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Glossary

Every finance word, in plain English.

96 terms across markets, banking, retirement, taxes, risk, alternatives, and behavior. Search or browse.

96 terms
4

401(k)

Retirement

A workplace retirement account funded with pre-tax (or Roth) contributions, often with employer matching. Limits are set by the IRS each year.

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Why it matters

The 401(k) is the single most important wealth-building tool most American workers have, mostly because of the employer match. A 100% match on the first 4-6% of your salary is, almost literally, free money. Skipping it is like turning down a raise. Understanding how vesting, contribution limits, and the Roth vs. traditional choice work can mean tens of thousands of extra dollars over your career.

Real-life example

Imagine earning $60,000 with a 100% employer match on the first 5%. If you contribute 5% ($3,000), your employer adds $3,000. Over a 35-year career with steady contributions and an 8% average return, that match alone (without your own contributions) compounds to roughly $500,000+. Skipping the match for one decade is a six-figure mistake.

Related terms
5

529 plan

Retirement

An education savings account with tax-free growth and tax-free withdrawals when used for qualified education expenses.

A

Accredited investor

Alternatives

An SEC designation for investors with sufficient income or net worth. Required to access many private investments.

Annuity

Retirement

An insurance contract that pays a stream of income, often for life. Some are simple; many are complex products with high fees and surrender charges.

Asset allocation

Risk

How you split your money across asset classes — typically stocks, bonds, and cash. Drives most of your portfolio's behavior.

AUM

Markets

Assets Under Management. The total dollars a fund or advisor manages.

B

Beta

Risk

How much a stock moves relative to the broad market. Beta of 1 = moves with the market. Beta of 1.5 = swings about 1.5× as much.

Bid / Ask

Markets

The bid is the highest price someone will pay; the ask is the lowest price someone will sell for. The difference between them is the spread.

Bond

Markets

A loan you make to a government or company in exchange for regular interest payments and the return of the original amount on a future date.

Brokerage account

Markets

A regular taxable investment account at a firm like Fidelity, Schwab, or Vanguard. No contribution limits; no special tax treatment.

C

Call option

Risk

The right to buy something at a specified price by a specified date.

Capital gain

Taxes

The profit when you sell an investment for more than you paid for it. Held over a year = long-term gain (lower tax rate). Held a year or less = short-term (higher tax rate).

Capital gain (long)

Taxes

The profit when you sell an investment for more than you paid for it. If you held the investment for more than one year, it's a long-term capital gain — taxed at lower rates (currently 0%, 15%, or 20% federal depending on your income).

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Why it matters

The difference between long-term and short-term capital gains is one of the few places in tax law where waiting literally pays. Sell a stock at a profit after 11 months: you might owe 22-37% in federal tax. Sell the same stock at the same profit after 13 months: you might owe 15%. That's a meaningful difference for the same gain — driven entirely by the calendar.

Real-life example

You bought $5,000 of an index fund in January 2023, and it grew to $7,000 by December 2024. If you sell in December 2024 (held over a year), the $2,000 gain is taxed as long-term — likely 15%, so you'd owe about $300 federal. If you'd sold in November 2023 (held under a year), the same $2,000 gain might have been taxed as short-term at your ordinary income rate of 24%+, costing roughly $480.

Capital loss

Taxes

The amount you lose when you sell an investment for less than you paid. Can offset capital gains and reduce your tax bill.

Capital loss (defined)

Taxes

The amount you lose when you sell an investment for less than you paid for it. The IRS lets you use capital losses to offset capital gains, and up to $3,000 of losses can be deducted against ordinary income each year. Excess losses carry forward to future years.

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Why it matters

Capital losses are one of the few places where 'losing' actually saves you money — but only if you know the rules. Tax-loss harvesting (intentionally selling losers to capture losses) is a common strategy used by investors and roboadvisors. The trap: the wash sale rule disallows the loss if you buy back the same investment within 30 days. Done wrong, you get the loss with no tax benefit.

Real-life example

Say you have $5,000 in capital gains this year. You also bought a stock at $10,000 that's now worth $7,000. If you sell that stock, the $3,000 loss offsets your $5,000 gain, and you'd only owe tax on $2,000. At a 15% long-term capital gains rate, that saves about $450 in tax. But if you buy the same stock back within 30 days, the wash sale rule kicks in and you lose the deduction.

