CFA Level I terms: P

P-hacking is reworking an analysis (another period, another benchmark, dropping awkward months) until a result crosses the significance line, then reporting only that version.

P-values, p-hacking and critical values from software Quantitative Methods

The p-value is the smallest significance level at which $H_0$ would be rejected. In the example, t = 2.25 with 35 degrees of freedom has a one-tailed p-value of 0.015: reject at 5%, not at 1% (critical value 2.438).

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

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

A par bond sells at its par value because its coupon equals the rate. A discount bond sells below par: with a 5% coupon when new bonds pay 6%, the bond is short 1 per year, and its price drops by the present value of that shortfall.

Pricing a bond from its yield to maturity Fixed Income

A bond priced at par has a yield equal to its coupon, so the same number is also the bond's yield. Plotted against maturity, par rates form the par curve.

Par rates from spot rates Fixed Income

The par rate for a maturity is the coupon rate that makes a bond, valued with today's spot rates, worth exactly 100.

Par rates from spot rates Fixed Income

The fixed rate of a new swap is chosen so that the swap is worth nothing to either side on day one. That rate is the par swap rate, and it is the swap's price.

The swap price: solving for the par swap rate Derivatives

So the swap rate is the par yield: the coupon a bond would need to sell at par on the same curve. That is why the swap curve works as a benchmark yield curve, and it links this module to the term-structure lessons in Fixed Income.

The swap price: solving for the par swap rate Derivatives

Move yields by one percentage point right after purchase, the kind of parallel shift where every yield changes by the same amount, once.

Investment horizon, price risk vs reinvestment risk, and duration gap Fixed Income

A parameter is a value that describes the whole population, such as its mean μ or standard deviation σ. A sample statistic is the matching value computed from the sample, such as X̄ or s.

Sampling methods and sampling error Quantitative Methods

A parametric test assumes the data follow a particular distribution, often the normal, and meet conditions on randomness, sample size and variance; it uses parameters such as the mean and variance.

Parametric vs non-parametric tests Quantitative Methods

This is a parametric test of correlation: it assumes both variables are approximately normally distributed. It is the test of the Pearson correlation coefficient, the ordinary correlation $r$.

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

Parametric value at risk assumes normal returns and uses only the standard deviations and the correlation. Historical VaR uses the actual tail.

Historical simulation and historical value at risk Quantitative Methods

The parametric variance–covariance method assumes returns are normal and describes them with the standard deviation.

Value at risk from the normal distribution Quantitative Methods

Same class, same treatment. Creditors at one seniority level are one class, whatever their maturity, and share pari passu (equally, pro rata).

Seniority, recovery rates and notching Fixed Income

A pari passu clause ("equal footing") ensures the bond is treated the same as the issuer's other debt of similar rank.

Bond indentures and covenants Fixed Income

References must say you are a candidate for the CFA designation, and must not imply a partial designation (except as authorized or permitted by CFA Institute) or cite an expected completion date.

Standard VII(B): Reference to CFA Institute, the CFA Designation, and the CFA Program Ethical and Professional Standards

Key rate duration (also called partial duration) can: it measures a bond's sensitivity to a change in the benchmark yield at one maturity, with all other rates held constant.

Key rate duration Fixed Income

A partially amortizing bond has level payments too, but they leave part of the principal outstanding, which is repaid as a balloon payment with the final payment.

Bullet, amortizing and sinking fund bonds Fixed Income

Participating preference shares pay the standard dividend plus an extra amount when profits pass a set level. This is upside for the investor.

Common shares and preference shares Equities

Do not knowingly take part in, or help, a violation of law or of the Code and Standards. That is participation in violations.

Standard I(A): Knowledge of the Law Ethical and Professional Standards

If you may trade at most a set percentage of ADV each day (a participation limit), divide the position, as a multiple of ADV, by that limit and round up to whole days.

Liquidity: market float, average daily volume and turnover Equities

A private limited company (a limited liability company, or LLC, in the United States, a GmbH in Germany or a société à responsabilité limitée, or SARL, in France) caps the number of owners and restricts share transfers, and in many places it is taxed as a pass-through business.

