CFA Level I terms: R

Priority over common shares shows up as a lower discount rate, the required return on preferred stock r_p, and r_p below r_e.

Valuing preferred stock, and how call, put and conversion features change value Equities

Noise. There are two gauges. R-squared (R²) is the share of the stock's variation explained by the market (in a one-factor regression the correlation is √R²).

Estimating the cost of equity with the CAPM and the market model Equities

The R-squared of a CAPM regression is the share of the variance of the asset's excess returns explained by the market's: the systematic share.

Estimating beta with a CAPM regression Quantitative Methods

The collateral manager builds the pool: most of the loans are bought before closing, and the rest during the ramp-up period after it.

Collateralized debt obligations and CLOs Fixed Income

Computers produce the draws by random number generation: a program produces draws that behave as random. A uniform draw is turned into a standard normal with the inverse normal function, NORM.INV(RAND(), 0, 1) in a spreadsheet.

Monte Carlo simulation Quantitative Methods

A random variable is a rule that gives every outcome of an uncertain event a number. In finance it is often called a stochastic variable.

Random variables and distribution functions Quantitative Methods

The range is the largest value minus the smallest. It is quick, but it ignores every observation in between.

Range, mean absolute deviation, variance and standard deviation Quantitative Methods

The simplest measure of how much returns vary is the range of annual returns: the best year minus the worst year.

Macro and micro risk and the risk-return trade-off Quantitative Methods

It is the correlation of the rank positions of two variables rather than of their values. If the highest value of X always goes with the highest value of Y, the ranks agree perfectly and the coefficient is +1.

Spearman rank correlation: the non-parametric test Quantitative Methods

If the rank is not a whole number, either take the nearer neighbor or use rank and linear interpolation: take a weighted mix of the two neighboring losses, with weights that follow the fractional part of the rank.

Historical simulation and historical value at risk Quantitative Methods

Rank ordering each criterion, with weights, is an alternative that keeps near misses in view.

Sell-side, buy-side and activist short-seller research Equities

Many non-parametric tests work on ranks (the order of the observations) rather than on the raw numbers. Ranks suit ordinal data, which carry order but not size, such as credit grades.

Parametric vs non-parametric tests Quantitative Methods

A rapid amortization provision protects investors. If defaults rise or the pool cannot be replenished with good receivables, the revolving period ends early and principal is returned to investors straight away.

Credit card, auto loan and solar ABS Fixed Income

The underwriter structures and sells the securities. Rating agencies rate each tranche.

The securitization process and its parties Fixed Income

An agency can also publish a rating outlook, positive or negative, when creditworthiness is improving or worsening but a rating change is not yet warranted.

Credit ratings: uses and limitations Fixed Income

Analysts first scale the numbers, then compare them. Ratio analysis relates one figure to another.

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

A way for the decision maker to justify the act to themselves, such as "the business will grow into it" or "it reverses next quarter".

Why managers misreport, and what stops them Financial Statement Analysis

A regression beta is called the raw beta. The adjusted beta is a weighted average of the raw beta and 1.0.

Estimating the cost of equity with the CAPM and the market model Equities

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 manufacturer holds raw materials, work in progress and finished goods, and the mix moves with the flow of production and sales.

Inventory disclosures, turnover and days of inventory Financial Statement Analysis

Razor-razorblade pricing combines a low price on the initial equipment with high-margin prices on the repeat-purchase consumables it needs.

Pricing and revenue models Corporate Finance

RCF to net debt divides one by the other. Unlike debt to EBITDA, a higher figure means lower leverage.

Financial ratios in credit analysis Fixed Income

Reading an assumption table means turning growth rates into two directions.

From the forecast model to an equity value Equities

Real assets are mostly tangible physical assets that produce cash flows now or later, or serve as a store of value.

What makes an investment alternative: features and categories Alternative Investments

Real earnings management changes what the business does. Examples: cutting research or advertising spending, postponing maintenance, or giving year-end discounts to pull sales forward.

Reporting quality vs earnings quality, and the quality spectrum Financial Statement Analysis

Real estate is borrowed or ownership capital in land or buildings, commercial or residential. real estate investment trusts (REITs) are the listed way in.

What makes an investment alternative: features and categories Alternative Investments

A real estate investment trust (REIT) is a tax-advantaged trust that owns, operates and sometimes develops income-producing property, or finances it.

Real estate: features and ways to invest (direct, REITs, funds) Alternative Investments

The real exchange rate corrects for that by adjusting for price levels in both countries. It tells you how much foreign goods cost compared with home goods.

Nominal vs real exchange rates Economics

Real GDP growth volatility, measured by the standard deviation of annual growth, makes revenue harder to predict, so more volatility is weaker.

Sovereign credit analysis: the key ratios Fixed Income

If real GDP grows faster than the real interest rate on the debt, tax revenue grows faster than the interest bill and the ratio can fall.

Does the size of national debt matter? Economics

Invest abroad with little leverage.

The foreign exchange market and who trades in it Economics

A real option is a choice built into a business project: the right, but not the obligation, to delay, abandon, expand or shrink it.

Forward exchange rates and option values by no arbitrage Quantitative Methods

The real return is the return after removing inflation. Use it to compare across countries and periods with different inflation.

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

Short-term government bills, for example a 30-day Treasury bill, stand in for it. It is made of the real risk-free rate, the reward for delaying real consumption (time preference), and the inflation rate, the expected loss of purchasing power.

Required return: risk-free rate, inflation and risk premia Quantitative Methods

That is arbitrage-free pricing. It does not need to know investors' risk aversion (how much they dislike risk) or the real-world probability of an up move.

Risk neutrality: why real-world probabilities do not matter Derivatives

Realizability is the test: under International Financial Reporting Standards (IFRS) recognition needs future taxable profit to be probable, and under US generally accepted accounting principles (US GAAP) the asset is recognized if realization is more likely than not (above 50%).

Deferred tax assets and liabilities Financial Statement Analysis

Realized and unrealized returns differ in whether you sold. An unrealized return (a "paper gain") is the change in value of an investment you still hold.

