Long version MBF

Ch 1: The 6 parts of the financial system with examples

Six parts: (1) money, (2) financial instruments, (3) financial markets, (4) financial institutions, (5) government regulatory agencies, (6) central banks. Together they move resources from savers to borrowers across time and move risk to whoever can best bear it.

Ch 1: The 6 parts of the financial system with examples - examples and details

Money: cash, checking deposits, debit balances. Instruments: stocks, bonds, mortgages, insurance, futures. Markets: NYSE, Nasdaq, bond markets. Institutions: banks (JPMorgan Chase), securities firms (Schwab), insurers (State Farm), pension funds. Regulators: SEC, FDIC, Dodd-Frank (2010), Basel III. Central banks: Federal Reserve, ECB, Bank of England (1694). Regulation = the rules; supervision = oversight via examination. Instrument = the contract; institution = the firm; market = the venue. In autumn 2008 the system broke and credit froze even for healthy firms.

Ch 1: The 5 core principles with examples of how they operate

(1) Time has value; (2) risk requires compensation; (3) information is the basis for decisions; (4) markets determine prices and allocate resources; (5) stability improves welfare. The principles do not change even as institutions do.

Ch 1: The 5 core principles with examples of how they operate - examples and details

CP1: a 4-year $10,000 car loan at 4% needs 48 payments of $226 = $10,848; the extra $848 is rent for time. CP2: insurers charge more than expected claims; junk bonds pay very high rates. CP3: lenders check income and credit before a mortgage; poor screening fueled pre-2007 defaults. CP4: a firm issues stocks/bonds to fund a factory; the price investors pay steers capital. CP5: automatic stabilizers (unemployment insurance) and central bank action cushion downturns. Principles combine: junk bond price = PV of payments (time) discounted at a high rate (risk). 2007-09 crisis: CP3 failed (bad screening) then CP4 (markets froze) then CP5 was needed (government stabilization).

Ch 2: What is money

Money is an asset generally accepted as payment for goods and services or repayment of debt. Three functions: means of payment (most important), unit of account, store of value. Money is not income (a flow) or wealth (assets minus liabilities). | FORMULA: Prices without money: n(n-1)/2

Ch 2: What is money - examples and details

Means of payment: avoids barter's double coincidence of wants; payment is final. Unit of account: without money n goods need n(n-1)/2 prices (100 goods = 4,950; 10,000 goods = ~50 million). Store of value: carries purchasing power forward; money is a poor store (no interest, inflation) but is held because it is liquid. Liquidity = ease of turning an asset into a means of payment without loss of value (currency > checking > savings > Treasuries > stocks > houses > art). Fiat money has value because others accept it and government makes it legal tender and accepts it for taxes (Monopoly money has no value outside the game).

Ch 2: Currency alternatives to the greenback: past and present and future prospects

Past: commodity money (gold, silver, salt) and early paper money; paper issued without credible limits failed (Stockholm Banco, Continentals, assignats, Confederate dollars). Present: checks, cards, electronic transfers, mobile money, cryptocurrencies compete but mostly run on dollars; Bitcoin fails all three functions of money. Future: less money as means of payment, fewer units of account, liquid financial assets replace money as store of value.

Ch 2: Currency alternatives to the greenback: past and present and future prospects - examples and details

PAST: Gold was the most common money (durable, divisible, rare) but governments abandon it in crises. Stockholm Banco (1661) over-issued and failed. Continentals (1775): $200M printed, worthless by 1781. French assignats: 40 billion printed, worthless by late 1790s. Confederate dollars worthless after the war. Lesson = time consistency: fiat works only if government credibly limits printing. PRESENT: Checks (11.5% of noncash payment value 2016) are instructions not money. Debit cards: twice as many transactions as credit. Credit cards: a loan, not money. ACH is over half of noncash payment value; Fedwire about $2.9 trillion/day. Apps (Venmo, Zelle, Apple Pay) sit on bank accounts. M-Pesa (Kenya 2007) leapfrogged richer countries. Bitcoin: not widely accepted, unstable unit of account (-22% to +32% daily), unstable store of value (~$20k Dec 2017 to under $3.2k a year later), tied to crime (Silk Road). US cash about $1.6 trillion outstanding. FUTURE: FedNow (announced 2019); store of value role on the way out; cryptocurrency hopes exceed reality (slow vs Visa; anonymity collides with anti-money-laundering rules); forecasting payment tech is hard.