Organizational forms of businesses Corporate Finance

They earn the pass-through rate, and the pool's rate is measured as a weighted average.

Mortgage pass-throughs and CMOs Fixed Income

Pass-through securities are true securitizations. The pool is moved off the balance sheet into a separate legal entity, which issues securities backed by it.

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

They now also make passive investing possible: an index fund or exchange-traded fund aims to replicate an index at low cost, while active investing tries to beat a benchmark through security selection and timing.

Rebalancing, reconstitution and what indexes are used for Quantitative Methods

Passive management replicates the returns of a market index at low cost. Most assets are still actively managed, but passive is growing.

The asset management industry Portfolio Construction

Holding the market and adjusting only the lending or borrowing is a passive portfolio strategy: it lands on the CML.

The capital market line Portfolio Construction

Service cost goes to profit. It is the present value of the extra pension the employees earned by working one more year (current service cost).

Defined contribution vs defined benefit pension plans Financial Statement Analysis

Analysts treat patents as a temporary barrier: a patent gives its owner the exclusive right to sell a product or technology, but only until it expires.

Porter's Five Forces and economic moats Equities

A path-dependent option pays according to the prices along the way, not only the final price. An Asian option pays the excess of the final price over the average price during its life, if positive.

Monte Carlo simulation Quantitative Methods

Payables turnover converts into the number of days of payables by 365 ÷ turnover, the average time the company takes to pay suppliers.

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

The payment date is the day the company transfers the dividend electronically.

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

A payment-in-kind (PIK) feature lets the issuer pay interest by increasing the principal outstanding instead of paying cash.

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

Regulator and supervisor of the payments system. Transfers between banks, within the country and across borders, need robust, standardized procedures.

The role of central banks Economics

The payoff is what the option is worth at expiration, before counting what was paid for it. The profit subtracts the premium.

Call and put options: payoff and profit at expiration Derivatives

The payout and growth trade-off needs care. A firm that pays out more keeps less to reinvest, so it grows more slowly.

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

The same idea applies to a payout ratio and dividend growth question on the exam: multiply the EPS growth factor by the ratio of the new payout to the old one.

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

This is a parametric test of correlation: it assumes both variables are approximately normally distributed. It is the test of the Pearson correlation coefficient, the ordinary correlation $r$.

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

The pecking order theory starts from a different place: asymmetric information. Managers know more about the company's prospects than outside investors do, and investors know it.

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

Choose a group of companies with similar characteristics: the peer group, ideally with similar cash flow, risk and growth.

Valuing with multiples: comparables and forecasted fundamentals Equities

A comparison with peer historical averages shows how the company has done relative to a benchmark under similar market and business conditions over time.

Trailing, current and forward multiples Equities

A firm that wants to expand its footprint quickly may use penetration pricing, willingly pricing low or discounting to build scale and market share at the expense of margins.

Pricing and revenue models Corporate Finance

Every investor forms an estimate of intrinsic value. That estimate is a perceived value, and the estimates investors produce are called perceived value indicators.

Market price, intrinsic value and perceived value Equities

Every investor forms an estimate of intrinsic value. That estimate is a perceived value, and the estimates investors produce are called perceived value indicators.

Market price, intrinsic value and perceived value Equities

Keep percent versus percentage point straight: a margin rising from 8% to 9% is a rise of 1 percentage point, or 12.5% in percent terms.

Functional forms: log-lin, lin-log and log-log models Quantitative Methods

The percentage bid-ask spread divides that by the lowest ask.

Where shares trade: exchanges, off-exchange and over the counter Equities

The second is the percentage of revenue (net revenue), which puts every line on the same yardstick as the income statement.

Reading a cash flow statement: sources, uses and common-size Financial Statement Analysis

The first base is the percentage of total inflows for inflows and of total outflows for outflows. The second is the percentage of revenue (net revenue), which puts every line on the same yardstick as the income statement.

Reading a cash flow statement: sources, uses and common-size Financial Statement Analysis

Duration gives the straight-line estimate of the percentage price change for a yield change. Convexity adds the curvature that the line misses, and that second term is the convexity adjustment.