CD (Certificate of Deposit)

Banking

A time deposit at a bank with a fixed interest rate and a fixed term. Withdrawing early usually triggers a penalty.

Commodity

Alternatives

A raw material or basic good — gold, oil, wheat, copper. Often traded via ETFs or futures contracts.

Correction

Markets

A drop of 10% or more from a recent high — less severe than a bear market.

Cost basis

Taxes

The original amount you paid for an investment, used to calculate gains or losses when you sell.

Cryptocurrency

Alternatives

A digital asset whose ownership is tracked on a blockchain — a public, distributed database.

D

Deflation

Markets

A sustained decrease in the average prices of goods and services. The opposite of inflation. Rare in modern economies — generally considered a sign of severe economic distress when it does happen.

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Why it matters

Deflation sounds nice ('things get cheaper!') but is actually one of the scariest economic outcomes. When prices fall, people delay purchases (waiting for even lower prices), which slows the economy, which causes layoffs, which reduces spending further. Japan's 'lost decades' (1990s-2000s) involved long deflation that crushed economic growth. The Federal Reserve fights deflation aggressively because once it sets in, it's very hard to escape.

Real-life example

During the Great Depression (1929-1933), U.S. prices fell about 25% — true deflation. People who could afford to buy got things cheap. But mass unemployment (peaking at 25%) meant most people couldn't afford anything at any price. Deflation usually accompanies — and amplifies — economic collapse, not prosperity.

Dollar-cost averaging (DCA)

Behavior

Investing a fixed amount on a regular schedule regardless of price. Removes the need to time the market.

Dow Jones (DJIA)

Markets

An index of 30 large, established U.S. companies. Older and less representative than the S&P 500, but widely quoted in headlines.

Drawdown

Risk

The peak-to-trough decline of an investment. A 50% drawdown means the investment fell 50% from its high before recovering.

Drawdown (defined)

Risk

The peak-to-trough decline of an investment, expressed as a percentage. A 50% drawdown means an investment fell 50% from its all-time high before recovering. Even diversified portfolios experience drawdowns; the question is how big and how long.

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Why it matters

Drawdowns are the actual experience of risk. Average annual returns sound abstract, but a 40% drawdown is a visceral, sleepless-night kind of feeling. The honest test of whether your portfolio matches your risk tolerance isn't 'can I handle the average return?' — it's 'can I handle the worst drawdown without selling?' Most retirement projections quietly assume you won't sell during drawdowns. Most investors do.

Real-life example

The S&P 500 fell about 34% in just over a month in early 2020 (the COVID crash). An investor with $200,000 saw it become $132,000 in five weeks. Within five months it recovered. But the experience — opening a brokerage app and seeing $68,000 of your retirement savings disappear — is something words don't capture. That's drawdown.

E

EPS

Markets

Earnings per share. A company's net income divided by total shares outstanding.

ETF

Markets

Exchange-Traded Fund. A bundle of many investments that trades on a stock exchange like a single stock. Often used to own broad slices of the market cheaply.

Expense ratio

Markets

The annual fee a fund charges, expressed as a percent of assets. A 0.05% expense ratio costs $5 per year for every $10,000 invested.

F

FDIC insurance

Banking

U.S. government insurance covering up to $250,000 per depositor, per bank, per ownership category. Protects your money if the bank fails.

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Why it matters

FDIC insurance is one of the most important consumer protections in U.S. finance. As long as your money is in an FDIC-insured account and you stay within the limits, you genuinely cannot lose it to a bank failure. Understanding the per-bank, per-ownership-category structure matters when you have meaningful savings — exceeding the limit at one bank means part of your money isn't covered.

Real-life example

When Silicon Valley Bank failed in March 2023, every depositor with under $250,000 was made whole quickly via FDIC. The customers who had problems were ones holding millions in single accounts — they exceeded the per-bank cap. A simple fix would have been spreading deposits across multiple FDIC-insured banks, keeping each balance under $250,000.

