CFA Level I terms: T

All three rely on the t-distribution, a symmetric, bell-shaped curve with fatter tails than the normal that depends on the degrees of freedom: the number of independent pieces of information left after estimating what the test needs.

t-tests of a mean, a difference in means and paired differences Quantitative Methods

The t-statistic for a correlation follows a t-distribution with $n-2$ degrees of freedom. If $|t|$ is larger than the critical value, reject $H_0$ and call the correlation statistically significant.

Is a correlation significant? The t-test of correlation Quantitative Methods

The t-test of the slope then asks how many standard errors the estimate sits from the hypothesized slope $B_1$.

Goodness of fit and testing the regression coefficients Quantitative Methods

Counting. Proxy votes go to the tabulator or registrar, which counts them and reports the results to the company.

How shareholders vote: proposals, proxies, proxy advisors and asset managers Equities

Deliberately deviating from policy weights to add value from forecasts of near-term returns, for example holding more equities for a quarter because you expect them to beat bonds;.

Asset classes, strategic asset allocation and portfolio construction Portfolio Construction

A tag cloud (also called a word cloud) sizes words by how often they appear. A mind map varies the idea: instead of frequency, it shows how concepts are related.

Data science: processing, visualization and text analytics Quantitative Methods

More events in the tails of a distribution than a probability model expects. It is a facet of market risk, but ignoring it is a form of model risk.

Financial and non-financial risks, and how they interact Portfolio Construction

The shares stop trading and the buyers take full control, in a take-private transaction. Targets look undervalued or would benefit from restructuring.

Public vs private equity: venture capital, buyouts and PIPEs Equities

It is the frontier portfolio with the highest Sharpe ratio, the optimal risky portfolio. It is also called the tangency portfolio, because the line from the risk-free rate touches the frontier there (the last lesson of this module draws that line).

The minimum-variance portfolio and the efficient frontier Quantitative Methods

Tangible collateral ("hard" collateral) is physical and identifiable: property, plant and equipment, inventory, cash and marketable securities.

Assessing corporate creditworthiness Fixed Income

Instead they set a target capital structure, usually a range such as 30%–50% debt rather than one number. A range makes sense because market values keep moving, issuing securities has costs and minimum deal sizes, and managers want to take advantage of good financing windows (for instance, borrowing more than planned when investors are…

Optimal and target capital structure, pecking order and agency costs Corporate Finance

Forecasting borrowing year by year is hard, so analysts often assume the firm finances growth at a target debt ratio, DR = total debt ÷ (total debt + total equity).

Dividend discount and free-cash-flow-to-equity models Equities

The target semi-deviation, also called the target downside deviation, measures the spread of returns below a target B.

Semi-deviation, downside deviation and the coefficient of variation Quantitative Methods

The central bank also decides the inflation measure, the level and the horizon. A bank with this is both target and operationally independent.

Inflation targeting vs exchange rate targeting Economics

The target semi-deviation, also called the target downside deviation, measures the spread of returns below a target B.

Semi-deviation, downside deviation and the coefficient of variation Quantitative Methods

Fixed parity with a wider band (up to ±2%)

Exchange rate regimes and their effects on trade and capital flows Economics

These target-return weights come from the portfolio return being a weighted average, solved for the weight.

The minimum-variance portfolio and the efficient frontier Quantitative Methods

A tariff is a tax on imported goods. An import quota caps the quantity that may be imported, usually through import licenses.

Tariffs, quotas, export subsidies and their welfare effects Economics

The tax base is the amount the tax authority attributes to an asset or liability. The carrying amount is the figure in the balance sheet.

Accounting profit vs taxable income: temporary and permanent differences Financial Statement Analysis

The tax burden is the share of pretax profit the company keeps. The interest burden is the share of EBIT left after interest.

DuPont analysis: three-step and five-step ROE Financial Statement Analysis

Tax concerns depend on the investor's status. Some investors, such as many pension funds, are exempt.

IPS constraints: liquidity, time horizon, taxes, legal and unique circumstances Portfolio Construction

Tax credits (for example for research spending) reduce the tax bill itself, so they lower the effective rate. A consistently low effective rate relative to peers is not wrong in itself, but read the reconciliation in the next lesson to see whether it will last.