Ch 2: What M2 is and how to calculate it

M2 is the broad measure of money: M1 plus small time deposits (under $100k), savings deposits and money-market deposit accounts, and retail money-market mutual fund shares. It is the most commonly quoted aggregate because it moves most closely with interest rates and economic growth. | FORMULA: M1 = Currency (public) + Traveler's checks + Demand deposits + Other checkable deposits; M2 = M1 + Small time deposits + Savings and MMDAs + Retail MMMFs

Ch 2: What M2 is and how to calculate it - examples and details

Include: currency held by public, traveler's checks, demand and other checkable deposits (M1); savings accounts; $10k CDs; retail MMMFs. Exclude: currency in bank vaults, $250k CDs (large time deposits), stocks, bonds, T-bills, credit card limits. Why M2 not M1: after inflation passed 10% in the late 1970s/early 1980s banks created interest-paying money-market accounts and funds moved from M1 to the rest of M2, so M1 stopped being useful.

Ch 2: What M2 is and how to calculate it - worked numbers and practice

Worked example (Feb 2019 billions): M1 = 1633.7 + 1499.8 + 626.0 = about 3759.4; M2 = 3759.4 + 580.6 + 9276.4 + 861.4 = 14477.8. Practice: currency 500 (50 in vaults) so public holds 450; demand 400; other checkable 150; M1 = 1000; adding savings 1200 + small time 300 + MMMF 200 gives M2 = 2700. Moving $5000 checking to savings: M1 falls 5000; M2 unchanged. Savings used to buy a Treasury bond: M2 falls.

Ch 2: How the payments system works: the different methods

The payments system is the web of arrangements that lets people exchange goods, services and assets. Three methods: cash (final immediately), checks (clear through the Fed or a clearinghouse), and electronic payments (debit cards, credit cards, ACH, Fedwire, apps, mobile money). All use money at some stage and central banks are involved because the economy depends on the system working.

Ch 2: How the payments system works: the different methods - examples and details

Cash: final on handover; risk is theft. Check path: you give check to merchant; merchant deposits it and is credited; merchant's bank sends image to Fed or clearinghouse; Fed credits merchant bank's reserve account and debits your bank's reserve account (the step that uses money); your bank debits your account; payment not final until the return window passes. Debit card: moves your deposits to merchant same day. Credit card: issuing bank pays merchant and lends to you. ACH: automated electronic check for recurring payments (paychecks, utilities). Fedwire: Fed's interbank system, 631,000 transfers worth about $2.9 trillion on a typical 2018 day. Apps/digital wallets: Venmo, Zelle, Apple Pay, PayPal. Mobile money: M-Pesa. Every payment is a chain: initiation, identity verification, funds confirmation, discharge, verification. US lags because of no post-WWII rebuild, Fed check support since 1914, network externalities and incumbent fees (Visa 1-3%).

Ch 3: Define and explain financial instruments, financial markets and financial institutions

Financial instrument: the written legal obligation of one party to transfer something of value, usually money, to another party at a future date under specified conditions. Financial markets: places where financial instruments are bought and sold. Financial institutions (intermediaries): firms that provide access to financial markets for savers and borrowers.

Ch 3: Define and explain financial instruments, financial markets and financial institutions - examples and details

Instrument parts: written legal obligation (government-enforced), something of value, future date (fixed or event-triggered), specified conditions (dividends only if profitable; insurance only if you crash). Two classes: underlying (stocks, bonds) and derivatives (futures, options, swaps; used to shift risk). Value rises with bigger, sooner and more certain payments. Markets: primary (new issues; Facebook 2012 IPO) vs secondary (resale); exchange (NYSE) vs OTC dealers vs electronic networks; money market (under 1 year) vs bond market (over 1 year); debt/equity vs derivatives. Institutions: depository (deposits to loans), insurance (premiums to securities), pension funds, securities firms (brokers, investment banks, mutual funds, hedge funds), finance companies, GSEs (Fannie Mae, Freddie Mac).

Ch 3: The core functions each provides to the financial system

Instruments: means of payment, store of value, transfer of risk. Markets: liquidity, information (prices), risk sharing. Institutions: lower transaction costs, lower information costs (screening and monitoring), asset transformation, brokerage/access.

Ch 3: The core functions each provides to the financial system - examples and details

Instruments: employees paid in stock (late 1990s); bonds and stocks carry wealth forward; wheat futures shift price risk from farmer to buyer; insurance shifts accident risk. Markets: sell stock in seconds (liquidity); prices summarize what investors know; investors diversify by trading. Institutions: standardized mortgages and policies cut transaction costs; loan officers screen borrowers (asymmetric information); banks turn short-term demand deposits into 30-year mortgages. A well-run market needs low transaction costs, accurate information, investor protection and cheap contract enforcement.

Ch 3: How they interact with one another and help us in daily life

Institutions create and sell instruments, markets price and trade them, and prices guide institutions and savers. Indirect finance runs saver to bank to borrower; direct finance runs saver to a firm's bond or stock (often via broker or investment bank). In daily life this is how we pay, borrow, insure, save for retirement, and how firms fund factories.