Holding period return Quantitative Methods

The total return adds the dividend received. Here $r_E$ is the realized rate of return.

Price return, total return and the price of a share Equities

The realized value is cash already received from exits and distributions. The unrealized value is the estimated worth of what is still held.

IRR and multiple of invested capital (MOIC) Alternative Investments

So the opinion gives reasonable assurance: the statements are very probably free of material misstatement, but nobody promises they are exact.

Regulatory filings, notes, MD&A and the audit report Financial Statement Analysis

A reasonable basis means he understands the model, has tested it and can support the recommendation. Communication with clients means telling clients, promptly, about material changes in the process, as well as the costs and risks.

Cases on duties to employers and investment analysis Ethical and Professional Standards

You must make reasonable efforts to ensure that everyone under your supervision or authority complies with applicable laws, rules, regulations, firm policies and the Code and Standards.

Standard IV(C): Responsibilities of Supervisors Ethical and Professional Standards

Managers give five reasons for share repurchases.

Dividends, share repurchases, stock splits and the dividend timetable Equities

Rebalancing means adjusting the weights of the securities already in the index so that they match the weighting rule.

Rebalancing, reconstitution and what indexes are used for Quantitative Methods

Rebalancing back to target costs trading, so a common recommendation is a systematic, pre-defined rebalancing frequency (for example once a year), which keeps the portfolio aligned with its strategy and risk without trading on every move.

Portfolio returns over time: buy-and-hold, drift and rebalancing Quantitative Methods

Many investors write down a strategic asset allocation, also called the policy portfolio: the baseline allocation of assets to asset classes, given the client's objectives. It is normally an appendix, alongside the rebalancing policy that says when and how the weights are brought back to target.

The investment policy statement (IPS) Portfolio Construction

A recapitalization adds or increases debt in the portfolio company and pays the fund a dividend from the new capital structure.

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

Receivables turnover and days of sales outstanding (DSO) do the same for customer credit.

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

If rates fall, the value of a receive-fixed swap as a long bond rises. If the curve slopes upward and rates follow their forwards, a par fixed-rate bond drifts to a discount as time passes, which is the receiver's loss in the example above.

Swap value after inception: time and rate changes Derivatives

Availability, or the recency effect. The recency effect is the tendency to recall recent events more vividly and give them undue weight.

How biases show up in markets: momentum, bubbles and value Portfolio Construction

The recognition criteria then add two tests: the benefits are probable, and the cost can be measured reliably.

Purchased, internally developed and acquired intangibles Financial Statement Analysis

Time to see that the economy has changed (data arrive late and are revised)

Fiscal stance, structural deficits and policy lags Economics

a reconciliation from the non-GAAP measure to the GAAP one, which is the reconciliation requirement;.

Non-GAAP measures and other presentation choices Financial Statement Analysis

Reconstitution changes the securities in the index. On the reconstitution date the provider re-applies the selection rules: it adds new securities that qualify and removes those that no longer do, because they became too small, merged, delisted or changed style.

Rebalancing, reconstitution and what indexes are used for Quantitative Methods

The record date is the day on which shareholders registered with the securities depositary are treated as the owners entitled to the dividend.

Dividends, share repurchases, stock splits and the dividend timetable Equities

You must develop and maintain appropriate records (record retention) to support your investment analyses, recommendations, actions and other investment-related communications with clients and prospects.

Standard V(C): Record Retention Ethical and Professional Standards

Records are the property of the firm. Records you create as part of your work for your employer belong to the employer.

Standard V(C): Record Retention Ethical and Professional Standards

In a recourse loan, the lender can claim the shortfall from the borrower. In a non-recourse loan, the lender can look only to the property.

Residential mortgage loans: the features that matter Fixed Income

Step 1 is the recoverability test: is the carrying amount more than the undiscounted cash flows the asset is expected to produce?

Impairment and derecognition of PP&E and intangibles Financial Statement Analysis

In one step: compare the carrying amount with the recoverable amount, the higher of two values. Fair value less costs to sell is what a sale would net.

Impairment and derecognition of PP&E and intangibles Financial Statement Analysis

Negative, starting to narrow (trough)

The business cycle and its four phases Economics

The recovery rate is the share of a claim that comes back in default. It rises with seniority because the priority of claims decides who is repaid before the money runs out.

Seniority, recovery rates and notching Fixed Income

The second input is how much of that claim comes back. The recovery rate (RR) is the percentage of the claim recovered.

Credit risk: probability of default and loss given default Fixed Income

Bottom-up evidence differs by industry and depends on the mix of recurring and episodic revenue. Some companies grow by selling more to the same customers; others need new products, new channels or new customers.

Revenue drivers and pricing power Equities

A redemption fee discourages withdrawals and offsets transaction costs for the investors who remain. A gate lets the manager limit or suspend redemptions for a time, at the manager's discretion.

Leverage, redemptions, lockups and gates Alternative Investments

A floating-rate bond resets its coupon each period to a reference rate (a short-term market rate, such as a 3-month interbank rate) plus a fixed margin that reflects the issuer's risk.

Pricing bonds: zero-coupon, coupon and perpetual Quantitative Methods

A reference to the CFA designation must be accurate and must not suggest a partial designation. Candidacy rests on enrollment: a person is a candidate while enrolled to sit a specified exam, or while awaiting the results of one already sat.

Cases on conflicts of interest and CFA responsibilities Ethical and Professional Standards

Any compensation, consideration or benefit you receive from, or pay to, others for recommending a product or service. These referral fees can be cash, soft dollars or benefits in kind, and the Standard works in both directions: you must also disclose what you pay to someone who sends you clients.

Standard VI(C): Referral Fees Ethical and Professional Standards

Two names to know: the refinancing rate is how some central banks label their policy rate (the Bank of England uses the two-week repo rate), and the federal funds rate is the US interbank rate on overnight lending of reserves, which the Federal Open Market Committee steers to a target by adding or draining reserves.

