, r_market) / Var(r_market). Covariance of the stock's returns with the market's returns, divided by the variance of the market's returns. Also the slope of the regression of stock excess returns (Y) on market excess returns (X).

Beta Interpretation

Beta = 1: moves in lockstep with the market. Beta > 1: amplifies market moves -- more volatile/aggressive. Beta < 1: dampens market moves -- less volatile/defensive. Beta < 0 (rare): moves opposite the market.

What Beta Measures

Beta captures only the risk you CANNOT diversify away -- the portion of a stock's volatility tied to the whole market moving. CAPM says this is the risk you get compensated for.

Portfolio Weighted Return Formula

rp = w1r1 + w2r2 + ... + wn*rn. Weights (wi) must sum to 1. The portfolio's return is the weighted average of the returns of all assets, where each weight equals the proportion of total money invested in that asset.

Portfolio Return vs. Portfolio Risk

Portfolio RETURN = simple weighted average of component returns. Portfolio RISK (standard deviation) is NOT a simple weighted average -- it also depends on the covariance between assets. Diversification can make portfolio risk lower than either individual asset's risk.

CAPM Formula (Security Market Line)

E(ri) = R_f + Beta_i x [E(R_market) - R_f]. Risk-free rate, plus beta times the market risk premium. Plotted, this is the Security Market Line (SML).

Alpha (CAPM)

The gap between a stock's actual/expected return and what CAPM predicts given its beta. Positive alpha: stock plots ABOVE the SML -- outperforming relative to its risk. Negative alpha: underperforming relative to risk.

CAPM Key Assumptions

Investors are rational mean-variance optimizers. Single-period horizon. Homogeneous expectations. Can borrow/lend at a common risk-free rate. No taxes or transaction costs. All securities publicly traded. Market portfolio = optimal risky portfolio.

APT (Arbitrage Pricing Theory)

Generalizes CAPM. Instead of one factor (the market), APT allows MULTIPLE systematic risk factors (e.g., interest rates, inflation, market returns). Built on a no-arbitrage argument rather than the full CAPM assumption set.

APT -- Well-Diversified Portfolio

Nonsystematic (firm-specific) risk has been diversified away, leaving ONLY systematic risk. This is the foundation of the APT argument.

Fama-French Three-Factor Model

Extends CAPM with two additional factors: SMB (Small Minus Big -- size factor) and HML (High Minus Low book-to-market -- value factor), in addition to the market factor.

CAPM vs. APT

CAPM: simpler, one factor (market), full equilibrium assumptions. APT: more factors, built on no-arbitrage only. Same family logic: you get paid for risk you cannot diversify away. APT does not insist there is only one source of that risk.

Arbitrage

Earning a riskless profit from a relative mispricing, using ZERO net investment. You fund the trade by simultaneously selling something overpriced to buy something underpriced.

Arbitrage Portfolio

Requires zero net investment, carries zero risk, yet generates a positive expected return. If this exists it is a genuine free lunch -- and won't last because investors will immediately exploit it.

Zero-Net-Investment (Arbitrage)

The trade is self-financing -- proceeds from the short (selling overpriced) side fund the long (buying underpriced) side. No money required to enter the trade.

Why Arbitrage Matters for Asset Pricing

Even if no one is actively arbitraging right now, the POSSIBILITY that someone would jump on a mispricing is what keeps market prices roughly in line with models like CAPM and APT.

Security Characteristic Line (SCL)

Ri = alpha_i + beta_i x R_market + e_i. A regression of a stock's excess returns (Y) against the market's excess returns (X). Slope = beta (systematic risk). Intercept = alpha (abnormal return). Residual = firm-specific noise.

Slope -- Beta (Regression)

How much the stock's return changes for each 1-point change in the market's excess return. This is the stock's systematic risk exposure. Steeper slope = higher beta = more market sensitivity.

Intercept -- Alpha (Regression)

The stock's expected excess return when the market's excess return is zero. In a perfectly CAPM-priced world, alpha = 0. Positive alpha: stock earns more than its beta-risk alone justifies. Negative alpha: stock underperforms relative to its risk.

Residual (e) in Regression

The leftover, firm-specific scatter around the regression line in each period -- the part of the return the market factor does NOT explain. Represents nonsystematic (diversifiable) risk.

R-Squared (SCL)

The proportion of the stock's return variance explained by the market (systematic risk share). Low R-squared: most of the stock's variance is firm-specific. High R-squared: stock moves mostly with the market. Tight scatter around the line = high R-squared.

Technical Analysis

Studies past price and volume patterns to predict future price moves. Uses resistance levels (price ceilings) and support levels (price floors). Assumes markets are NOT fully efficient. Contradicts weak-form EMH.

Resistance Level

A price ceiling unlikely to be broken upward, based on historical trading patterns. Used in technical analysis.

Support Level

A price floor unlikely to be broken downward, based on historical trading patterns. Used in technical analysis.

Fundamental Analysis

Studies the underlying business to estimate intrinsic value. Examines earnings, dividend prospects, interest rate outlook, and firm risk. Assumes price = discounted value of expected future cash flows. Compares intrinsic value to current market price. Contradicts semistrong-form EMH.