Ch 3: How they interact with one another and help us in daily life - examples and details

Buying a house: mortgage instrument, pooled into an MBS sold in bond market, via bank/broker, Fannie Mae guarantees. Retirement: index fund shares, stock market, mutual fund company or 401(k). Car insurance: insurance contract; insurer invests premiums in bonds. Farmer: futures contract on futures exchange via broker. Factory: corporate bond, primary then secondary market, investment bank underwrites. Coffee: bank deposit (money) via interbank payments. Breakdown: 2007-09 shadow banks held mortgage instruments funded with short-term borrowing; when markets stopped trading, institutions could not sell or borrow and the system froze (Lehman failed Sept 15 2008).

Ch 4: Relationship between present value and future value and how they react to time and the interest rate

FV = PV(1+i)^n and PV = FV/(1+i)^n are the same equation run in opposite directions. Higher interest rates and longer time raise FV but lower PV. The further away a payment, the more its PV falls when rates rise. | FORMULA: FV = PV(1+i)^n ; PV = FV/(1+i)^n

Ch 4: Relationship between present value and future value and how they react to time and the interest rate - examples and details

Larger payment raises both proportionally. PV of $100: at 1%: 1yr $99.01, 10yr $90.53, 20yr $81.95; at 5%: $95.24, $61.39, $37.69; at 10%: $90.91, $38.55, $14.86. Going from 1% to 5% cuts 1-year PV about 4% but 10-year PV over 30%, which is why long-term bonds are riskier.

Ch 4: How those variables influence decisions of actors in the financial system

Every borrowing, lending and investing decision compares payments on different dates using present value. Firms invest when IRR exceeds borrowing cost; lenders set payments so PV equals the loan; investors price bonds and stocks as PV of expected payments; households save based on future value.

Ch 4: How those variables influence decisions of actors in the financial system - examples and details

Firm: tennis-racket machine costs $1M and pays $150,000/yr for 10 years so IRR = 8.14%; buy if borrowing costs less. Lender: $1M over 10 years needs $129,505/yr at 5% or $149,030 at 8%. Bond investor: price = PV of coupons + face value; falls when rates rise. Stock investor: PV of dividends. Household: $1,000/yr for 40 years at 4% = $98,826. Student: college return about 8% real vs 2-4% loan rates. Homeowner: paying down a 5% mortgage earns a riskless 5%. Policymaker: $1 of loss in 100 years is worth $0.37 at 1%, $0.14 at 2%, under $0.02 at 4%. Lender: $225 loan repaid 3 x $100 (IRR 15.9%) vs 2 x $125 (IRR 7.3%).

Ch 4: How compound interest works

Compound interest is interest earned on previously earned interest. Each period's interest is added to the balance and the next period's interest is computed on the larger balance, so growth accelerates. You cannot multiply the annual rate by the years. | FORMULA: Years to double = 72 / rate(%)

Ch 4: How compound interest works - examples and details

Two years at 5% on $100: $100 + $5 + $5 + $0.25 (interest on interest) = $110.25 = 100 x 1.05^2. Simple vs compound at 5%: 5yr $125.00 vs $127.63; 10yr $150.00 vs $162.89. Rule of 72: 5% doubles in 14.4 years; 10% in 7.2 years. Keep i and n in the same units: monthly rate equal to 5% a year = 1.05^(1/12) - 1 = 0.41% (not 5/12); 0.5% a month = 1.005^12 - 1 = 6.17% a year; 20% over 5 years = 1.2^(1/5) - 1 = 3.71% a year.

Ch 4: Calculate PV, FV and compound interest

Steps: convert rate to decimal; match units of i and n; compute (1+i)^n; multiply for FV or divide for PV. Compound interest earned = FV - PV. | FORMULA: FV = PV x (1+i)^n ; PV = FV/(1+i)^n ; Interest = FV - PV ; Annuity PV = (C/i)[1 - 1/(1+i)^n] ; Perpetuity PV = C/i

Ch 4: Calculate PV, FV and compound interest - examples and details

FV: $2,000 at 6% for 8 years = 2,000 x 1.5938 = $3,187.70; compound interest $1,187.70 (simple would be $960). PV: $5,000 in 4 years at 7% = 5,000/1.3108 = $3,814.48. PV of $100 in 6 months at 5% = $97.59. Rate: $1,000 to $1,500 in 6 years = 1.5^(1/6) - 1 = 6.99%. Time: $100 to $800 at 10% = 3 doublings x 7.2 = 21.6 years. Stream: $100/yr for 3 years at 5% = 95.24 + 90.70 + 86.38 = $272.32.

Ch 4: Calculate PV, FV and compound interest - worked numbers and practice

Practice: $750 at 4% for 12 yrs = $1,200.77; $10,000 due in 15 yrs at 6% = $4,172.65; $3,000 at 8% for 5 yrs = $4,407.98 (interest $1,407.98); $1,000 in 3 yrs ($863.84) beats $1,100 in 5 yrs ($861.88) at 5%.