Estimating price change with duration and convexity Fixed Income

Quartiles make four groups, quintiles five, deciles ten and percentiles one hundred. The second quartile, the 50th percentile and the median are the same value.

Quartiles, percentiles and box plots Quantitative Methods

Perfect capital markets. No taxes, transaction costs or bankruptcy costs, and everyone has the same information.

Modigliani–Miller propositions Corporate Finance

Perfect competition sits at one end, with many identical sellers and no pricing power. At the other end is monopoly, a single seller with no close substitute.

The four market structures compared Economics

The performance appraisal of alternatives therefore needs more scrutiny. Because the return distribution is usually less normal, the risk and return measures built for stocks and bonds fit less well.

Why alternative investment performance is hard to judge Alternative Investments

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

The performance fee is a share of profits (often 20%) that rewards results. It is also called an incentive fee or carried interest ("carry").

Fees and waterfalls: hurdle, catch-up, high-water mark, clawback Alternative Investments

Performance measurement and reporting. The manager compares results with the IPS benchmark and reports to the client.

The three steps of the portfolio management process Portfolio Construction

Identify the separate performance obligations: each distinct good or service promised.

Revenue recognition: the five-step model Financial Statement Analysis

Performance presentation requires results to be fair, accurate and complete. The investor should be able to rely on them as a full picture.

Cases on market integrity and duties to clients Ethical and Professional Standards

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

Costs with no link to future revenue, such as administrative salaries and rent, are period costs, expensed when incurred.

Expense recognition: capitalizing vs expensing Financial Statement Analysis

The periodic and perpetual inventory systems give the same results for FIFO and specific identification. They can differ for LIFO and weighted average.

FIFO, LIFO and weighted average when prices rise or fall Financial Statement Analysis

A periodic report is shorter, because its readers already know the company.

Equity research reports: contents, ratings and price targets Equities

A swap has periodic settlement, one payment at the end of each period under a single contract. An FRA has one settlement, made at the start of its interest period and discounted.

A swap as a series of forwards: what is the same and what is different Derivatives

The MRR is like the "spot" price on that date and the swap rate is the agreed "forward" price, so the periodic settlement value to the fixed-rate payer has the same form as the payoff of any long forward.

Swap value after inception: time and rate changes Derivatives

A yield is a rate per period turned into an annual figure, and the annual figure only makes sense once you know how many periods went into it. That number is the periodicity, written $m$.

Periodicity: converting yields between compounding frequencies Fixed Income

The periodicity of a money market rate is $365 \div Days$, because the rate is simple interest, so it differs for every maturity.

Comparing money market instruments: bond equivalent yield Fixed Income

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

Permanent current assets are the base levels of inventory, receivables and staffing needed all year, and they stay fairly constant.

Working capital management approaches Corporate Finance

A permanent difference is recognized in one but never in the other, so it never reverses.

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

A permissioned network limits membership, often giving members different rights (a regulator might be allowed to view but not to validate, for instance).

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

A permissionless network is open to any user, every user can see every transaction, and any participant can perform every network function.

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

A perpetual bond pays a fixed coupon every period with no maturity and no face value. Its payments form a perpetuity, and the infinite sum collapses to one line.

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

A perpetual preferred stock has no maturity, so the dividends form a perpetuity.

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

Its payments form a perpetuity, and the infinite sum collapses to one line.

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

The Standard is not meant to police personal behavior. CFA Institute is aware that complaints are sometimes used to settle personal or political disputes, and has safeguards against that.

Standard I(D): Misconduct Ethical and Professional Standards

PESTLE analysis looks outside, at political, economic, social, technological, legal and environmental influences, and is more concerned with the industry's growth rate and how market share shifts between firms that adapt well and firms that do not.

PESTLE and the innovation matrix Equities

Pet projects are projects that get preferential treatment, sometimes without thorough analysis, sometimes with overly optimistic forecasts.

Capital allocation principles and pitfalls Corporate Finance

Phantom stock pays the value of notional shares and can be used where there is no traded stock, such as a private company or a business unit.

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

Physical risks are damage to or loss of assets from severe weather, which is expected to become more frequent.