Effective, statutory and cash tax rates Financial Statement Analysis

A tax loss carryforward will shelter future profit, so it is an asset, but only if the company is likely to earn that profit.

Deferred tax assets and liabilities Financial Statement Analysis

A tax rate change forces a remeasurement. Deferred taxes are valued at the enacted rate expected when they reverse, so both DTLs and DTAs rescale.

Deferred tax assets and liabilities Financial Statement Analysis

Accounting profit (pretax income) is the profit before tax in the income statement. Taxable income is the income on the tax return under tax law.

Accounting profit vs taxable income: temporary and permanent differences Financial Statement Analysis

A taxable temporary difference will increase taxable income in future (more tax later), so it creates a deferred tax liability.

Accounting profit vs taxable income: temporary and permanent differences Financial Statement Analysis

Learn the interest received classification, the dividends received classification, the interest paid classification and the dividends paid classification as a set of four. The taxes paid classification is operating in almost every case.

Cash flow statements under IFRS vs US GAAP Financial Statement Analysis

Software to be sold: expensed until technological feasibility is established, capitalized afterwards.

Purchased, internally developed and acquired intangibles Financial Statement Analysis

Technological influences mean that technology creates products, transforms business models, improves existing products or makes them obsolete.

PESTLE and the innovation matrix Equities

A new product or process can make yesterday's winner obsolete quickly.

The forecast horizon, normalized earnings and long-term forecasts Financial Statement Analysis

In a tender offer, a bidder invites shareholders to sell their shares directly.

Corporate governance mechanisms Corporate Finance

The maturity is the date of the final payment. The tenor is the time remaining until it.

The features of a bond Fixed Income

Repos run from overnight to a term repo, any maturity longer than one day. A repo can name a specific security, or a group of eligible securities, such as government bonds of a given maturity.

Repurchase agreements (repos) Fixed Income

One more is time to maturity: the maturity structure of interest rates, also called the term structure of interest rates, describes how yields change as the time to maturity changes.

Spot rates and pricing a bond with the spot curve Fixed Income

Analysts often keep it between the expected inflation rate and nominal gross domestic product (GDP) growth of the markets where the company earns its money: this is the range for terminal growth between inflation and nominal GDP growth.

Discount rates and terminal values Equities

The terminal value is the expected value of the share (or of the equity or firm) at the end of the forecast horizon; it stands for every cash flow after that.

Discount rates and terminal values Equities

A going concern is no longer certain, and the multiples of healthy peers distort the value.

Model construction by company life cycle: from venture to decline Equities

Then collapse everything after that into one number at period $n$, the terminal value at the end of the fast stage, using the constant growth formula.

Two-stage (multistage) growth models Equities

The terminal value for a high-growth company comes from a multiple of final-year revenue or earnings, once the model shows the company reaching scale.

From the forecast model to an equity value Equities

The most common use of a projected multiple is the terminal value from a multiple in a present value model. Forecast cash flows for n years, then value everything after year n as the year-n figure times a multiple.

Trailing, current and forward multiples Equities

The multiple should come from the terminal value peer group: firms that look like the company at the end of the forecast.

Trailing, current and forward multiples Equities

How much it weighs depends on the horizon: the shorter the forecast horizon, the larger the share of value that sits in the terminal value. This is the link between terminal value share and forecast horizon.

Discount rates and terminal values Equities

The shorter the fast stage, the larger the share of value left in the terminal value: with 10 growing 8% a year, then 3%, at 9%, the terminal value is 85% of the value over three years, 77% over five and 62% over ten. This is the terminal value share of intrinsic value.

Two-stage (multistage) growth models Equities

A record built from the best account, or one that drops terminated accounts, shows only the survivors and overstates what a typical client received.

Standard III(D): Performance Presentation Ethical and Professional Standards

The test dataset (also called the testing dataset) judges how well the model predicts on data it has never seen.

AI and machine learning: supervised, unsupervised, reinforcement, deep Quantitative Methods

The test of a single mean compares one sample's mean with a hypothesized value, using the statistic from the four-step lesson: t = (X̄ − μ₀) ÷ (s ÷ √n), with n − 1 degrees of freedom.

t-tests of a mean, a difference in means and paired differences Quantitative Methods

The test of a single variance compares the sample variance with a hypothesized value. The sample-size rules for choosing t or Z do not apply to chi-square and F tests.