Ch 4: How real and nominal interest rates are affected by inflation

Nominal rate is in current dollars; real rate is adjusted for inflation. Fisher equation: i = r + expected inflation. When expected inflation rises, nominal rates rise to keep the real rate roughly constant. If actual inflation differs from expected, wealth shifts between borrowers and lenders. | FORMULA: i = r + expected inflation ; exact: (1+i) = (1+r)(1+expected inflation)

Ch 4: How real and nominal interest rates are affected by inflation - examples and details

Ex ante real = nominal - expected inflation; ex post real = nominal - actual inflation. Inflation higher than expected: borrower wins, lender loses; lower than expected: lender wins, borrower loses. Real rate can be negative. Evidence: T-bill rates above 15% in 1980-81 fell to about 5% by 1986 as inflation fell. Examples: CD 5% with 3% expected inflation = 2% real. Loan 7% with 3% expected inflation (4% real); actual inflation 2% gives realized real 5%: lender gains. Nominal 4% with expected inflation 6% = -2% real. High inflation exact: r = 5% and expected inflation 100% gives (1.05)(2.00) - 1 = 110%, not 105%.

Ch 5: The role of risk in pricing financial instruments

Most investors are risk averse, so they require a risk premium to hold risky instruments. The riskier the instrument, the less investors pay for its promised payments, so its price is lower and its expected return higher. | FORMULA: Risk premium = expected return on risky investment - risk-free return

Ch 5: The role of risk in pricing financial instruments - examples and details

Risk = uncertainty about future payoff over a horizon relative to a benchmark. Risk averse = prefers certain return to an uncertain one with the same expected value. Insurance proves risk aversion (premiums exceed expected payouts yet people buy). Early 2019 5-year yields: JCPenney 25.09%, J&J 2.59%, Treasury 2.42% so risk premiums 22.67 vs 0.17 points. Default example: bond promises $105 with 10% chance of paying nothing and risk-free rate 5%: price $90, promised yield 16.67%, premium 11.67 points. Appears in default premiums (Ch 6), rating spreads and term premiums (Ch 7), equity risk premium (Ch 8).

Ch 5: The role of risk in pricing financial instruments - worked numbers and practice

Practice: bond yields 6.5% vs Treasury 2.5% = 4 point premium.

Ch 5: Idiosyncratic vs systematic risk with examples

Idiosyncratic (unique) risk affects few firms or people and can be diversified away. Systematic (economywide) risk affects everyone at once and cannot be diversified away. Idiosyncratic risk changes your share of the pie; systematic risk changes the size of the pie.

Ch 5: Idiosyncratic vs systematic risk with examples - examples and details

Idiosyncratic: Ford loses market share, factory fire, one person's car accident, a drug failing trials. Systematic: recession, change in consumer/business confidence, political climate. Oil spike hurts Ford but helps ExxonMobil: idiosyncratic for the economy as a whole. Systemic risk (threat to the whole financial system, e.g. Lehman) is different. Great Moderation: GDP more stable while household income more volatile.

Ch 5: How firms calculate risk and whether they can account for everything

Firms list all outcomes, assign probabilities (usually from history), and compute expected value, variance and standard deviation; for catastrophic risk they use value at risk (VaR). They cannot account for everything: probabilities come from the past, rare tail events and changing correlations are hard to model, and unquantifiable uncertainty cannot be priced. | FORMULA: EV = sum p x payoff ; SD = sqrt(sum p x (payoff - EV)^2) ; Leverage ratio = cost / owner's contribution

Ch 5: How firms calculate risk and whether they can account for everything - examples and details

Steps: list outcomes (probabilities sum to 1); EV = sum of p x payoff; variance = sum of p x (payoff - EV)^2; SD = sqrt(variance); VaR = worst loss at a given probability and horizon. Case 1: $1,000 to $700 or $1,400 (50/50): EV $1,050, SD $350, VaR $300. Case 2: $100/$700/$1,400/$2,000 with probs .1/.4/.4/.1: EV $1,050, SD $528, VaR $900 (riskier at same EV).

Ch 5: How firms calculate risk and whether they can account for everything - worked numbers and practice

Practice: $50/$100/$150 with .2/.6/.2 gives EV $100, SD $31.62. Leverage: borrowing half doubles expected return and SD. Mortgage: ARM average looks fine but worst case loses the house. Limits: history-based probabilities; black swans (2011 Japan tsunami); changing correlations (rating models ignored nationwide house-price fall so AAA securities collapsed); extrapolation and search for yield; hidden risks (OTC derivatives); unquantifiable uncertainty; systemic interactions (everyone selling at once).