Monetary policy tools and the transmission mechanism Economics

The Refinitiv Business Classification (TRBC), from Refinitiv.

Industry classification: GICS, ICB, TRBC and other groupings Equities

The same signal appears when two regime periods are pooled: the residuals are small in the early years and large in the later years because the relationship changed.

The four regression assumptions and what residual plots reveal Quantitative Methods

A regional trading bloc is a group of countries that agree to lower and gradually remove barriers to trade, and sometimes to the movement of labor and capital, among themselves.

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

Regionalism sits between bilateral and multilateral: cooperation within a bloc, which may exclude outsiders.

Geopolitical risk and the four country archetypes Economics

Today Eurobonds, domestic bonds and foreign bonds are all registered bonds, with ownership recorded by name or serial number.

Domestic, foreign and Eurobonds, and how bonds are taxed Fixed Income

Down the chain. The materials travel from the company through the securities depository and the custodian to a shareholder voting service and on to the beneficial owner.

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

Duplicate or diversify supply chains across several countries.

Globalization vs nationalism: gains, costs and rollback Economics

Regression analysis fits a line between a variable and its drivers, for example a retailer's sales against consumer spending.

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

The regression approach estimates the multiple statistically after controlling for one or more company characteristics, for example with a multiple regression across the peer group.

Valuing with multiples: comparables and forecasted fundamentals Equities

The regression coefficients are the intercept, $b_0$, and the slope coefficient, $b_1$. The error term, $\varepsilon_i$, is everything about $Y_i$ that the line does not capture.

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

A regression of asset growth on revenue growth works like the expense regression of the last lesson. "Grow with revenue" means a = 0 and b = 1.

Asset and financing models Equities

Growing an expense at its own past rate ignores its link to revenue. A regression of expense changes on revenue changes uses that link.

Expense models: margins, itemization and operating leverage Equities

Regret-aversion bias is avoiding decisions out of fear they will turn out poorly. It has two sides: errors of commission (actions that were taken and went wrong) and errors of omission (actions that could have been taken but were not).

Emotional biases: loss aversion, overconfidence and four more Portfolio Construction

A regular cash dividend is paid at known intervals: quarterly in the United States and Canada, usually semiannually in Europe and Japan, and usually annually in Scandinavia, China and elsewhere.

Dividends, share repurchases, stock splits and the dividend timetable Equities

Regulated infrastructure (utilities whose prices a regulator sets) and basic social infrastructure usually have lower risk and lower expected return.

Infrastructure risk, return and diversification Alternative Investments

A new law, license regime or price cap can change a business's economics almost overnight. It is a turning point only when it breaks with what the company has long lived with; rules that keep moving at their usual pace are already in the trend.

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

Regulation of AI in finance is evolving quickly, driven by data privacy, the need for algorithms to be transparent and the risk that automated decisions spread problems through the system.

Large language models and generative AI in finance Quantitative Methods

Regulatory compliance projects are imposed by a third party (a law, a regulator) and are needed to avoid fines or to keep operating.

Types of capital investments Corporate Finance

Securities regulators require registration, periodic disclosure, an audit opinion and a management report, ask responsible individuals to certify the filings (with legal penalties for false certifications in the United States), review filings and enforce rules with fines, bans and prosecutions.

Why managers misreport, and what stops them Financial Statement Analysis

Weak compliance or poor reporting exposes a company to legal risk (lawsuits from shareholders, employees, creditors or others for breach of contract, bylaws or rights) and regulatory risk (investigations and penalties for breaking the law).

Corporate governance risks and benefits Corporate Finance

The legal protection of holders is unclear, rules are still evolving, and some countries have banned trading or ownership outright.

Digital assets: risk, return and diversification Alternative Investments

In reinforcement learning a program learns by trial and error, acting in an environment and receiving rewards and penalties.

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

A dividend received during the period can buy more shares at the price on the dividend payment date, written $P_{PD}$. These are reinvested dividends.

Price return, total return and the price of a share Equities

When you are reinvesting at the risk-free rate, you grow the dividend to its value at the end of the period and put that value in the ordinary total-return formula.

Price return, total return and the price of a share Equities

The yield to maturity is the return you earn only under the reinvestment assumption: you hold to maturity, nothing defaults and every coupon is reinvested at the yield itself.

Implied return and implied growth Quantitative Methods

You reinvest each coupon you receive, which earns reinvestment income: the interest on interest that makes a bond's realized return differ from its coupon rate.

The sources of return from a fixed-rate bond Fixed Income

When the price falls, rates tend to be low, so the losses are financed cheaply. This reinvestment of daily gains works in the long's favor, so the long prefers the futures contract and is willing to pay more for it.

Why forward and futures prices differ Derivatives

The reinvestment rate is the share of after-tax EBIT put back into depreciation-replacing and new capital spending and working capital.

Enterprise value multiples Equities

The reinvestment ratio asks whether operations alone paid for this year's long-term asset purchases. The debt payment ratio does the same for long-term debt repayments, and the dividend payment ratio for dividends.

Cash flow performance and coverage ratios Financial Statement Analysis

Reinvestment risk is the chance that cash returned early must be reinvested at lower rates than the bond pays.

Bullet, amortizing and sinking fund bonds Fixed Income

Founders or managers dealing with the company in ways that benefit themselves, such as buying unsellable inventory into another entity they own.

Warning signs of earnings manipulation Financial Statement Analysis

The coefficient of variation (CV) fixes this by expressing the standard deviation relative to the mean. It is a measure of relative dispersion.

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

Relative market share can matter more than absolute share: a firm with 12% of a market is the leader if the rest is split among many small rivals, but a follower if it is the third of four.

Revenue drivers and pricing power Equities

This ratio form says how much more one unit invested in A grows than one unit invested in B over a period. The result is the relative outperformance of A over B.

Long-run asset class returns and their components Quantitative Methods

A higher real rate (d/f) means foreign goods cost more in real terms. The home resident's relative purchasing power abroad is then lower.