Federal funds rate

Markets

The interest rate banks charge each other for overnight loans. The Fed targets this rate; it ripples through the entire economy.

Federal Reserve (Fed)

Markets

The U.S. central bank. Sets short-term interest rates and tries to balance employment and price stability.

Fiduciary

Risk

A legal standard requiring an advisor to act in the client's best interest. Not all financial advisors are fiduciaries — always ask.

FINRA

Markets

Financial Industry Regulatory Authority. A self-regulatory body overseeing U.S. brokerage firms and registered representatives.

G

Growth stock

Markets

A stock priced for high expected future growth. Often pays no dividend; profits are reinvested.

H

Hedge fund

Alternatives

An actively managed pool of money using complex strategies — often shorting, leverage, derivatives. Open mostly to institutional and accredited investors.

High-yield savings (HYSA)

Banking

A savings account that pays a meaningfully higher interest rate than a typical brick-and-mortar bank account.

HSA

Retirement

Health Savings Account. Available with high-deductible health plans. Triple-tax-advantaged: deductible going in, growing tax-free, and tax-free for medical expenses.

I

I-Bond

Banking

A U.S. savings bond with an interest rate that adjusts with inflation. Bought directly from TreasuryDirect.gov; annual purchase limits apply.

Index fund

Markets

A fund that tries to match the performance of a market index, like the S&P 500. No human picks the holdings, which keeps fees very low.

IPO

Markets

Initial Public Offering. The first time a company sells its shares to the public on a stock exchange.

IRA

Retirement

Individual Retirement Account. A retirement account you open yourself, separate from any employer. Both Traditional and Roth versions exist.

L

Large-cap / Mid-cap / Small-cap

Markets

Categories by market cap. Roughly: $10B+ is large, $2B–$10B is mid, under $2B is small. Boundaries vary.

Liquidity

Risk

How quickly you can convert an investment to cash without significantly affecting its price. Stocks are liquid; private real estate is not.

M

Margin

Risk

Borrowing money from your broker to buy investments. Amplifies gains and losses; can result in losing more than you invested.

Market cap

Markets

Market capitalization. A company's stock price multiplied by total shares outstanding. The market's estimate of the company's total equity value.

Money market account

Banking

A type of savings account that often pays a competitive yield. Offered by banks and credit unions; FDIC-insured.

Money market fund

Banking

An investment fund holding very short-term, very safe debt. Different from a money market account — not FDIC-insured but generally considered very stable.

Mutual fund

Markets

Like an ETF, a bundle of investments — but priced once a day at the close of trading instead of all day long. Often more expensive than ETFs.

N

Nasdaq Composite

Markets

An index of all companies listed on the Nasdaq exchange. Heavily weighted toward technology companies.

O

Options

Risk

Contracts giving the right (not the obligation) to buy or sell something at a set price by a certain date. Powerful and risky; not appropriate for beginners.

Order types (market / limit)

Markets

A market order trades at the next available price. A limit order trades only at a specified price or better.

P

Private equity

Alternatives

Funds that buy whole companies, typically using debt, then try to improve them and sell them years later.

Put option

Risk

The right to sell something at a specified price by a specified date.

R

Rebalancing

Risk

Periodically adjusting your portfolio back to your target mix by selling overweight categories and buying underweight ones.

REIT

Alternatives

Real Estate Investment Trust. A company that owns income-producing real estate; required by law to distribute most of its taxable income to shareholders.

Required Minimum Distribution (RMD)

Retirement

The amount the IRS forces you to withdraw from certain retirement accounts each year starting in your 70s. Roth IRAs don't have this requirement during the original owner's lifetime.

Risk tolerance

Behavior

How much portfolio decline you can stomach without selling. Educational segmentation only — not a recommendation to take a specific level of risk.

Robo-advisor

Markets

An online service that automatically builds and manages a diversified portfolio for you, usually using ETFs, for a low fee.

Roth

Retirement

An account or contribution type where you pay tax now in exchange for tax-free withdrawals in retirement, including all the gains.