Chi-square and F-tests of variance Quantitative Methods

A test of independence asks whether the pattern of counts is what you would get if the two characteristics had nothing to do with each other.

Chi-square test of independence with a contingency table Quantitative Methods

Subtract within each pair, then run a one-sample t-test on the differences. This is the test of paired differences, or paired t-test (older texts call it the paired comparisons test).

t-tests of a mean, a difference in means and paired differences Quantitative Methods

Use the test of the difference in means when the two samples are unrelated and both populations are roughly normal with the same variance.

t-tests of a mean, a difference in means and paired differences Quantitative Methods

The test of the difference in variances divides one sample variance by the other.

Chi-square and F-tests of variance Quantitative Methods

The test of the intercept works the same way, with $t = (\hat{b}_0 - B_0) \div s_{\hat{b}_0}$ and $n-2$ degrees of freedom.

Goodness of fit and testing the regression coefficients Quantitative Methods

Unbiased forecasts mean an intercept of 0 and a slope of 1, so test each against its own hypothesized value. This is the test of unbiased forecasts.

Goodness of fit and testing the regression coefficients Quantitative Methods

The test statistic measures how far the sample result is from the hypothesized value, counted in standard errors.

How a hypothesis test works: four steps from claim to decision Quantitative Methods

The testing policies protect the integrity of the exam, so breaking them compromises it. The Handbook's examples include bringing written material into the computer-based test center, looking at other candidates' screens, disruptive conduct at the test center, and filing a fraudulent deferral request to postpone an exam date.

Standard VII(A): Conduct as Participants in CFA Institute Programs Ethical and Professional Standards

Tests against a known value compare a mean or variance with a target: "does the fund's mean return beat its 8% target?"

How a hypothesis test works: four steps from claim to decision Quantitative Methods

Tests comparing two unknown values compare two means or two variances: "is fund A more volatile than fund B?"

How a hypothesis test works: four steps from claim to decision Quantitative Methods

Tests of association ask whether a relationship exists: "do bond returns move with changes in the policy rate?"

How a hypothesis test works: four steps from claim to decision Quantitative Methods

Text analytics uses computer programs to analyze and derive meaning from large unstructured text or voice datasets: filings, reports, earnings calls, social media, email and surveys.

Data science: processing, visualization and text analytics Quantitative Methods

Invests in themes or assets tied to ESG factors.

ESG considerations in portfolio planning and construction Portfolio Construction

Yes, but evolves over time.

How geopolitical risk affects investments Economics

A theme index follows an investor trend that cuts across industries and sizes. Examples are companies selling mainly to domestic consumers, owners of long-lived infrastructure assets, companies screened for compliance with Islamic law, or companies screened on environmental, social and governance principles.

Types of equity indexes Equities

A leptokurtic distribution is fat-tailed (also called long-tailed). A platykurtic one is thin-tailed (short-tailed).

Skewness and kurtosis Quantitative Methods

Some securities did not exist for the whole window. Thinly traded securities have sparse or stale prices.

Historical simulation and historical value at risk Quantitative Methods

Third-party information. Once you incorporate it into your work, it becomes your responsibility.

Standard I(C): Misrepresentation Ethical and Professional Standards

Research from a broker, bank or research house is third-party research. In both cases you must make reasonable efforts to confirm it is sound before relying on it.

Standard V(A): Diligence and Reasonable Basis Ethical and Professional Standards

Outside the company, third-party sources are either public or proprietary.

IFRS vs US GAAP, new standards and other information sources Financial Statement Analysis

The threat of new entrants is how easily newcomers can compete away profits. Barriers to entry such as large capital needs, strong brands, regulation and scale keep the threat low.

Porter's five forces: how competition shapes prices and costs Financial Statement Analysis

The threat of substitutes is the risk that customers switch to a different kind of product that meets the same need.

Porter's five forces: how competition shapes prices and costs Financial Statement Analysis

So the analyst judges the strategy looking forward, with three tests of a competitive strategy: the Five Forces, the PESTLE (political, economic, social, technological, legal and environmental) influences, and the company's own resources.