Nominal vs real exchange rates Economics

A relative rating compares it with a benchmark: an index, an industry or regional benchmark, or the other companies the analyst covers.

Equity research reports: contents, ratings and price targets Equities

Investors who care about risk-adjusted returns with low correlation to common asset classes track alternatives through relative returns, a fund's performance compared with that of similar investments.

Fund of funds fees, survivorship bias and backfill bias Alternative Investments

Relative risk aversion is the share of wealth the investor is prepared to put at risk.

Risk preferences, mean–variance utility and indifference curves Quantitative Methods

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

Relative valuation uses indicators such as the price-to-earnings (P/E) ratio or the price-to-book (P/B) ratio, compared with a relevant peer group.

Market price, intrinsic value and perceived value Equities

Information is decision-useful when it has two fundamental characteristics. It has relevance, meaning it can affect a decision (omitting or misstating it would matter, which is the idea of materiality).

Reporting quality vs earnings quality, and the quality spectrum Financial Statement Analysis

Strip the comparables' leverage out to get the unlevered beta, which holds business risk only. Then put the company's own leverage back to get its relevered beta.

Industry betas, the market risk premium and country risk Equities

Remeasurements go to OCI and are never recycled to profit. They are the actuarial gains and losses (changes in assumptions such as turnover, mortality, retirement age and salary growth) and the difference between the plan assets' actual return and the part already in net interest.

Defined contribution vs defined benefit pension plans Financial Statement Analysis

Less often it increases an existing bond, which is a reopening, at a price that may be far from par.

Primary and secondary bond markets vs equity markets Fixed Income

Taking profits, interest or capital back home is repatriation, and limits on it are one common control.

Capital restrictions: why governments limit capital flows Economics

There, market is built from replacement cost, the amount it would cost to buy or make the same goods now, and a normal profit margin.

Lower of cost and net realizable value (and write-down reversals) Financial Statement Analysis

Read the same result another way: 0.2778 shares, partly paid for by borrowing 17.09 against the sure payoff, behave exactly like the call. That mix is a replicating portfolio: a portfolio with the same value and payoffs as the option.

Forward exchange rates and option values by no arbitrage Quantitative Methods

Replication means recreating a position's cash flows from other assets. For a forward, the building blocks are the underlying asset and a loan at the risk-free rate.

Replication and the no-arbitrage forward price Derivatives

The difference between what the borrower gets now and what it pays back is interest, quoted as the repo rate.

Repurchase agreements (repos) Fixed Income

The report presentation itself should keep a record of the research behind it and be ready to supply the omitted factors on request.

Standard V(B): Communication with Clients and Prospective Clients Ethical and Professional Standards

A segment becomes a reportable segment when it passes a size test, and the coverage test makes sure the reported segments explain most of the business.

Regulatory filings, notes, MD&A and the audit report Financial Statement Analysis

In the purchase agreement the seller makes representations and warranties about the loans it sells, such as their quality and eligibility.

The special purpose entity and bankruptcy remoteness Fixed Income

An index fund cannot practically buy every one of 10,000 or more bonds, many of which rarely trade. It uses representative sampling: a smaller set of bonds chosen to match the index's duration, credit mix and sector weights.

Bond indexes and how they differ from equity indexes Fixed Income

Representativeness bias is classifying new information by its resemblance to something familiar, and missing that it may differ.

Behavioral biases in analyst forecasts and how to fix them Financial Statement Analysis

A repurchase agreement (repo) is the sale of a security with a simultaneous agreement by the seller to buy the same (or a similar) security back from the buyer on a future repurchase date, at an agreed repurchase price.

Repurchase agreements (repos) Fixed Income

A repurchase agreement (repo) is the sale of a security with a simultaneous agreement by the seller to buy the same (or a similar) security back from the buyer on a future repurchase date, at an agreed repurchase price.

Repurchase agreements (repos) Fixed Income

A repurchase agreement (repo) is the sale of a security with a simultaneous agreement by the seller to buy the same (or a similar) security back from the buyer on a future repurchase date, at an agreed repurchase price.

Repurchase agreements (repos) Fixed Income

Reputational risk follows from unmanaged conflicts or governance failures, and the costs can be large, especially for listed companies that investors, analysts and the market watch closely.

Corporate governance risks and benefits Corporate Finance

The spread they want is the required margin, also called the discount margin (DM). The quoted margin is fixed at issue, so when the two drift apart the price leaves par.

Floating-rate notes: quoted margin and discount margin Fixed Income

The required rate of return is the minimum return an investor must expect to receive to accept an investment. Delaying consumption has an opportunity cost: the value of the best alternative you give up when you choose one course of action.

Required return: risk-free rate, inflation and risk premia Quantitative Methods

The required return is the return investors demand for holding the share.

Implied return and implied growth Quantitative Methods

Today's price should equal the present value (PV) of what you expect to receive: the dividends during the holding period and the price at the end, discounted at the required return on equity, $r_e$.

Price return, total return and the price of a share Equities

The discount rate is the required return on equity (cost of equity), $r_e$, the return shareholders demand for the risk they bear.

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

Priority over common shares shows up as a lower discount rate, the required return on preferred stock r_p, and r_p below r_e.

Valuing preferred stock, and how call, put and conversion features change value Equities

Discount each coupon and the par value at the market discount rate: the return the market demands on bonds of the same risk and maturity. It also goes by required yield or required rate of return, and a quoted price implies it as the yield-to-maturity.

Pricing a bond from its yield to maturity Fixed Income

Take a benchmark rate, usually a government yield at the same maturity, then add the required yield spread that comparable bonds of the issuer's credit quality pay over it.

Matrix pricing Fixed Income

Drawing a new sample from the one you hold in this way is resampling: in a resample the same size as the original, some items appear several times and others not at all.

Bootstrapping: simulating from the data you have Quantitative Methods

Unless clients pay for it directly, research as a cost center earns no revenue, so firms choose which industries to cover, how many companies and what kind.