Ch 5: Common methods of reducing risk

Diversification (holding more than one risk), in two forms: hedging (opposite payoffs) and spreading (unrelated payoffs). Also insurance, limiting leverage, and matching risk to time horizon and wealth. Diversification removes only idiosyncratic risk. | FORMULA: SD of n independent identical stocks = SD / sqrt(n)

Ch 5: Common methods of reducing risk - examples and details

Hedging: 3M and Texaco paying opposite amounts: one stock EV $110 SD $10; half each = always $110, SD $0. Examples: airline buying oil futures, farmer selling wheat futures. Spreading: 3M and Microsoft independent: SD $7.10; three stocks $5.80; four $5.00 (SD about $10/sqrt(n)); 16 stocks = $2.50. Insurance: insurers pool millions of independent policies; disability insurance under-bought (1 in 4 twenty-year-olds disabled 90+ days). Limit leverage: multiplies worst case. Match risk to horizon: a 25-year-old can absorb a 25% loss, a 60-year-old can't. Webvan: Shaheen's $280M of stock went to zero in 2001.

Ch 6: What is a bond

A bond is a promise to make a series of payments on specific future dates, issued as part of an arrangement to borrow. The issuer receives money today; the bondholder receives coupons and/or face value later. Its price is the present value of its promised payments, so bond prices and interest rates move in opposite directions.

Ch 6: What is a bond - examples and details

Vocabulary: coupon payment (yearly interest), coupon rate (coupon/face value), face/par value (final repayment), maturity date. Issuers: governments (U.S. Treasury, state/local) and corporations (Ford, Walmart); over $28 trillion government and $10 trillion corporate outstanding by 2018. History: Spain's kings defaulted 14 times (1557-1696); Alexander Hamilton created first US bonds; Reading Railroad bond (1945) $1,000 3.5% coupon 50 years with paper coupons.

Ch 6: What distinguishes zero (discount) coupon bonds, coupon bonds and fixed-payment loans

Zero-coupon: one payment (face value) at maturity, sells below face; the discount is the interest. Coupon bond: periodic coupons plus face value at maturity. Fixed-payment loan: equal installments that include interest and principal (amortized), so nothing large is due at the end. | FORMULA: Zero: P = F/(1+i)^n ; Coupon: P = sum C/(1+i)^t + F/(1+i)^n ; Fixed-payment: loan = sum Payment/(1+i)^t

Ch 6: What distinguishes zero (discount) coupon bonds, coupon bonds and fixed-payment loans - examples and details

Zero: T-bills, commercial paper; $100 one-year at 5% = $95.24; six-month $97.59; three-month $99.02; $95 T-bill yields 100/95 - 1 = 5.26%; 2-year $1,000 zero at 6% = $890.00. Coupon: Treasury notes/bonds, corporate bonds; 3-year 5% coupon $1,000 face at 4% = 48.08 + 46.23 + 933.43 = $1,027.75; 3-year 6% coupon at 5% market rate = $1,027.23. Fixed-payment: mortgages, car loans; $100,000 30 years at 8% = $8,882.57/yr. Consol (perpetuity): P = C/i ($1 a year at 5% = $20).

Ch 6: Common methods of pricing bonds: current yield, holding period return, yield to maturity

YTM is the interest rate that equates the bond's price with the PV of all its payments if held to maturity (most complete measure). Current yield = annual coupon / price (ignores capital gains). Holding period return = current yield + capital gain, for a bond sold before maturity. At par: coupon rate = current yield = YTM. | FORMULA: Current yield = Annual coupon / Price ; HPR = Coupon/Price paid + (Price sold - Price paid)/Price paid ; YTM: solve Price = sum C/(1+i)^t + F/(1+i)^n

Ch 6: Common methods of pricing bonds: current yield, holding period return, yield to maturity - examples and details

Ordering: discount bond: coupon rate < current yield < YTM; par: all equal; premium bond: coupon rate > current yield > YTM. One-year 5% coupon $100 face: price $99 gives CY 5.05% and YTM 6.06%; price $101 gives CY 4.95% and YTM 3.96%. HPR: 10-year 6% bond bought at $100 and sold in a year: rates fall to 5% price $107.11 so HPR 13.11%; rates rise to 7% price $93.48 so HPR 0.52%.

Ch 6: Common methods of pricing bonds: current yield, holding period return, yield to maturity - worked numbers and practice

Practice: $1,000 bond with $70 coupon at $950: CY 7.37%, YTM higher. One-year 8% coupon bond at $980: YTM = 1080/980 - 1 = 10.20%. Buy $1,000, $50 coupon, sell $1,040: HPR 9%; sell $960: 1%. Bond risks: default, inflation, interest rate risk (worse for long maturities).

Ch 7: How bonds are risk rated; the common agencies; investment grade vs junk at each

Independent agencies (Moody's, Standard & Poor's, Fitch) assess the likelihood a borrower makes its promised payments. Investment grade is Baa or higher at Moody's and BBB or higher at S&P and Fitch; anything below is speculative (junk or high-yield). Lower ratings mean higher default risk, lower prices and higher yields.