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Why it matters

Roth accounts are uniquely valuable because they protect you from one of retirement's biggest unknowns: future tax rates. With a traditional account, you're betting tax rates will be lower when you retire. With Roth, you've already paid the tax — what you withdraw is yours, no matter what Congress does decades from now. For young investors with 30+ years of growth ahead, Roth is often the math winner.

Real-life example

Imagine you contribute $7,000 to a Roth IRA at age 25 and it grows at 8% for 40 years. By age 65 it's worth about $152,000 — and every dollar comes out tax-free. With a traditional IRA, that same $152,000 might be taxed at 22-24% on withdrawal, costing $33,000+ in taxes. Same starting amount, same returns; Roth keeps more of what compounded.

S

S&P 500

Markets

An index of about 500 of the largest publicly traded companies in the U.S. Frequently used as the benchmark for U.S. stock market performance.

SEC

Markets

The U.S. Securities and Exchange Commission. The federal regulator overseeing public markets, brokerages, and investment advisers.

Sequence of returns risk

Retirement

The risk of bad market returns early in retirement. Even with the same average return, early losses combined with withdrawals can permanently shrink a portfolio.

Short selling

Risk

Borrowing a stock and selling it, hoping to buy it back later at a lower price. Losses are theoretically unlimited.

Stablecoin

Alternatives

A cryptocurrency designed to track the value of an external asset, usually the U.S. dollar.

Stock

Markets

A small share of ownership in a company. Owning one share of a company with one billion shares means you own one billionth of it.

Suitability standard

Risk

A weaker standard than fiduciary. Requires only that an investment be 'suitable' for the client, not necessarily the best option for them.

T

T-bill (Treasury Bill)

Banking

Short-term U.S. government debt sold at a discount and maturing in one year or less. Considered the safest dollar investment in the world; exempt from state and local income tax.

Target-date fund

Retirement

A fund that automatically adjusts its mix as a target year approaches, becoming more conservative as you near retirement.

TIPS

Banking

Treasury Inflation-Protected Securities. Government bonds whose principal adjusts with inflation, helping protect purchasing power.

Traditional (account)

Retirement

An account where contributions may be tax-deductible today, growth is tax-deferred, and withdrawals in retirement are taxed as ordinary income.

Treasury bond

Banking

A long-term U.S. government bond, typically 20 or 30 years to maturity.

Treasury note

Banking

A medium-term U.S. government bond, typically 2 to 10 years to maturity.

V

Value stock

Markets

A stock trading at a low price relative to current earnings, book value, or other fundamentals. Often pays dividends.

Venture capital

Alternatives

Funds that invest in early-stage startups, expecting most to fail and a few to become very valuable.

Vesting

Retirement

The schedule on which employer contributions to your 401(k) become fully yours. Leaving early can mean forfeiting unvested matches.

W

Wash sale

Taxes

Selling an investment at a loss and buying it back within 30 days. The IRS disallows the tax deduction on the loss when this happens.

Y

Yield

Markets

The annual income from an investment, expressed as a percent of its price. A $100 stock paying $3 in dividends has a 3% dividend yield.

Featured Conceptsƒ formulavisual

The 19 concepts with built-in formulas, illustrations, or both. Best place to start if you're new — or curious how the math actually works.

APR

ƒ formulaBanking

Annual Percentage Rate. The yearly cost of borrowing, including most fees. Used to compare loans and credit cards.

APR (simple)
APR = (Periodic rate × periods per year) + fees expressed annually
  • ·APR is a simple annualized rate — does not include compounding
  • ·On a credit card, daily rate × 365 = APR
  • ·Mortgage APR includes fees rolled into the rate calculation

Example: Credit card with daily periodic rate of 0.0548%: APR = 0.0548% × 365 ≈ 19.99%

APY

ƒ formulaBanking

Annual Percentage Yield. The yearly return on a savings account, factoring in compounding. Used to compare savings account rates apples-to-apples.

APY formula
APY = (1 + r/n)^n − 1
  • ·r = nominal annual rate (decimal)
  • ·n = number of compounding periods per year
  • ·APY ≥ r — the more frequent the compounding, the more APY exceeds r

Example: 5% APR compounded monthly: APY = (1 + 0.05/12)^12 − 1 ≈ 5.12%

Bear market

visualMarkets

A sustained period of falling stock prices. The standard rough definition is a 20% or greater decline from a recent high, lasting weeks or months.