Sell-side, buy-side and activist short-seller research Equities

IFRS capitalizes development costs once the criteria are met; US GAAP generally expenses them. Research costs are expensed under both standards.

Expense recognition: capitalizing vs expensing Financial Statement Analysis

Under IFRS the company splits an internal project into two phases. The research phase (looking for new knowledge) is expensed.

Intangible assets: finite vs indefinite lives Financial Statement Analysis

In the European Union (EU), the second Markets in Financial Instruments Directive (MiFID II) requires asset managers to pay for sell-side research separately from trade execution.

Sell-side, buy-side and activist short-seller research Equities

A reserve currency is one that is fully convertible and held by foreign central banks and other investors as part of their foreign exchange reserves.

Sovereign credit analysis: qualitative factors Fixed Income

Higher FX reserves to GDP and a higher reserve ratio are stronger. A higher external debt burden and a higher share of debt falling due within 12 months are weaker.

Sovereign credit analysis: the key ratios Fixed Income

The reserve requirement is the fraction of deposits a bank must hold in reserve. A higher requirement limits money creation.

Monetary policy tools and the transmission mechanism Economics

The rate is observed on a reset date at the start of the period and the interest is paid at the end. That timing is called paying in arrears.

Floating-rate notes: quoted margin and discount margin Fixed Income

Bring critical production back to the home country.

Globalization vs nationalism: gains, costs and rollback Economics

The exam splits it into two sectors: residential real estate (homes) and commercial real estate (property leased to tenants for business or as rental housing).

Real estate: features and ways to invest (direct, REITs, funds) Alternative Investments

The miss, $e_i = Y_i - \hat{Y}_i$, is the residual: actual minus fitted. It is the sample's estimate of the error term.

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

Shareholders hold the residual claim: they receive what is left after every other claim is met, and the board decides how much of that is paid out as dividends.

Debt vs equity: lenders and shareholders Corporate Finance

Residual income is the profit a company earns above the opportunity cost of its shareholders' capital, also called economic profit.

Dividends, FCFE, FCFF or residual income: which cash flow, which discount rate Equities

The residual income model works differently. Residual income is the profit left after charging the required return on equity ($r_e$) against book equity: net income − $r_e$ × book value of equity (BVE).

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

The book value per share is the value at the start of the period, so the charge is for the capital shareholders had invested during the year. This is residual income per share.

Dividends, FCFE, FCFF or residual income: which cash flow, which discount rate Equities

You cannot see the errors themselves, but you can see their sample estimates, the residuals. A residual plot shows the residuals against X (or against time).

The four regression assumptions and what residual plots reveal Quantitative Methods

A residual tranche collects whatever cash flow remains after every other tranche is paid. It suits investors who can accept and hedge the risk, such as hedge funds and long-term institutions.

Mortgage pass-throughs and CMOs Fixed Income

Protecting the program and the designation.

The seven Standards of Professional Conduct at a glance Ethical and Professional Standards

Responsible investing is the broad umbrella for principles that require environmental, social and governance (ESG) themes to be considered when deciding whether to invest in a company and while owning it.

ESG considerations in portfolio planning and construction Portfolio Construction

Emerging market debt is often in a restricted domestic currency, one with limited convertibility into other currencies because it is illiquid.

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

Comply with firm policies, including a restricted list: if the firm will not publish an adverse view of a corporate client, remove the company from the research universe and release only factual information.

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

Blackout period or restricted period. Investment staff cannot trade personally around client trades. In a large firm that is close to a total ban, because the firm trades most securities continuously.

Standard VI(B): Priority of Transactions Ethical and Professional Standards

Market float is the number of shares free to trade in the public market: shares outstanding minus restricted shares, or other shares not available for trading.

Liquidity: market float, average daily volume and turnover Equities

Restricted stock and restricted stock units (RSUs) are forfeited if the employee leaves before vesting. Performance shares are earned by meeting targets such as earnings or return on assets, which can tempt managers to manipulate those numbers.

Share-based compensation: stock grants, options and SARs Financial Statement Analysis

Restricted stock and restricted stock units (RSUs) are forfeited if the employee leaves before vesting. Performance shares are earned by meeting targets such as earnings or return on assets, which can tempt managers to manipulate those numbers.

Share-based compensation: stock grants, options and SARs Financial Statement Analysis

Pay. Share-based compensation pays staff in shares. A common form is restricted stock units (RSUs): shares granted to employees that cannot be sold until a vesting period, possibly several years, ends.

Primary and secondary equity markets: issuing shares and why trading matters Equities

Investors therefore impose more constraints, written as restrictive covenants in the indenture (or loan agreement).

Long-term funding: investment-grade vs high-yield issuers Fixed Income

They do not include restructuring charges or a loss on closing one plant, which stay in continuing operations.

Non-recurring items, discontinued operations and accounting changes Financial Statement Analysis

Result compilation and analysis collects those outputs into a distribution and reads the average, the spread and the tails.

Historical, bootstrap or Monte Carlo: the four-step engine Quantitative Methods

Earnings quality, also called results quality, is about the results behind the information: the earnings, cash flow and balance sheet the business actually produced.

Reporting quality vs earnings quality, and the quality spectrum Financial Statement Analysis

Retained cash flow (RCF) is cash flow from operations less dividends: the cash left in the business. Net debt is debt less cash and marketable securities, because that cash could repay debt.

Financial ratios in credit analysis Fixed Income

Share capital rose from 1,000 to 1,150, so shares worth 150 were issued. Retained earnings went from 4,000 to 4,725 with net income of 1,125.

Investing and financing cash flows: asset sales, debt and dividends Financial Statement Analysis

Balance sheet. Cash is opening cash plus the net change. Working capital lines come from the days.

Forecasting working capital, capex, cash flow and the balance sheet Financial Statement Analysis

Retrospective application restates the earlier periods shown, so the trend is comparable and the cumulative effect goes into opening retained earnings.

Non-recurring items, discontinued operations and accounting changes Financial Statement Analysis

Their return from price appreciation only depends on what the next buyer will pay. The main driver of price is demand for a limited supply.