Ch 7: How bonds are risk rated; the common agencies; investment grade vs junk at each - examples and details

Scale (Moody's / S&P-Fitch): Aaa/AAA best (J&J, Microsoft, Canada); Aa/AA (Alphabet, P&G); A/A (JPMorgan, Wells Fargo, China); Baa/BBB lowest investment grade (Hewlett Packard, Italy, Portugal); Ba/BB junk (Goodyear, Nokia, Brazil); B/B (Hertz, Greece); Caa-C / CCC-C highly speculative (Venezuela); D default. High rating comes from low debt, high profitability and sizable cash. Many insurers, pension funds and banks cannot hold below Baa/BBB so a downgrade forces sales and raises costs. Junk types: fallen angels (MCI WorldCom A to Ba in 2002; Greece A in 2010 to C) and little-known issuers. Commercial paper: Moody's P-1/P-2/P-3 and S&P A-1/A-2/A-3 are prime grade. Weaknesses: issuers pay for ratings (conflict of interest); AAA subprime tranches were downgraded heavily.

Ch 7: Risk structure vs term structure of interest rates and how they affect a given bond

Risk structure: bonds with the same maturity but different risk (default risk and taxes); yield = Treasury yield + default-risk premium. Term structure: bonds with the same risk but different maturities, shown by the yield curve. A given bond's yield depends on both who issued it and when it matures. | FORMULA: Bond yield = Treasury yield (same maturity) + default premium ; Long rate = average expected short rates + term premium

Ch 7: Risk structure vs term structure of interest rates and how they affect a given bond - examples and details

Term structure facts: yields of different maturities move together; short rates more volatile; long rates usually higher. Expectations hypothesis (long rate = average of expected short rates) explains facts 1 and 2 only. Liquidity premium theory (adds a term premium rising with maturity) explains all three. Example: 1-year rates 5%, 6%, 7% give 3-year rate 6%; with 0.5% term premium 6.5%. Yield curve: upward = normal; flat = rates expected to fall slightly; inverted = rates expected to fall significantly (recession signal about a year ahead). A 10-year Baa bond yield = expected average short rate + term premium + Baa default premium. Downgrade raises default premium; expected Fed hikes raise expected short rates; inflation uncertainty raises term premium. Baa-Treasury spread widens before recessions (peaked 5.6 points 2007-09).

Ch 7: Risk structure vs term structure of interest rates and how they affect a given bond - worked numbers and practice

Practice: 10-yr Treasury 3% and Baa 5.2% = 2.2 point (220 bp) spread; 1-yr rates 2/3/4/5% with 0.75% term premium = 4.25%.

Ch 7: What bonds are benchmarked against, why, and how the relationship changes

Bonds are benchmarked against U.S. Treasury securities of the same maturity because Treasuries have little default risk and are very liquid. Other bonds are quoted as a spread over Treasuries. Spreads widen when the economy weakens or investors panic (flight to quality) and narrow in good times.

Ch 7: What bonds are benchmarked against, why, and how the relationship changes - examples and details

Why Treasuries: little default risk, deep liquid markets, full range of maturities, government can pay in dollars. Changes: Treasury yield moves shift all other yields; recession approaching widens spreads most for junk; flight to quality (Russia default Aug 1998: Treasuries +10% in price, Brazilian bonds -1/3, CP-T-bill spread doubled from 0.5 to over 1 point); issuer's finances worsen widens its spread (JCPenney 22.67 points in 2019); booms narrow spreads (sometimes too far, search for yield). Even the benchmark can change: S&P downgraded Treasury debt to AA+ in Aug 2011. Foreign bonds also quoted vs Treasuries (Mar 2019: Germany 10-yr 251.5 bp below US).

Ch 7: How tax rates influence investor decisions; taxable vs tax-free bond

Investors care about after-tax returns. Corporate bond interest is taxable; municipal bond interest is exempt from federal income tax, so munis can pay lower yields and still be equally attractive. The higher the tax rate, the bigger the gap, so munis appeal most to high-income investors. | FORMULA: Tax-exempt equivalent = Taxable yield x (1 - t) ; Taxable equivalent = Muni yield / (1 - t) ; Break-even t = 1 - muni/taxable

Ch 7: How tax rates influence investor decisions; taxable vs tax-free bond - examples and details

Book example: $100 one-year 6% taxable bond at 30% tax: interest $6, tax $1.80, after-tax $4.20 = 4.2% tax-free equivalent. Decision: corporate 5% vs muni 3.6%: at 22% bracket corporate after-tax = 3.9% so buy corporate; at 35% bracket = 3.25% so buy muni; break-even tax rate = 1 - 3.6/5 = 28%.