Visual
SUSTAINED FALL — bear market (≥20% drop)
Why it matters

Bear markets are when most investors quietly destroy their wealth — not from the market falling, but from selling at the bottom because the pain becomes unbearable. Studies consistently show that the worst behavior happens during bear markets. The investors who do well long-term are usually the ones who don't sell during them.

Real-life example

From October 2007 to March 2009, the S&P 500 fell about 57%. An investor with $100,000 watched it become roughly $43,000. The investors who panicked and sold near the bottom locked in massive losses. The investors who held — and especially those who kept buying — recovered everything within a few years and went on to massive gains.

Bull market

visualMarkets

A sustained period when stock prices are rising and investor confidence is high. Often defined informally as a 20% or greater rise from a recent low, lasting months or years.

Visual
SUSTAINED RISE — bull market
Why it matters

Bull markets feel great while they're happening, but they're when investors make their biggest mistakes. Confidence rises, risk-taking increases, and people convince themselves that 'this time is different.' Understanding what a bull market is — and that it always eventually ends — helps you keep your head when everyone else is losing theirs.

Real-life example

The S&P 500 from March 2009 through February 2020 was the longest bull market in U.S. history — about 11 years. A $10,000 investment in an S&P 500 index fund at the start would have grown to roughly $40,000+ by the end, despite a few scary dips along the way.

Compound interest

ƒ formulavisualBehavior

Interest earned on the interest you already earned. Over decades, this is the dominant force in long-run wealth growth.

Visual
simplecompoundtime →$
Compound interest formula
A = P × (1 + r/n)^(n×t)
  • ·A = final amount
  • ·P = principal (starting amount)
  • ·r = annual interest rate (decimal, e.g. 0.08 for 8%)
  • ·n = times compounded per year (12 = monthly, 365 = daily)
  • ·t = number of years

Example: $5,000 at 8% annual, compounded monthly for 40 years: A = 5000 × (1 + 0.08/12)^(12×40) ≈ $121,000

Why it matters

Compound interest is the engine behind every retirement account, every savings goal, and every long-term investment plan. It's also the engine behind credit card debt — running in reverse, against you. Understanding how it works practically is the difference between financial confidence and confusion.

Real-life example

Invest $5,000 once at age 25 at 8% per year. By age 65, it grows to about $109,000 — without you adding another dollar. The original $5,000 made you $104,000 in 'free' money, all from compounding. The same $5,000 invested at age 45 only grows to about $23,000 by 65. Time is the multiplier.

Diversification

visualRisk

Spreading money across many investments to reduce the impact of any single one performing badly.

Visual
1concentrateddiversifiedvs
Why it matters

Diversification is sometimes called 'the only free lunch in investing' — meaning it reduces risk without sacrificing expected returns. The math works because different investments don't all move together: when stocks fall, bonds may hold up; when U.S. stocks struggle, international stocks may thrive. Concentration is what kills portfolios, especially when investors load up on their employer's stock or a single 'hot' company.

Real-life example

An employee at Enron in 2000 had most of their 401(k) in Enron stock. When Enron collapsed in 2001, many lost both their jobs AND their retirement savings simultaneously. A diversified portfolio holding Enron alongside hundreds of other companies would have lost a small fraction. Diversification doesn't prevent losses — it prevents catastrophic ones.

Dividend

ƒ formulavisualMarkets

A small cash payment a company sends to its shareholders, usually quarterly, out of its profits. Not all companies pay them.

Visual
companyprofits$Q1$Q2$Q3$Q4youshareholderprofit share, paid quarterly
Dividend yield formula
Dividend Yield = Annual Dividend per Share ÷ Stock Price
  • ·Annual Dividend = quarterly dividend × 4 (or trailing 12 months)
  • ·Stock Price = current market price
  • ·Result is expressed as a percentage
  • ·Note: a high yield may mean a falling stock price, not necessarily a good buy

Example: Stock at $50 paying $0.50 quarterly ($2 annually): Yield = 2 ÷ 50 = 4%

Future value

ƒ formulaBehavior

How much a sum of money today will be worth in the future, after growing at a given rate. The math behind every retirement projection.