Digital assets: risk, return and diversification Alternative Investments

A return objective states what the portfolio should earn. It is half of the client's objectives, and it must be realistic: consistent with the risk objective and with the market environment.

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

Return on assets (ROA) is the awkward one: net income is after interest but assets are funded by lenders too. Some analysts fix the mismatch by adding back after-tax interest.

Profitability ratios: margins and returns on capital Financial Statement Analysis

For constant growth, the sustainable growth rate of FCFF is the reinvestment rate times the return on capital.

From the forecast model to an equity value Equities

The return on capital (ROC) is next year's after-tax EBIT divided by the book value of capital. Divide EV = FCFF ÷ (WACC − g) by book value of capital and you get the justified EV to book value of capital.

Enterprise value multiples Equities

From these an analyst can compute return on invested capital (ROIC), also known as return on capital employed.

Return on invested capital (ROIC) Corporate Finance

Return on common equity removes the preferred holders' share from both sides.

Profitability ratios: margins and returns on capital Financial Statement Analysis

The return on equity (ROE) is profit to shareholders divided by their equity.

Debt vs equity: lenders and shareholders Corporate Finance

DuPont analysis (the return on equity decomposition) shows whether ROE comes from earning a good margin, using assets efficiently, borrowing, or paying little tax.

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

Operating ROA and return on invested capital (ROIC) both exclude interest from the numerator. ROIC taxes the EBIT, so it shows the after-tax return on all capital employed.

Profitability ratios: margins and returns on capital Financial Statement Analysis

Return on invested capital (ROIC) is the after-tax operating profit earned on the capital that lenders and owners have put into the business.

Industry size, growth, profitability and concentration Equities

The return on investment (ROI) here is the multiple of the original investment that comes back, with no cash flows in between.

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

A pre-tax variant, EBIT over average debt plus equity, is sometimes called return on total capital. Use whichever definition the question gives.

Profitability ratios: margins and returns on capital Financial Statement Analysis

The result is return smoothing: reported returns look steadier than the underlying value really is, and the volatility of returns and their correlation with other assets look lower than they would be if the assets were sold.

Why alternative investment performance is hard to judge Alternative Investments

A return-generating model estimates an asset's expected return from a few measurable inputs. The most general form is a multi-factor model: the asset's expected excess return is the sum of its exposures to a set of factors, each multiplied by that factor's risk premium.

Systematic vs nonsystematic risk and return-generating models Portfolio Construction

The revaluation model carries it at fair value, and IFRS allows it only where an active market exists. US GAAP allows the cost model only.

Intangible assets: finite vs indefinite lives Financial Statement Analysis

A company that uses the revaluation model also discloses the date, how fair value was obtained, the carrying amount it would have under the cost model and the revaluation surplus.

PP&E disclosures, fixed asset turnover and asset age Financial Statement Analysis

revenue bonds finance one project, such as a road, bridge, tunnel or water utility, and are repaid from the project's tolls or fees.

Agency, municipal and supranational bonds Fixed Income

Split revenue growth into its revenue drivers, forecast each, and compound them. The drivers are volume growth (more or fewer units), price/mix (price changes plus a shift toward pricier or cheaper products) and the foreign currency effect (translating foreign sales into the reporting currency).

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

Revenue growth is not cash flow growth, and the difference is the caution of this section (revenue growth versus cash flow growth).

Two-stage (multistage) growth models Equities

The revenue model covers market size, market share, segments and changes in demand.

Why build a disaggregated model, and at what level of detail Equities

Available seat kilometers (ASKs) measure an airline's capacity. Revenue per ASK is what each unit of capacity earns, so revenue is the product of the two.

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

Sales per square meter is revenue over selling space. Service firms use revenue per employee and net income per employee.

Industry-specific ratios and using ratios to forecast Financial Statement Analysis

Since 2018 International Financial Reporting Standards (IFRS) and US generally accepted accounting principles (GAAP) share one standard, so revenue recognition works the same way under both.

Revenue recognition: the five-step model Financial Statement Analysis

Then check revenue relationships. Compare revenue growth with peers and the economy.

Warning signs of earnings manipulation Financial Statement Analysis

A reversal of a write-down lowers cost of sales, so profit goes up in the year of the recovery.

Lower of cost and net realizable value (and write-down reversals) Financial Statement Analysis

This is reverse cash-and-carry arbitrage. As traders pile in, the forward price rises (and spot falls) until the gap closes.

Replication and the no-arbitrage forward price Derivatives

Seen from the lender's side, the same trade is a reverse repurchase agreement (reverse repo).

Repurchase agreements (repos) Fixed Income

A reverse stock split (also called a share consolidation) does the opposite, as in a 1-for-4 reverse split. None of these three moves cash or changes the company's value.

Dividends, share repurchases, stock splits and the dividend timetable Equities

Suspension removes membership and the right to use the designation for a period. Revocation ends the right to use the CFA designation for good.

How the Code and Standards are enforced: the Professional Conduct Program Ethical and Professional Standards

A revolving credit agreement (revolver) is the most reliable source of short-term bank funding. It is a multiyear commitment, with pricing and commitment fee like a committed line, but lenders also ask for covenants that require or restrict borrower actions, as in a bond indenture.

Short-term funding for companies: credit lines, secured loans and commercial paper Fixed Income

Derivative price change for a change in interest rates.

Measuring risk: probability, VaR, CVaR and sensitivities Portfolio Construction

Ricardian equivalence is the sovereign counterpart of the Modigliani–Miller theorem: under strict conditions, the maturity a government chooses does not change the present value of the taxes taxpayers will pay.

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

The traditional models explain trade by differences between countries. The Ricardian model points to differences in technology.

Benefits and costs of international trade Economics

On day one the lessee records a right-of-use asset and a lease liability, both equal to the present value of the lease payments.

Leases: finance vs operating and lessee accounting (IFRS vs US GAAP) Financial Statement Analysis

A one-tailed test asks about one direction only and puts all of the rejection region in that tail: the right-tail test when the claim is "greater than", the left-tail test when it is "less than".