Ch 7: How tax rates influence investor decisions; taxable vs tax-free bond - worked numbers and practice

Practice: taxable 8% at 25% tax = 6% muni equivalent; muni 4.2% at 40% tax = 7% taxable equivalent. Treasury interest taxed federally not by states. Munis: general obligation (taxing power) or revenue bonds (project).

Ch 8: Common stock: powers stockholders have and how they are compensated

Common stock is an ownership share in a firm. Stockholders are residual claimants on profits, can vote at the annual meeting to elect the board of directors, can sell their shares, and have limited liability. They are compensated by dividends and capital gains (and buybacks), but only after everyone else is paid. | FORMULA: Return = D/P0 + (P1 - P0)/P0 ; Fundamental price P = D(1+g)/(rf + rp - g)

Ch 8: Common stock: powers stockholders have and how they are compensated - examples and details

Residual claim: paid after workers, suppliers, bondholders and banks; big in good years, nothing in bad ones. Limited liability: lose at most what you invested (Webvan shareholders did not owe its debts). Voting: elect board, replace poor managers. Transferability: easy trading. Compensation: dividends (not guaranteed), capital gains, buybacks. Why risky: residual claim plus leverage ($1,000 firm earning $80 or $160: all-equity 12% expected return SD 4%; 80% debt at 10%: 20% return SD 20%).

Ch 8: Common stock: powers stockholders have and how they are compensated - worked numbers and practice

Practice: buy $40, dividend $1.20, sell $44 = 3% + 10% = 13%. Dividend-discount: D=$2, g=3%, rf=2%, rp=5% gives $51.50.

Ch 8: Price-weighted vs value-weighted indexes with examples of each

A price-weighted index gives more weight to stocks with higher share prices regardless of company size (the Dow Jones Industrial Average, Nikkei 225). A value-weighted index weights each firm by market capitalization (price x shares) and measures change in total market wealth (S&P 500, Nasdaq Composite, Wilshire 5000, TOPIX). Neither is better; they answer different questions. | FORMULA: Market cap = Price x Shares outstanding

Ch 8: Price-weighted vs value-weighted indexes with examples of each - examples and details

Dow: 30 large US firms, created 1884 by Charles Dow. S&P 500: 500 largest firms. Nasdaq: 2,500+ mostly tech. Wilshire 5000: broadest.

Ch 8: Price-weighted vs value-weighted indexes with examples of each - worked numbers and practice

Worked example: Stock A $50 x 100M shares (cap $5B); Stock B $100 x 10M shares (cap $1B). A rises 15%: price-weighted +5% ($150 to $157.50); value-weighted +12.5% ($6B to $6.75B). B rises 15%: price-weighted +10%; value-weighted +2.5%. Price-weighted driven by high-priced shares; value-weighted driven by big companies. Practice: $20 (500M shares) and $200 (10M shares); the $200 stock rises 10%: price-weighted +9.1%; value-weighted +1.7%. Compare countries by percentage change not index level.

Ch 8: Efficient market theory and what it means about how markets react to information

Prices of financial instruments reflect all available information, so markets adjust immediately when fundamentals change. Future price movements are unpredictable (only unexpected news moves prices), so no one can consistently beat the market average and active management should not outperform a broad index year after year.

Ch 8: Efficient market theory and what it means about how markets react to information - examples and details

If you could forecast a rise tomorrow, buying today would push the price up today. Managed portfolios return about 1% less than market averages. Consistent beating of the market means insider information (illegal), more risk, luck, or inefficiency. Luck looks like skill: 300 million coin-flippers, after 20 days 286 people have about $1.05 million (Bernstein). Limits: bubbles and crashes (dot-com 1999-2000, China 2015 margin loans, US housing); efficient does not mean prices are always right, only that changes cannot be systematically predicted.

Ch 8: Efficient market theory and what it means about how markets react to information - worked numbers and practice

Practice: manager beat S&P three years in a row = likely luck or extra risk.

Ch 8: Long-run vs short-term risk of bonds vs stocks

In the short run stocks are much riskier than bonds (one-year real stock returns about -40% to +50%). Over long holding periods the picture reverses: Siegel found 25-year average real stock returns ranged 2.5% to 11.2% and were never negative, and from 1871 to 1992 bonds never beat stocks over any 30-year period. Bonds carry interest rate and inflation risk over long horizons.

Ch 8: Long-run vs short-term risk of bonds vs stocks - examples and details

Short run stocks: -40% (1932) to +50% (1936); last 50 years -35% (2008) to +31% (1996). Long run stocks: about 6.5% annualized since 1871; big declines tend to be followed by rebounds. Bonds: interest rate risk (2.75% 30-year Treasury bought 2012 lost about 5% by 2019), default risk, inflation risk accumulates. Takeaways: young investors with long horizons hold stocks; a 60-year-old or a house down payment next year can't afford a short-run crash. Caveat: Shiller's CAPE 28.8 in early 2019 vs 16.93 long-run average suggests lower future returns.