Future value formula (lump sum)
FV = PV × (1 + r)^n
  • ·FV = future value (what you're solving for)
  • ·PV = present value (today's amount)
  • ·r = annual rate of return (decimal)
  • ·n = number of years

Example: $10,000 at 7% for 30 years: FV = 10,000 × (1.07)^30 = $76,123

Why it matters

Future value lets you answer 'if I invest $X today, what will it be worth in N years?' This is the core math behind retirement planning, savings goal calculators, and the case for starting young. Without it, you can't reason about long-term financial decisions.

Real-life example

$10,000 invested at 7% per year for 30 years grows to about $76,000. The same $10,000 at 7% for 40 years grows to about $150,000. Adding a single decade nearly doubles the result — that's why time horizon matters more than timing.

Inflation

visualMarkets

The gradual rise in the average prices of goods and services over time. Measured most commonly by the Consumer Price Index (CPI), which tracks a basket of typical household purchases. Healthy economies tend to have low, steady inflation around 2%.

Visual
$1today$110 yrs$130 yrssame dollar, less buying power
Why it matters

Inflation is the silent tax on cash. If your money sits in a checking account earning 0.01% while inflation is 3%, you're losing about 3% of your buying power each year, even though your account balance hasn't changed. This is why 'just saving cash' is not actually safe over long time periods. It's also why investing — even with risk — is often the more conservative long-term choice for money you don't need soon.

Real-life example

$100 in 1995 had the buying power of about $200 in 2024 — meaning prices roughly doubled over those 30 years. Someone who kept $100,000 in cash from 1995 to 2024 still has $100,000 in their account. But that money buys about half as much. If they'd invested it in the S&P 500 instead, it would have grown to roughly $1.4 million — about 14x ahead even after accounting for inflation.

P/E ratio

ƒ formulavisualMarkets

Price-to-earnings ratio. The stock price divided by the company's annual earnings per share. A rough measure of how expensive a stock is.

Visual
PRICE$20 paid÷EPS$1 earned=20
P/E ratio formula
P/E = Stock Price ÷ Earnings Per Share (EPS)
  • ·Stock Price = current market price of one share
  • ·EPS = annual earnings ÷ shares outstanding
  • ·Higher P/E = market expects more growth (or stock is overvalued)
  • ·Lower P/E = mature/value stock (or business problems)

Example: Stock at $100 with EPS of $5: P/E = 100 ÷ 5 = 20. Investors pay $20 for every $1 of annual earnings.

Present value

ƒ formulaBehavior

How much a future sum of money is worth today, after discounting for the rate of return you could earn in the meantime. The reverse of future value.

Present value formula
PV = FV ÷ (1 + r)^n
  • ·PV = present value (today's worth)
  • ·FV = future value (the amount in the future)
  • ·r = discount rate (typically risk-adjusted)
  • ·n = number of years until the money arrives

Example: $100,000 received in 20 years, discounted at 6%: PV = 100,000 ÷ (1.06)^20 = $31,180

Why it matters

Present value teaches a critical insight: a dollar in 30 years is worth far less than a dollar today. It's how lottery winners decide between lump sum and annuity, how pension valuations work, and why 'I'll save more later' costs more than people realize.

Real-life example

Lottery offers $1 million today OR $50,000/year for 30 years ($1.5M total). At a 6% discount rate, the future $50K/year stream has a present value of about $688,000 — less than the $1M lump sum. The lump sum is mathematically worth more even though it's smaller.

Recession

visualMarkets

A meaningful, broad-based decline in economic activity that lasts more than a few months. The technical definition (used by the U.S. National Bureau of Economic Research) considers GDP, employment, industrial production, and income — not a simple formula.

Visual
RECESSION2+ quarters of contracting GDP
Why it matters

Recessions are when economic narratives turn dark — layoffs rise, headlines get scary, and investing decisions get harder. But recessions are normal: the U.S. has had 11 since 1948. They typically last about 11 months. The investors who panic and sell during recessions consistently underperform the ones who keep buying. Understanding what a recession is — and how often they happen — helps you stay rational when the news is at its worst.