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

They stay on its balance sheet but are segregated for the covered bondholders, a step called ringfencing.

Covered bonds Fixed Income

The caveat is rising correlation. As institutions join the market and digital assets trade more like other risk assets, correlations with traditional assets have risen, particularly when markets are uncertain.

Digital assets: risk, return and diversification Alternative Investments

Risk acceptance keeps the exposure but does it efficiently. Self-insurance is bearing a risk that is undesirable but too costly to remove by outside means.

Modifying risk: prevention, acceptance, transfer and shifting Portfolio Construction

The first benefit is risk allocation, and its most common form is risk transfer. A derivative lets a user trade, hold or offset exposure to an underlying without buying or selling it, and it moves the risk to a party who is able and willing to hold it.

Why use derivatives: the four benefits Derivatives

The willingness to take risk, also called the risk attitude, is more subjective and is gauged by talking to the client or with a questionnaire.

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

A risk averse investor takes the sure USD 2,000. The draw must offer a higher expected value before it is worth taking.

Risk aversion, utility and indifference curves Portfolio Construction

That is arbitrage-free pricing. It does not need to know investors' risk aversion (how much they dislike risk) or the real-world probability of an up move.

Risk neutrality: why real-world probabilities do not matter Derivatives

The risk aversion coefficient A is the extra return the investor demands for taking additional risk. Use returns and standard deviations as decimals (8% is 0.08, and a σ of 15% gives σ² = 0.0225).

Risk aversion, utility and indifference curves Portfolio Construction

The next step, especially for quantitatively oriented managers, is risk budgeting: deciding the overall risk to take (set when the IPS was written) and dividing it between the sources of return.

Asset classes, strategic asset allocation and portfolio construction Portfolio Construction

When risk is built into every key decision, the organization has an effective risk culture. Governance needs visible commitment from the top, because rules alone do not change behavior.

Risk governance, risk tolerance and risk budgeting Portfolio Construction

Risk drivers are the fundamental underlying factors that create risk. They sit at three levels: global and domestic macroeconomies (set partly by governments and central banks through taxes, regulation and monetary and fiscal policy), industries (some stable, some highly cyclical) and individual companies.

Measuring risk: probability, VaR, CVaR and sensitivities Portfolio Construction

The risk exposure is what the organization actually stands to gain or lose, and in the simplest case it is the position multiplied by the driver.

What risk management is, and the risk management framework Portfolio Construction

The thing varying from path to path is a risk factor, an uncertain input such as a share's return. Each gets a probability distribution and parameters.

Monte Carlo simulation Quantitative Methods

The risk factor approach goes further and budgets exposure to factors, such as value or momentum, in the hope of capturing the associated premiums.

Risk governance, risk tolerance and risk budgeting Portfolio Construction

Risk governance is the top-down process and guidance that directs risk management activities to align with and support the overall goals of the enterprise.

Risk governance, risk tolerance and risk budgeting Portfolio Construction

The risk interactions can be traced along a chain: a market move creates credit risk, and credit risk brings settlement, operational and legal risk with it..

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

Risk management is the process by which an organization or individual defines the level of risk to be taken, measures the level of risk being taken, and adjusts the latter toward the former, with the goal of maximizing the value of the company or portfolio, or the satisfaction (utility) of the individual.

What risk management is, and the risk management framework Portfolio Construction

A risk management committee gives managers a regular forum to discuss the risk framework and key issues. It parallels the board's deliberations at an operational level.

Risk governance, risk tolerance and risk budgeting Portfolio Construction

A risk management framework is the infrastructure, process and analytics needed to support effective risk management.

What risk management is, and the risk management framework Portfolio Construction

A risk neutral investor is indifferent. Only the expected return matters, never the risk.

Risk aversion, utility and indifference curves Portfolio Construction

It says the option's price equals its expected payoff, discounted at the risk-free rate, when the expectation uses the right probabilities: the ones under which the share itself is expected to earn exactly r. This is risk neutrality used as a pricing device.

Risk neutrality: why real-world probabilities do not matter Derivatives

Risk parity. Critics of mean–variance methods point to their sensitivity to small errors in forecast returns and correlations.

Asset classes, strategic asset allocation and portfolio construction Portfolio Construction

A risk premium is extra expected return for bearing risk, where risk means the chance that the actual return differs from the expected one.

Required return: risk-free rate, inflation and risk premia Quantitative Methods

Risk prevention and avoidance means taking steps so that the risk is not borne at all, or is less likely. Avoiding every risk is neither possible nor wise, because avoidance gives up the benefit of the activity.

Modifying risk: prevention, acceptance, transfer and shifting Portfolio Construction

A client's risk profile is the single most important input to suitability. Pay particular attention to leverage and limited liquidity in derivatives and synthetic products, which bear directly on whether they suit the client.

Standard III(C): Suitability Ethical and Professional Standards

A risk seeking investor takes the draw, and might even prefer a draw worth USD 1,800 on average to the sure USD 2,000, because the uncertainty itself is enjoyable.

Risk aversion, utility and indifference curves Portfolio Construction

Risk shifting changes the distribution of risk outcomes. Where insurance moves a loss to a pool, shifting moves part of the distribution of outcomes to another market participant, and is the bulk of hedging for financial organizations.

Modifying risk: prevention, acceptance, transfer and shifting Portfolio Construction

Risk tolerance is the amount of risk an investor will accept to reach a goal. It moves opposite to risk aversion, and it changes with age, health, wealth, family circumstances and the economic climate.

Risk preferences, mean–variance utility and indifference curves Quantitative Methods

The first benefit is risk allocation, and its most common form is risk transfer. A derivative lets a user trade, hold or offset exposure to an underlying without buying or selling it, and it moves the risk to a party who is able and willing to hold it.

Why use derivatives: the four benefits Derivatives

Maximize the Sharpe ratio.