Technical vs. Fundamental Analysis

Technical: 'What does the price chart say people will do next?' Fundamental: 'What is this company actually worth?' EMH is more skeptical of technical analysis (contradicts weak-form) than fundamental analysis (only contradicts semistrong-form).

Exchange Rate

The rate at which domestic currency converts into foreign currency. For international investments, total return depends on TWO layers: (1) return on the foreign asset in its local currency, and (2) the change in the exchange rate when converting back to home currency.

Currency Risk in International Investing

A foreign stock market can perform well in local currency but look poor in USD if that country's currency weakened against the dollar -- or vice versa. Investing internationally means making TWO bets: on the foreign market AND on that country's currency vs. your own.

Correlation Formula

rho(A,B) = Cov(rA, rB) / (sigma_A x sigma_B). Rescales covariance into a number between -1 and +1. Makes correlations comparable across different asset pairs.

Correlation Values

rho = +1: perfectly positive -- two assets move together exactly. rho = 0: no relationship -- returns are unrelated. rho = -1: perfectly negative -- two assets move exactly opposite each other.

Correlation and Diversification

Lower correlation = more risk reduction from combining assets in a portfolio. Even positive-but-less-than-1 correlation still provides some benefit. Negative correlation is the diversification jackpot -- losses in one asset tend to be offset by gains in the other.

Covariance vs. Correlation

Covariance tells you the direction and rough tendency of co-movement. Correlation tells you the STRENGTH of that relationship on a clean, comparable scale (-1 to +1). Correlation is what analysts actually quote and compare across asset pairs.

Federal Funds Rate

The rate at which banks lend reserves to OTHER BANKS overnight. This is normal, first-resort short-term borrowing in the market among banks.

Discount Rate

The rate at which the FEDERAL RESERVE lends directly to a bank via the discount window. A backup safety valve when banks cannot borrow from each other. Historically carries a stigma -- needing the Fed directly can signal a bank could not get funds elsewhere.

Fed Funds vs. Discount Rate

Federal funds rate: bank-to-bank, everyday market rate, first resort. Discount rate: Fed-to-bank, backup safety valve, last resort. The Fed funds rate is what the Fed targets via open market operations to influence the economy.

LEI Components (10 Total)

1) Avg weekly hours of production workers. 2) Initial unemployment claims. 3) Manufacturers new orders (consumer goods). 4) ISM Index of New Orders. 5) New orders for nondefense capital goods. 6) New private housing permits. 7) Yield curve spread (10-yr Treasury minus fed funds). 8) S&P 500. 9) M2 money supply growth. 10) Consumer expectations index.

Coincident Indicators

Move WITH the economy simultaneously: employees on nonfarm payrolls, personal income less transfer payments, industrial production, manufacturing and trade sales.

Lagging Indicators

Move AFTER the economy: average duration of unemployment, the prime rate, trade inventories-to-sales ratio, consumer installment credit-to-income ratio.

Why Leading Indicators Matter

These are things businesses and consumers tend to adjust BEFORE they actually change hiring, spending, or production -- early warning signals rather than after-the-fact confirmations.

Core Macro Variables

GDP: total market value of goods/services produced. Unemployment rate: share of labor force without jobs. Inflation: rate at which general price level rises -- erodes real returns. Interest rates: higher rates reduce PV of future cash flows. Budget deficit: government spending exceeds revenue. Sentiment: consumer optimism/pessimism driving spending.

Demand Shock vs. Supply Shock

Demand shock: an event that affects the DEMAND for goods and services in the economy. Supply shock: an event that affects PRODUCTION CAPACITY or costs.

Policy Tools (Macro)

Fiscal policy: government spending and taxation to stabilize economy. Monetary policy: Fed actions influencing money supply and interest rates. Supply-side policy: policies addressing the economy's productive capacity -- incentivizing workers/owners to produce more.

Business Cycle Phases

Expansion --> Peak --> Contraction (recession) --> Trough --> back to Expansion. Cyclical industries (above-average sensitivity) do best in expansions. Defensive industries (below-average sensitivity) hold up better in contractions.

Current Yield Formula

Current Yield = Annual Coupon Payment / Bond Price. A quick non-present-value shortcut. Example: 8% coupon on $1,000 par bond priced at $1,276.76 --> Annual coupon = $80 --> Current Yield = $80 / $1,276.76 = 6.27%

Solving for Price Using Current Yield

Price = Annual Coupon Payment / Current Yield. Rearrange the current yield formula when you are given the yield and need to back into price.

Accrued Interest Formula

Accrued Interest = (Annual Coupon / 2) x (Days since last coupon / Days in coupon period). Invoice Price = Flat Price + Accrued Interest.

Premium vs. Discount Bond Yield Relationships

Premium bond (price > par): Coupon Rate > Current Yield > YTM. Discount bond (price < par): Coupon Rate < Current Yield < YTM. At par: all three are equal.

Current Yield vs. YTM

Current yield is a snapshot -- like a dividend yield, it ignores everything that happens at maturity (no capital gain/loss, no compounding over time). YTM properly accounts for the FULL time value of money over the bond's life. They only equal each other when the bond sells at par.