Real-life example

In 2008, the U.S. entered a major recession. Unemployment doubled from about 5% to 10%. The S&P 500 fell roughly 50% peak to trough. Headlines were apocalyptic. By 2013, the S&P had fully recovered. Investors who kept their 401(k) contributions going through 2008-2009 — buying at scary low prices — ended up dramatically ahead of those who 'paused' until things felt safer.

Sharpe ratio

ƒ formulaRisk

A measure of risk-adjusted return. Tells you how much extra return you got per unit of risk taken — useful for comparing investments with different risk profiles.

Sharpe ratio formula
Sharpe = (Return − Risk-free rate) ÷ Standard deviation
  • ·Return = portfolio's actual return
  • ·Risk-free rate = yield on short-term U.S. Treasury bills
  • ·Standard deviation = volatility (typically annualized)
  • ·Higher = better risk-adjusted performance

Example: Fund returning 10% with 12% volatility, T-bills at 4%: Sharpe = (10-4) ÷ 12 = 0.5

Why it matters

Two investments with the same return aren't equally good if one is wildly volatile and the other is steady. Sharpe ratio adjusts for that. It lets you ask 'was this return worth the risk?' Higher is better. Above 1.0 is generally considered good; above 2.0 is very good; above 3.0 is excellent.

Real-life example

Fund A returns 12% with 20% volatility. Fund B returns 9% with 8% volatility. Risk-free rate is 4%. Fund A: (12-4)/20 = 0.40 Sharpe. Fund B: (9-4)/8 = 0.625 Sharpe. Fund B delivered more return per unit of risk — better risk-adjusted performance, despite lower headline returns.

Standard deviation

ƒ formulaRisk

A statistical measure of volatility. A higher number means a wider range of typical price movement.

Standard deviation (population)
σ = √( Σ(x − μ)² / N )
  • ·x = each individual return
  • ·μ = average (mean) return
  • ·N = number of observations
  • ·Σ = sum across all observations
  • ·σ (sigma) = the resulting standard deviation

Example: S&P 500 has historical annual standard deviation of about 15-20% — meaning a one-year return within ±15-20% of average is statistically 'normal.'

Time horizon

ƒ formulavisualBehavior

How long you have until you actually need the money. The single most important factor in deciding what to do with it. A 25-year-old saving for retirement and a 60-year-old retiring next year may have the same dollar amount, but their right answers look completely different.

Visual
$2k10y$4.7k20y$10k30y$1,000 invested at 8%same amount, very different outcomes
Rule of 72 (estimating doubling time)
Years to double ≈ 72 ÷ Annual return rate
  • ·Quick mental math for compound growth
  • ·Annual return = expected percentage return (e.g., 8 for 8%)
  • ·Result = approximate years until your money doubles
  • ·Useful for thinking in time horizons rather than dollar amounts

Example: At 8% annual return: 72 ÷ 8 = 9 years to double. So $10K becomes $20K in 9 years, $40K in 18 years, $80K in 27 years.

Why it matters

Time horizon answers a question most people skip: 'when do you actually need this?' Money you need in 6 months should never be in stocks. Money you don't need for 30 years probably shouldn't sit in cash. Matching investments to time horizon is what makes risk reasonable. Mismatching it — putting next year's down payment in crypto, or 40-year retirement money in a checking account — is what creates real financial damage.

Real-life example

Two people each have $50,000. Person A needs it in 18 months for a down payment; the right answer is a high-yield savings account or short-term Treasury — preservation matters more than growth. Person B doesn't need it for 30 years; the right answer is a diversified stock portfolio — growth matters more than short-term stability. Same dollar amount, opposite strategies, both correct. Time horizon decides.

Time value of money

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The principle that money today is worth more than the same amount of money in the future — because money you have now can be invested and grow. Every financial calculation involving the future depends on this idea.