Ch 8: Means to diversify risks in the stock market

Hold many stocks whose returns are not perfectly correlated, most easily through mutual funds and ETFs (especially low-cost index funds). Diversify across industries and countries, mix stocks with bonds, hedge with opposite-moving assets, avoid single-stock concentration (including your employer), limit leverage and hold long term. Diversification removes idiosyncratic risk but not systematic risk. | FORMULA: SD of n independent stocks = SD / sqrt(n)

Ch 8: Means to diversify risks in the stock market - examples and details

Spreading: SD falls with 1/sqrt(n) (3M + Microsoft $10 to $7.10; four stocks $5.00). Index funds: fees about 0.2% vs 0.8% for managed funds: $10,000 over 20 years at 5% = $26,533 vs $23,660. Across industries: oil spike hurts automakers, helps energy. Hedging: 3M + Texaco SD $0. International: benefit declined as markets became more correlated. Avoid concentration: Shaheen's $280M in Webvan went to $0. Limit leverage: China 2015 margin-fueled crash. Fund checklist: affordability, liquidity, diversification, management, cost. Cannot remove systematic risk (2008: -35%), which is why stocks pay an equity risk premium.

FORMULA: M1

Currency held by public + traveler's checks + demand deposits + other checkable deposits

FORMULA: M2

M1 + small time deposits (under $100k) + savings deposits and money-market deposit accounts + retail money-market mutual fund shares

FORMULA: Future value (FV)

FV = PV x (1 + i)^n

FORMULA: Present value (PV)

PV = FV / (1 + i)^n

FORMULA: Compound interest earned

FV - PV

FORMULA: Rule of 72

Years to double = 72 / interest rate (%). 5% = 14.4 years; 10% = 7.2 years

FORMULA: Annual rate from total growth

(Ending value / Starting value)^(1/n) - 1

FORMULA: Annuity PV and perpetuity PV

Annuity: PV = (C/i)[1 - 1/(1+i)^n]. Perpetuity (consol): PV = C/i

FORMULA: Fisher equation

i = r + expected inflation (nominal = real + expected inflation). Exact: (1+i) = (1+r)(1+expected inflation)

FORMULA: Ex ante vs ex post real rate

Ex ante = nominal - expected inflation. Ex post = nominal - actual inflation

FORMULA: Expected value and standard deviation

EV = sum of (probability x payoff). SD = square root of sum of probability x (payoff - EV)^2

FORMULA: Risk premium

Expected return on risky investment - risk-free return

FORMULA: Leverage ratio

Cost of investment / owner's contribution

FORMULA: SD of n independent identical stocks

SD of one stock / square root of n

FORMULA: Zero-coupon bond price

P = F / (1 + i)^n

FORMULA: Coupon bond price

P = sum of C/(1+i)^t + F/(1+i)^n

FORMULA: Current yield

Annual coupon / price paid

FORMULA: Holding period return

Coupon/price paid + (price sold - price paid)/price paid = current yield + capital gain

FORMULA: Yield to maturity (YTM)

The rate i that makes the price equal the PV of all payments if held to maturity

FORMULA: Bond ordering rule

Discount: coupon rate < current yield < YTM. Par: all equal. Premium: coupon rate > current yield > YTM

FORMULA: Risk structure of interest rates

Bond yield = Treasury yield (same maturity) + default-risk premium

FORMULA: Term structure (expectations hypothesis and liquidity premium)

Long rate = average of expected 1-year rates (+ term premium under liquidity premium theory)

FORMULA: Tax-exempt equivalent yield

Taxable yield x (1 - t)

FORMULA: Taxable-equivalent yield

Muni yield / (1 - t)

FORMULA: Break-even tax rate (muni vs taxable)

t = 1 - (muni yield / taxable yield)

FORMULA: One-year stock return

Dividend/P0 + (P1 - P0)/P0

FORMULA: Stock fundamental value (dividend-discount)

P = D(1 + g) / (rf + rp - g)

FORMULA: Market capitalization

Price x shares outstanding (used in value-weighted indexes)

Ch 2 practice: currency $500B (of which $50B in bank vaults), demand deposits $400B, other checkable $150B, savings and MMDAs $1,200B, small time $300B, large time $250B, retail MMMFs $200B. Find M1 and M2.

Currency held by public = 450. M1 = 450 + 400 + 150 = $1,000B. M2 = 1,000 + 1,200 + 300 + 200 = $2,700B (large time deposits excluded).

Ch 2 practice: someone moves $5,000 from checking to savings. Effect on M1 and M2?

M1 falls by $5,000; M2 is unchanged (both accounts are in M2).