ESG factors investors consider Corporate Finance

Listed companies can raise private equity capital too, through a PIPE (private investment in public equity). New or existing shares (or convertibles) are sold privately to selected investors, usually institutions, at a fixed price.

Private equity strategies: buyouts, venture capital and growth equity Alternative Investments

Plagiarism means presenting someone else's text, data or ideas as your own. Quoting sources with credit is fine.

Professionalism cases: law, independence, misrepresentation, misconduct, competence Ethical and Professional Standards

in plain language: clear to the reader it is aimed at.

Standard I(C): Misrepresentation Ethical and Professional Standards

The balance sheet shows one net figure, the funded status: the fair value of plan assets minus the defined benefit obligation (the present value of the promised pensions, discounted at a high-quality corporate bond yield).

Defined contribution vs defined benefit pension plans Financial Statement Analysis

A planned amortization class (PAC) tranche makes scheduled, fixed principal payments over a set period, as long as prepayments stay between a minimum and a maximum speed.

Mortgage pass-throughs and CMOs Fixed Income

The planning step starts with the client. A manager who does not understand the client's needs, meaning objectives and constraints, is unlikely to achieve appropriate results.

The three steps of the portfolio management process Portfolio Construction

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

Skewness and kurtosis Quantitative Methods

A secured bond adds a legal claim on specific assets. That claim is called a lien or a pledge, and the assets are the collateral.

Bond indentures and covenants Fixed Income

The sample mean x̄ is a point estimate of μ: one number standing in for the unknown population value. Wrap a range around it and you have an interval estimate, the subject of the next lesson.

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

Mixing them, 8% with 38.00 gives 35.88 and 12% with 52.00 gives 40.34, a range that is too narrow. Report a point estimate and value range together.

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

Software shows both: a license the customer installs and that you do not keep changing is a point in time sale, usually recognized up front, while cloud access is recognized over time.

Revenue recognition: the five-step model Financial Statement Analysis

A poison put is a put that investors can use if the issuer is taken over. It makes the takeover costlier because it creates an immediate claim on cash.

Callable, putable and convertible bonds Fixed Income

If events arrive independently at a constant average rate λ per unit of time, the number of events in an interval of length t follows a Poisson distribution.

Discrete distributions: uniform, binomial and Poisson Quantitative Methods

So the same boost to demand can favor different parts of the economy depending on the policy mix.

How monetary and fiscal policy interact Economics

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.

The investment policy statement (IPS) Portfolio Construction

The policy rate is the rate the central bank announces and is willing to lend to banks at.

Monetary policy tools and the transmission mechanism Economics

Political influences are government policy and action. Indirect ones are trade, fiscal and monetary policy, regulation and geopolitics.

PESTLE and the innovation matrix Equities

Because the variance is assumed equal, the two sample variances are combined into one estimate, the pooled variance, weighted by degrees of freedom. Δ₀ in the formula is the hypothesized difference between the means, usually 0.

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

The central limit theorem (CLT) says that, for any population with mean μ and finite variance σ², the sampling distribution of the sample mean from random samples of size n is approximately normal with mean μ (the population mean) and variance σ² ÷ n, once n is large.

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

For a whole group, a population, you divide by N and get the population variance. Its square root is the population standard deviation.

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

For a whole group, a population, you divide by N and get the population variance. Its square root is the population standard deviation.

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

Porter's five forces is a framework for judging how much of an industry's value its companies keep. Each force is a source of pressure on prices or costs.

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

The portfolio approach means judging each security by how it contributes to the investment characteristics of the whole portfolio, not on its own.

Why invest through a portfolio Portfolio Construction

A manager can run many funds, each holding several investments. The companies the funds own are called portfolio companies.

Private equity strategies: buyouts, venture capital and growth equity Alternative Investments

Portfolio construction. Using the target allocation, the security analysis and the IPS, the manager decides asset class, sector and security weights, keeps the risk within the client's tolerance, and trades.

The three steps of the portfolio management process Portfolio Construction

There are two ways to compute portfolio duration and portfolio convexity.