Visual
$100todayworth $100discount @ 6%over 30y$100in 30 yearsworth ~$17 todaya dollar today is worth more than a dollar tomorrow
Time value of money (discount formula)
Present Value = Future Value ÷ (1 + r)^n
  • ·Present Value = what a future dollar is worth today
  • ·Future Value = the amount you'll receive in the future
  • ·r = discount rate (the return you could earn instead, as a decimal)
  • ·n = number of years until you receive the money
  • ·Higher r or higher n = bigger discount applied

Example: $100,000 received in 20 years, discounted at 6%: PV = 100,000 ÷ (1.06)^20 ≈ $31,180. Today's $31K, invested at 6%, would grow to $100K in 20 years.

Why it matters

Time value of money is the concept underneath compound growth, mortgages, retirement planning, lottery payouts, pension valuations, and bond pricing. It's why a guaranteed $1 million in 30 years isn't actually worth $1 million today — and why deferring savings 'just for a few years' costs much more than people realize. Once you internalize this, financial decisions stop being about the dollar amount and start being about the dollar amount AND the timing.

Real-life example

A lottery offers $1 million today OR $50,000/year for 30 years (a $1.5 million 'larger' prize). At a 6% discount rate, the future $50K stream has a present value of about $688,000 — substantially less than the $1 million lump sum. The lottery's 'bigger' prize is mathematically smaller because of the time value of money. This is the same math used to price every bond, mortgage, and pension fund in the world.

Volatility

visualRisk

How much an investment's price moves up and down over time. Higher volatility means bigger swings (both up and down). Often used as a proxy for risk, though they're not exactly the same thing.

Visual
high volatility — wide swings around the average
Why it matters

Volatility is the price you pay for higher returns. Stocks have historically returned more than bonds because they're more volatile — investors demand a premium for tolerating the swings. Understanding volatility helps you set realistic expectations: a portfolio that returns 10% per year on average will not actually return 10% in any given year. It might return -25% one year and +35% the next.

Real-life example

Imagine two portfolios that both average 8% per year over a decade. Portfolio A returns roughly 8% every single year — very low volatility. Portfolio B returns +30%, then -10%, then +25%, then -15%, alternating wildly. Both end up at the same place mathematically, but portfolio B is much harder to actually live with — and most investors who hold portfolios like B end up selling at exactly the wrong time.

Yield (explained)

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The annual income an investment generates, expressed as a percentage of its price. A $100 stock paying $3 per year in dividends has a 3% dividend yield. A bond paying $40 per year on a $1,000 face value has a 4% yield. Different from total return, which also includes price changes.

Yield formula
Yield = Annual Income ÷ Current Price
  • ·Annual Income = dividends or interest paid per year
  • ·Current Price = today's market price (not the price you paid)
  • ·Yield rises when price falls; yield falls when price rises
  • ·This is why a falling stock can show a misleadingly high yield

Example: Stock at $50 paying $2/year in dividends: Yield = 2 ÷ 50 = 4%

Why it matters

Yield gets used and misused constantly in finance. A high yield can mean an investment is generating great income — or it can be a warning sign that the price has fallen sharply (because yield = income ÷ price). When you see a stock with a 12% dividend yield, the question isn't 'wow, free money?' It's 'why has this price collapsed enough to make the yield this high?' Yield without context is dangerous.

Real-life example

In 2024, several bank stocks had dividend yields in the 8-10% range — much higher than the S&P 500's typical 1-2%. The reason wasn't generosity; it was that bank stock prices had fallen sharply on concerns about commercial real estate exposure. Some of those high yields were sustainable; others got cut shortly after. Yield always tells you something — but rarely the whole story.

Yield curve

visualMarkets

A line plotting bond yields against their maturities. The shape of this curve is one of the most-watched signals about the state of the economy and what investors expect for the future.

Visual
3M2Y10Y30Yyieldnormal: long > short
Why it matters

A normal yield curve slopes upward — long-term bonds yield more than short-term ones, because investors demand more for tying up money longer. When the curve inverts (short-term rates higher than long-term), it has historically preceded most U.S. recessions over the last 50 years. Not perfectly, not immediately, but reliably enough that bankers, traders, and economists watch it closely.

Real-life example

In 2022-2023, the 2-year Treasury yield rose above the 10-year Treasury yield — an inversion. Many economists predicted a recession would follow within 12-18 months. The economy proved more resilient than expected, but the inversion still triggered widespread caution among institutional investors and changed how banks priced loans.

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