Competitive strategy: cost leadership, differentiation and focus Equities

Price varies with volume purchased or feature level.

Pricing and revenue models Corporate Finance

For raw land, farmland and timberland it is the soil, the climate, the geology (for mineral and drilling rights) and the location.

Raw land, timberland and farmland as investments Alternative Investments

A timberland investment management organization (TIMO) is an entity with forestry expertise that analyzes and acquires timberland, then manages it for institutional investors.

Raw land, timberland and farmland as investments Alternative Investments

The time horizon is the period over which the investor is investing: the accumulation period before assets are withdrawn, or the period until the client's circumstances change.

IPS constraints: liquidity, time horizon, taxes, legal and unique circumstances Portfolio Construction

Six factors set an option's value: the value of the underlying, the exercise price, the time to expiration, the risk-free interest rate, the volatility of the underlying, and any income from the underlying or carrying costs of owning it.

Six factors that move an option's value Derivatives

Bond markets are cut along three standard dimensions: issuer type (often called the sector), credit quality and time to maturity.

Bond market segments, issuers and investors Fixed Income

Two ideas build it. The time to receipt is how many years away each payment is.

Macaulay duration: definition and calculation Fixed Income

With time tranching, one pool is cut into bond classes with different expected maturities. In a sequential-pay structure, all principal from the pool, scheduled and prepaid, goes first to Tranche A until it is retired, then to Tranche B, then to Tranche C.

Prepayment risk and time tranching Fixed Income

The time value is everything else the buyer pays for: the chance that the option ends up worth more than that.

Exercise value, moneyness and time value Derivatives

It is never negative, because the holder can always walk away and lose nothing more than the premium. It shrinks as expiry nears, a process called time value decay, and is zero at expiration.

Exercise value, moneyness and time value Derivatives

A time-based split uses earlier data to train and later data to validate and test.

AI and machine learning: supervised, unsupervised, reinforcement, deep Quantitative Methods

Time-series data follow one entity over many periods (indexed by $t$). Panel data follow the same entities over many periods.

The regression line: slope, intercept and least squares Quantitative Methods

The result is the time-weighted rate of return.

Money-weighted vs time-weighted rate of return Quantitative Methods

Asset spending is less closely tied to revenue, and there is a timing mismatch: assets are bought before the revenue they produce.

Asset and financing models Equities

The timing of cash flows is therefore part of the manager's skill, and IRR is the yardstick that rewards or penalizes it.

IRR and multiple of invested capital (MOIC) Alternative Investments

A timing option gives up near-term returns in the hope of better information; investments can also be sequenced so that one project creates the option for the next.

Real options Corporate Finance

Tokenization is representing ownership rights to a physical asset (property, luxury goods, commodities) on a ledger.

Distributed ledgers and blockchain: how digital assets are recorded Alternative Investments

A too-strict answer goes beyond what the Standards ask: "never accept any gift", "report the colleague to CFA Institute", "resign immediately", "remove your name from every group report".

How to answer Ethics vignettes: a five-step method Ethical and Professional Standards

Top-down (macroeconomic and market) limitations hit the inputs to the cost of capital in the denominator (the weighted average cost of capital, WACC, and the required return on equity, $r_e$), which move with the economy.

Where DCF and growth models break down Equities

The forecast itself can follow a top-down analysis, which starts with a macroeconomic outlook, the company's growth relative to gross domestic product (GDP), its addressable market and market share, or a bottom-up analysis, which starts with its own revenue drivers and balance sheet.

Assessing corporate creditworthiness Fixed Income

Behind the drivers sits a choice between top-down and bottom-up forecasting. A top-down forecast starts at the economy: nominal gross domestic product (GDP) growth (real growth plus inflation), then the industry's growth relative to GDP, then the company's share of the industry.

Building a sales-based pro forma income statement Financial Statement Analysis

An estimate of total revenue across the whole industry over a period, usually published by a government statistics agency or a reputable data provider (retail sales statistics are a common example).

Industry size, growth, profitability and concentration Equities

A top-down revenue model first forecasts the overall market, often as units times price per unit. For a mature industry, that means demand within a macroeconomic forecast.