Portfolio duration and convexity Fixed Income

An asset that beats the rest of the portfolio ends the period with a bigger weight, and one that lags ends with a smaller one. That is portfolio drift: the weights change without any trade.

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

There are two ways to compute portfolio duration and portfolio convexity.

Portfolio duration and convexity Fixed Income

Portfolio flows go into stocks, bonds and other liquid assets and can leave quickly. 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

Portfolio investment flows are short-term holdings of foreign stocks and bonds.

Globalization vs nationalism: gains, costs and rollback Economics

The portfolio return is the sum of each weight times its asset's return, and the weights add up to 1.

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

Written with correlation, the covariance is ρσ₁σ₂. The portfolio standard deviation is the square root.

Portfolio variance, covariance and correlation Portfolio Construction

Portfolio variance has three parts: each asset's own variance scaled by its squared weight, and a cross term that counts the covariance twice.

Portfolio expected return, variance and the role of correlation Quantitative Methods

For an option-free bond the curve bends upward, which is called positive convexity: the curve always sits above its tangent line.

Convexity and the convexity adjustment Fixed Income

Favors companies with better ESG performance than peers.

ESG considerations in portfolio planning and construction Portfolio Construction

The value the formula gives is the company's value after the new money: the post-money valuation. Subtract the new equity to get the pre-money valuation, and divide the new equity by the post-money value to get the new investor's fractional ownership.

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

After the update you hold the posterior probability, the probability of the event given the news, also called the a posteriori or ex post probability.

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

The power of a test is the probability of correctly rejecting a false null.

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

Many have a pre-funding period, which lets the trust add eligible loans after closing. The payment often replaces part of the household's energy bill, which supports performance, and the bonds appeal to investors with sustainability goals.

Credit card, auto loan and solar ABS Fixed Income

Subtract the new equity to get the pre-money valuation, and divide the new equity by the post-money value to get the new investor's fractional ownership.

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

Pre-seed capital (angel investing) funds the idea: a business plan and an assessment of market potential. Amounts are small and come mostly from individuals.

Private equity strategies: buyouts, venture capital and growth equity Alternative Investments

EBITDA is a before-tax measure, so any rate applied to it must also be before tax, a pre-tax discount rate for EBITDA, unlike the after-tax WACC used for FCFF.

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

The Preamble explains why they matter: the Code and Standards together are the foundation of the profession's credibility and of the trust that clients and markets place in it.

The six principles of the Code of Ethics Ethical and Professional Standards

IPO participation. A hot IPO taken by staff looks like taking an opportunity from clients, or like a reward for future favors.

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

The dividend part of an expected return is usually the more predictable part, because companies try to keep dividends steady. That is the predictability of dividends.

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

Plug the new value of X into the fitted line. The result is the predicted value of Y.

Predicting Y and building a prediction interval Quantitative Methods

A prediction interval is the range expected to contain a single new observation of Y at a given X, with a stated confidence.

Predicting Y and building a prediction interval Quantitative Methods

The confidence intervals around forecasts are too narrow, so the expected variation is too small.

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

Preemptive rights are existing holders' first call on new shares, or on securities convertible into shares. They let a holder buy enough of the new issue to avoid dilution of her percentage stake.

Common shares and preference shares Equities

Preference shares (also called preferred stock) rank above common shares for dividends and for assets in a liquidation, but behind all debt.

Common shares and preference shares Equities

Take net income, remove what belongs to preferred dividends, and divide by the average number of common shares outstanding during the year.

Basic EPS and the weighted average number of shares Financial Statement Analysis

If the dividend never changes, the share is a perpetuity, exactly like the perpetual bond. The standard case is preferred stock: a fixed dividend, paid forever.

Valuing a stock from its dividends Quantitative Methods

A preferred stock with a maturity date is valued like a bond: the present value of the dividends plus the present value of par.

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

Contingent claims are non-linear derivatives: the payoff bends at the exercise price, and the buyer pays a premium for the right to choose.

Forward commitments vs contingent claims Derivatives

The coupon (6%) is above the yield (5%), so this is a premium bond: it trades above face value.

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

A prepayment lockout bans prepayment for a set period.