The minimum-variance portfolio and the efficient frontier Quantitative Methods

Performance evaluation asks how a portfolio did, and four measures turn the answer into a risk-adjusted return.

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

A risk-averse investor takes the sure INR 9,000, even though the gamble's expected value is higher. This investor aims to minimize risk for a given return.

Risk preferences, mean–variance utility and indifference curves Quantitative Methods

Maximize expected return.

The minimum-variance portfolio and the efficient frontier Quantitative Methods

A risk-free asset has zero standard deviation and zero correlation with everything else, so it contributes no risk of its own.

The capital allocation line and the optimal portfolio Portfolio Construction

The fiduciary call is a long call plus a risk-free bond paying X at expiry, where X is the exercise price. Both options are European options with the same strike and expiry.

Put–call parity: fiduciary call = protective put Derivatives

Because a risk-free return has no variance penalty, the utility of a risky portfolio equals the sure return that would make the investor equally happy. This is the risk-free equivalent return.

Risk aversion, utility and indifference curves Portfolio Construction

One share moves the portfolio by its price change, so h* shares cancel the option's change. This is the risk-free hedged portfolio: its end value does not depend on which state occurs.

The one-period binomial tree and the hedge ratio Derivatives

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

Because the value is certain, the risk-free portfolio must earn the risk-free rate, and that fixes the option's price.

Forward exchange rates and option values by no arbitrage Quantitative Methods

The risk-free rate is the return on an investment with no default risk and no reinvestment risk. Short-term government bills, for example a 30-day Treasury bill, stand in for it.

Required return: risk-free rate, inflation and risk premia Quantitative Methods

A risk-neutral investor looks only at expected value, so takes the gamble (10,000 is more than 9,000).

Risk preferences, mean–variance utility and indifference curves Quantitative Methods

The first term is the risk-neutral drift: the risk-free rate less half the variance, the log-return drift that makes the expected price grow at the risk-free rate.

Monte Carlo simulation Quantitative Methods

The answer is identical to the hedge price. This is risk-neutral pricing.

Pricing calls and puts with risk-neutral probabilities Derivatives

Instead of building a hedge, compute one number from the tree, the risk-neutral probability of an up move, weight the option's two payoffs with it, and discount the result at the risk-free rate.

Pricing calls and puts with risk-neutral probabilities Derivatives

Investors demand more expected return for more risk, and prices adjust until they get it. This is the risk-return trade-off.

Macro and micro risk and the risk-return trade-off Quantitative Methods

A risk-seeking investor prefers the gamble even at a lower expected value, as with lottery tickets and casinos.

Risk preferences, mean–variance utility and indifference curves Quantitative Methods

Returns decline step by step down to the safest, most secured form of lending, infrastructure debt. This is the risk–return ladder, and it mirrors public markets: investors are paid more for holding equity than debt, and more for junior than for senior claims.

Private capital in a portfolio: risk, return, vintage years and diversification Alternative Investments

Across long histories in the major markets, higher average returns came with higher volatility. That is the risk–return trade-off: in efficient markets, extra return over long periods cannot be had without accepting extra risk, so assets with more risk must offer more expected return.

How the major asset classes compare on return and risk Portfolio Construction

Then a riskless arbitrage exists: compare the dealer's forward with the parity value, buy the currency forward where it is cheap, and fund the other leg at the deposit rates.

Covered interest rate parity: forward rates from interest rates Economics

An arbitrage is a trade, or a set of trades, that gives a riskless profit with no net investment. You start with nothing, you finish with money, and no outcome of the market can leave you worse off.

Arbitrage and the law of one price Derivatives

Outline the significant risks and limitations of the process and of your recommendations. Use of leverage is generally significant.

Standard V(B): Communication with Clients and Prospective Clients Ethical and Professional Standards

That is a risk-free bond paying D minus a put on the firm's assets with strike D. This is risky debt: a risk-free bond with a short put attached.

Equity and debt as options on the firm Derivatives

Rivalry is the intensity of competition among existing firms. It is high with many similar competitors, high fixed costs, slow growth and excess capacity, because firms cut prices to fill plants.

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

Judge rivalry among existing competitors from price competition, product differentiation, the relative size of the major competitors and how their shares change, and the industry's growth and profitability.

Porter's Five Forces and economic moats Equities

ETFs and robo-advice. Exchange-traded funds track an asset class index cheaply and trade easily. Combined with algorithm-based advice (robo-advice), they give retail investors fast, inexpensive, liquid and diversified exposure.

Asset classes, strategic asset allocation and portfolio construction Portfolio Construction

A robo-adviser is one result: it builds a diversified portfolio from a client's goals and risk tolerance and keeps rebalancing it automatically.

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

A statistic is robust when it stays reliable even if the data contain outliers or do not follow the distribution you assumed.

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

A consistent estimator converges to the true value as the sample grows, and a robust estimator stays reliable when the data contain outliers or are not normal, for example by trimming extreme values before averaging.

The central limit theorem and the standard error of the mean Quantitative Methods

Non-parametric tests have robustness: they keep working when the data misbehave.

Parametric vs non-parametric tests Quantitative Methods

Rolling-window validation trains on a fixed-length window, validates on the period right after it, then moves the window forward and repeats.

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

Rollover risk is the risk that short-term debt cannot be refinanced when it falls due, or only on bad terms, which can push a company into default.

Working capital management approaches Corporate Finance

If each period's return adds a similar, independent amount of uncertainty, the variance over T periods is T times the one-period variance, so the standard deviation is √T times the one-period figure. This is the root-of-time law.

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

Farmland consists mainly of row crops (planted and harvested, sometimes more than once a year, depending on crop and climate) and permanent crops (orchards and vineyards that grow on trees or vines).

Raw land, timberland and farmland as investments Alternative Investments

The structure rests on CFA Institute's bylaws and the Rules of Procedure for Professional Conduct. The process covers testing policies as well as the Code and Standards, which is why exam conduct (a candidate sharing exam content online, for example) goes through it.

How the Code and Standards are enforced: the Professional Conduct Program Ethical and Professional Standards