Revenue models: historical, bottom-up and top-down Equities

A growth industry grows faster than the economy and is usually not sensitive to the cycle, because it has not yet reached full penetration of its total addressable market, the revenue it could earn if every potential customer bought.

Industry size, growth, profitability and concentration Equities

The largest possible market for the good or service.

Company life cycle and the addressable market Equities

Fixed asset turnover uses average net property, plant and equipment, and total asset turnover uses average total assets.

Activity ratios: turnover, days and the cash conversion cycle Financial Statement Analysis

A premium may be justified by savings elsewhere, such as a lower total cost of ownership, the total direct and indirect cost of owning an asset over its life.

Business model features Corporate Finance

The debt-to-equity ratio, long-term debt-to-equity, the total debt ratio and the financial leverage ratio all rise as the company borrows more.

Common-size balance sheets, liquidity and solvency ratios Financial Statement Analysis

Total debt to total assets shows how much of the asset base debt funds; EBITDA to interest expense shows how many times earnings before interest, taxes, depreciation, and amortization (EBITDA) cover the interest bill.

Capital investments and capital structure Equities

The answer is the total equity value, to set beside market capitalization.

From the forecast model to an equity value Equities

Technological influences mean that technology creates products, transforms business models, improves existing products or makes them obsolete. It is a key driver of total factor productivity, so analysts ask when and how it will change competition in an industry.

PESTLE and the innovation matrix Equities

Total portfolio context means you judge an investment by its place in the whole portfolio: its effect on diversification, its risk against the client's tolerance, and its fit with the required strategy.

Standard III(C): Suitability Ethical and Professional Standards

P(B) comes from the total probability rule: add up every route that can produce the information.

Bayes' theorem: updating a probability with new information Quantitative Methods

Weight each conditional expected value by the probability of its scenario and add. This is the total probability rule for expected value, and the result is the unconditional expected value, the overall forecast before you know which scenario happens.

Probability trees, conditional expectations and conditional variance Quantitative Methods

The total return is the return before any costs.

Gross, net, after-tax, real and leveraged returns Quantitative Methods

The total return index tracks price changes plus the income the constituents pay (dividends for shares, interest for bonds), treated as reinvested.

Index value, price return and total return Quantitative Methods

An asset's total risk is the variance of its returns. It has two parts, and only one of them is rewarded.

Systematic vs nonsystematic risk and return-generating models Portfolio Construction

Total working capital is a broad figure: all current assets minus all current liabilities.

The cash conversion cycle Corporate Finance

A relative risk objective is measured against a benchmark: "do not trail the index by more than 4% in any year", or a limit on tracking error, the standard deviation of the difference between portfolio and benchmark returns.

Risk and return objectives: willingness vs ability to take risk Portfolio Construction

A country that imports more than it exports (a trade balance deficit) must pay for the difference by borrowing from foreigners or selling assets to them.

Exchange rate regimes and their effects on trade and capital flows Economics

Trade creation happens when cheaper imports from a member replace costlier home production.

Trading blocs: free trade areas, customs unions, common markets and economic unions Economics

Trade credit is the time a supplier lets a customer wait before paying. Suppliers often add a prompt-payment discount for paying early.

Cost of trade credit Corporate Finance

Trade diversion happens when imports switch from a cheaper non-member to a costlier member, because only the non-member still pays the tariff.

Trading blocs: free trade areas, customs unions, common markets and economic unions Economics

In a trade sale the company, or a division of it, is sold by direct negotiation or auction to a strategic buyer: a business that wants more scale and scope in the same line of work.

How private equity exits: trade sale, IPO, SPAC and more Alternative Investments

The buyer then pays the full price: the present value of the remaining cash flows on the trade settlement date, which is the day the buyer pays and the seller delivers.

Accrued interest, flat price and full price Fixed Income

Use trading days, not calendar days: about 22 in a month and 252 in a year (some sources use 250). Five trading days make a week; 12 months a year; 52 weeks a year.

Scaling volatility over time: data frequency and the root-of-time law Quantitative Methods

Trading securities are debt securities bought to be sold, measured at fair value with changes in profit. IFRS calls the broader group fair value through profit or loss (FVPL): everything not in the other two categories, plus anything the company irrevocably elects there.