Commercial mortgage-backed securities (CMBS) Fixed Income

The borrower's most important right is the prepayment option: to repay more than the scheduled principal, in part or in full, before maturity.

Residential mortgage loans: the features that matter Fixed Income

A prepayment penalty compensates the lender if the borrower prepays when rates have fallen. It reduces the incentive to refinance.

Residential mortgage loans: the features that matter Fixed Income

prepayment penalty points are fees set in advance that a borrower who wants to refinance must pay. One point is 1% of the outstanding loan balance.

Commercial mortgage-backed securities (CMBS) Fixed Income

The prepayment risk in a mortgage bond is the risk that borrowers repay principal at a different pace from the contractual schedule.

Prepayment risk and time tranching Fixed Income

The future value (FV) of an amount today is what it grows to at the interest rate. The present value (PV) of a later amount is that growth undone.

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

Discount the free cash flow and the terminal value at WACC, not at the cost of equity. That is the present value at the weighted average cost of capital (WACC), and it gives the firm value.

From the forecast model to an equity value Equities

Four, plus one that analysts often reach for: dividends, free cash flow to equity (FCFE), free cash flow to the firm (FCFF) and residual income, and earnings before interest, taxes, depreciation, and amortization (EBITDA). These are the present value metrics.

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

Absolute valuation estimates the cash flows or asset prices that drive a share's intrinsic value, and it has two kinds of model: present value models and asset-based valuation models.

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

Suppose you can lock in today the price at which you will sell an asset on a future date. That future price is now a known amount, so it must be worth its present value of a known future price today, discounted at the risk-free rate.

Arbitrage and the law of one price Derivatives

The present value of income still to be paid is subtracted, and the present value of costs still to be incurred is added.

Valuing a forward when the asset pays income or has costs Derivatives

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, $r_e$. This is the present value of dividends and a future price.

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

Anything the market pays above that is the present value of growth opportunities (PVGO).

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

The present value of income still to be paid is subtracted, and the present value of costs still to be incurred is added.

Valuing a forward when the asset pays income or has costs Derivatives

The present value of the fixed and floating legs must match. The floating leg is valued at today's implied forward rate for each period, because the forward rate is the market's expectation of each future reset.

The swap price: solving for the par swap rate Derivatives

What it owes is not F₀(T) in today's money. It is the present value of the forward price, discounted at the risk-free rate over the remaining time T − t.

Forward price vs forward value: at initiation, during the life, at expiry Derivatives

The present-value weights are each payment's present value divided by the bond's full price, so they add up to 1.

Macaulay duration: definition and calculation Fixed Income

Presentation choices shape which number you see first and how you read it.

Non-GAAP measures and other presentation choices Financial Statement Analysis

Issuer sources outside the filings: earnings calls (webcast presentations and questions, not legally required), investor days (ad hoc, in-depth sessions), press releases, conversations with management and investor relations, the company website, and experiencing the products as a customer.

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

Pretax margin is after interest, and it picks up the effect of leverage and non-operating items. Net profit margin is after tax.

Profitability ratios: margins and returns on capital Financial Statement Analysis

The price currency (A, the numerator) is the currency the price is quoted in.

Exchange rate quotes and percentage change in a currency Economics

In a period of price inflation (a general rise in prices) companies usually raise selling prices, but customers buy less when they do. In price deflation (a general fall) the same logic runs backward.

Forecasting sales and costs with inflation or deflation Financial Statement Analysis

Price discovery means derivative prices reveal information about expected future prices and risk.

Why use derivatives: the four benefits Derivatives

The aim of price discrimination is to maximize profit when customers differ in willingness to pay. It can also make sense when some customers, such as large-volume buyers, cost less to serve.

Pricing and revenue models Corporate Finance

One measure is price elasticity: how much the quantity demanded changes when the price changes. Essentials such as prescription medicines or household electricity tend to be price inelastic (a price change barely moves demand); restaurant meals and designer clothing tend to be price elastic.

Revenue drivers and pricing power Equities

The size of the volume response is set by price elasticity of demand: how much quantity demanded changes for a given change in price.