Financial instruments: amortized cost, FVOCI and FVPL Financial Statement Analysis

Traditional asset managers run long-only equity, fixed income and multi-asset strategies and earn most of their revenue from asset-based fees.

The asset management industry Portfolio Construction

The ratio comes in two versions, trailing and forward P/E. Trailing uses EPS for the past year and forward uses next year's forecast.

Equity valuation models: present value, asset-based and relative Equities

The trailing dividend yield is the dividend rate divided by the current price, $Div_t \div P_t$. The leading dividend yield is the forecast dividends per share for the next year divided by the current price, $Div_{t+1} \div P_t$.

Price multiples: P/E, earnings yield, P/S, P/B and dividend yield Equities

A trailing multiple uses the prior 12 months of the denominator. A forward multiple uses the next 12 months. Lesson 5 goes into the time bases.

Valuing with multiples: comparables and forecasted fundamentals Equities

EPS is net income divided by the weighted average shares outstanding during the period. The trailing P/E uses the last four quarters of EPS, $EPS_t$.

Price multiples: P/E, earnings yield, P/S, P/B and dividend yield Equities

The trailing price-to-earnings ratio divides the price by the last year's earnings, E₀, instead. In the same model it is a little higher than the forward multiple, because E₀ is smaller than E₁.

Implied return and implied growth Quantitative Methods

The training dataset is where the model learns input–output relationships.

AI and machine learning: supervised, unsupervised, reinforcement, deep Quantitative Methods

The securities usually come in classes. Each tranche is a bond class with its own claim on the pool's cash.

Why securitize? Benefits for issuers, investors and markets Fixed Income

The pool is sliced into classes called tranches, with the senior tranche paid first. Securitization modules cover them in detail.

Bond indentures and covenants Fixed Income

Subtract transaction costs (trading costs, commissions and similar direct fees) and you have the gross return.

Gross, net, after-tax, real and leveraged returns Quantitative Methods

Determine the transaction price, including variable consideration such as bonuses or rebates only to the extent a significant reversal is unlikely.

Revenue recognition: the five-step model Financial Statement Analysis

Transaction validation for traditional assets happens in private ledgers kept by central intermediaries. Digital asset ownership and exchange are recorded on a decentralized ledger using cryptography.

How digital assets differ from stocks, bonds and currencies Alternative Investments

Transaction-based manipulation covers trading where you knew, or should have known, that your actions could distort the price of a security.

Standard II(B): Market Manipulation Ethical and Professional Standards

Adaptation. Fine-tuning or transfer learning then adapts the trained model to a specific task, such as summarizing credit reports.

Large language models and generative AI in finance Quantitative Methods

Transfer payments are welfare payments through the social security system: state pensions, housing and child benefits, tax credits, income support and unemployment benefits.

Fiscal policy tools and the fiscal multiplier Economics

No base-year cash flow and growth rate could describe what it was turning into. That is transformational growth.

Where DCF and growth models break down Equities

It is built on a transformer, a network design that handles long-range dependencies: how words far apart in a text relate to each other, which is what gives text its context and meaning. The model picks out the most relevant parts of an instruction or document and, drawing on what it learned, produces whole sentences and longer passages…

Large language models and generative AI in finance Quantitative Methods

Transition risks are losses from the move to a lower-carbon economy, through regulation, technology or shifting demand.

ESG factors investors consider Corporate Finance

Suppose home-workout apps spread: gym operators lose members, and makers of commercial gym equipment see orders fall. This kind of shift is a transitory risk factor when companies can adapt to it, for example an equipment maker that starts selling connected machines for the home.

Equity research reports: contents, ratings and price targets Equities

Transparency builds credibility. Many central banks publish regular inflation reports covering, usually in this order, money and credit, financial markets, the real economy (such as the labor market) and prices, followed by a growth and inflation forecast about two years ahead.

Inflation targeting vs exchange rate targeting Economics

Roads, bridges, tunnels, airports, seaports and railways. Income usually follows demand (traffic, port and airport charges, tolls, fares), so it carries market risk.

Infrastructure: economic vs social, greenfield vs brownfield Alternative Investments

For travel funding, pay for commercial transport and a hotel yourself. Issuers should not reimburse air travel.

Standard I(B): Independence and Objectivity Ethical and Professional Standards

Treasury bills mature in 1 to 12 months, usually pay no coupon and are sold at a discount to par. Treasury notes and bonds are medium- and long-term.

Sovereign debt: who borrows, in what currency, for how long Fixed Income

A capital-indexed bond scales the principal by the index, and the coupon is the fixed real rate times the adjusted principal.

Floating, step-up, inflation-linked and zero-coupon bonds Fixed Income

Treasury bills mature in 1 to 12 months, usually pay no coupon and are sold at a discount to par. Treasury notes and bonds are medium- and long-term.

Sovereign debt: who borrows, in what currency, for how long Fixed Income

The treasury stock method handles options and warrants. Assume they are exercised, then assume the exercise cash is used to repurchase shares at the average market price.

Diluted EPS: if-converted and treasury stock methods Financial Statement Analysis

Trend analysis asks whether ratios and common-size lines are improving or deteriorating, and is most useful when the business and its environment are stable.

Analysis tools: common-size, trend, cross-sectional and the limits of ratios Financial Statement Analysis

The Treynor ratio is the same idea with beta as the risk: excess return per unit of systematic risk.

Sharpe ratio, Treynor ratio, M² and Jensen's alpha Portfolio Construction

If they do not, there is a riskless profit called triangular arbitrage ("triangular" because it uses three currencies).

Currency cross-rates and triangular arbitrage Economics

The trimmed mean drops a set number (or percentage) of the lowest and highest observations, then averages what remains. n falls.

Mean, median, mode and what outliers do to them Quantitative Methods

In a triparty repo, a custodian or clearinghouse values and holds the collateral and administers cash and securities.

Repurchase agreements (repos) Fixed Income

In a true sale, all the seller's rights in the loans pass irrevocably and in full to the SPE under the law of the jurisdiction.

The special purpose entity and bankruptcy remoteness Fixed Income

True yield uses the actual payment dates. A payment pushed to Monday arrives later, so the present value falls and the yield with it.

Current yield, simple yield and yield conventions Fixed Income

Trust is a strong belief in the reliability of a person or institution. To earn it, a profession combines several features.

How professions build trust, and professionalism in investment management Ethical and Professional Standards

The trustee, usually a bank with no stake in the deal, looks after investors' interests. Once the pool is sold, it guards the assets, keeps the cash owed to noteholders until payment day, and sends the regular reports the prospectus promises.

The securitization process and its parties Fixed Income

More turnover comes from two sources: every bond has a finite life, and issuers keep selling new bonds. Bonds that fall under the minimum maturity, rating or size are removed at each rebalancing, and new issues are added.

Bond indexes and how they differ from equity indexes Fixed Income

The turnover ratio is ADV divided by market float: the share of the freely tradable shares that changes hands on a typical day.

Liquidity: market float, average daily volume and turnover Equities

Because the choice of risky portfolio does not use anyone's preferences, every investor who shares the same expectations picks the same one. This is the two-fund separation theorem: all investors hold a combination of two funds, the risk-free asset and the optimal risky portfolio.

The capital allocation line and the optimal portfolio Portfolio Construction

If the two population variances cannot be assumed equal, a two-sample t-test with unequal variances is used instead.

t-tests of a mean, a difference in means and paired differences Quantitative Methods

In a two-sided network, there are two types of user, such as buyers and sellers in an online marketplace. A multi-sided platform has two or more.

Network effects and platform business models Corporate Finance

The simplest case is the two-stage growth model. It gives the company two growth rates: a short-term growth rate g_s for a finite number of periods $n$, and a long-term growth rate g_l forever after.

Two-stage (multistage) growth models Equities

A two-tailed test asks whether the parameter is different from the hypothesized value in either direction, so the rejection region is split between both tails.

How a hypothesis test works: four steps from claim to decision Quantitative Methods

A Type I error is rejecting a true null hypothesis: a false positive, or false alarm. Its probability is the significance level, α.

Type I and Type II errors and the power of a test Quantitative Methods

A Type II error is failing to reject a false null hypothesis: a false negative, or missed signal.

Type I and Type II errors and the power of a test Quantitative Methods