Forecasting sales and costs with inflation or deflation Financial Statement Analysis

The cost of trading has three parts: the brokerage commission, the bid–ask spread and the price impact. Liquidity drives the last two.

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

The price return index, also called a price index, tracks price changes only. 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

In a period of price inflation (a general rise in prices) companies usually raise selling prices, but customers buy less when they do.

Forecasting sales and costs with inflation or deflation Financial Statement Analysis

Under price leadership one dominant firm, often with a share of 40% or more and usually the lowest-cost producer, sets the price.

Oligopoly pricing: kinked demand, Cournot, Nash and Stackelberg Economics

Some contracts also have price limits: a band around the previous day's settlement price outside which no trade may occur.

Futures contracts, daily settlement and margin calls Derivatives

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

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

The price return is the change in price that is independent of any payout. For a share it reflects the company's results, market sentiment and the economy.

Types of returns: assets, instruments and indicators Quantitative Methods

The price return index, also called a price index, tracks price changes only. 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

Price risk is the risk that the sale price falls, which hurts when rates rise. Both come from the same rate move, with opposite signs.

Investment horizon, price risk vs reinvestment risk, and duration gap Fixed Income

Almost every central bank names one overarching objective: price stability. In practice that means controlling inflation, so that money keeps its value as a medium of exchange and a unit of account.

The role of central banks Economics

A price taker must accept the market price, because its output is too small to move it. Under monopolistic competition there are many firms, each selling a slightly different product, so each has a little pricing power.

The four market structures compared Economics

The $E(\cdot)$ marks an expected value, because the future price is not known today. The expected price at the end is often an analyst's price target.

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

The price to free cash flow to equity is the price divided by next year's FCFE. Under constant growth it is the reciprocal of the gap between the cost of equity and growth.

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

The price to tangible book value removes intangible assets such as goodwill from book value.

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

The price value of a basis point (PVBP) is the change in a bond's full price for a 1 bp change in yield. Instead of using a duration figure, you reprice the bond a basis point down and a basis point up, take the difference and halve it.

Money duration and PVBP Fixed Income

The pairing rule decides which multiples make sense. This is price versus EV multiples: EV goes with figures that belong to lenders and shareholders together (revenue, earnings before interest and taxes (EBIT), EBITDA, free cash flow to the firm (FCFF), which includes after-tax interest to lenders, and book value of capital).

Enterprise value multiples Equities

The mark-to-market (MTM) value starts at zero and then moves with interest rates and with the passing of time. This is the price versus value of a swap distinction the exam tests.

Swap value after inception: time and rate changes Derivatives

Price above it and customers buy elsewhere; price below it and rivals follow, starting a price war. Over the long run, competition pushes price toward marginal cost, so returns settle around the cost of capital.

Revenue drivers and pricing power Equities

In price weighting each constituent's weight is its share price divided by the sum of all the prices. The aggregate is the sum of one share of each constituent, and the index value is that sum divided by a divisor.

Price-weighted and equal-weighted indexes Quantitative Methods

With a price-setting option, a firm facing demand beyond its capacity raises prices instead of output. With a production flexibility option, it changes output when demand differs from the forecast, for instance by adding overtime or extra shifts.

Real options Corporate Finance

The price-to-book (P/B) ratio compares the two.

Book value, market capitalization and enterprise value Equities

The price-to-book ratio (P/B) compares the price with the net assets shareholders own on the books. A higher P/B goes with a higher ROE relative to the cost of equity (the justified P/B of Lesson 1) and a higher payout.

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

The price-to-dividend multiple is the price divided by dividends per share. It is usually shown upside down as the dividend yield, dividends per share divided by price.

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

look at value to shareholders. The best known is the price-to-earnings (P/E) ratio.

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

The price-to-earnings ratio (P/E) divides a share price by earnings per share. Divide the Gordon value by next year's earnings and you get the forward price-to-earnings ratio, the price divided by expected earnings.

Implied return and implied growth Quantitative Methods

The price-to-earnings ratio (P/E) divides the share price by earnings per share. EPS is net income divided by the weighted average shares outstanding during the period.

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

A start-up valuation skips the near-term cash flows and focuses on the terminal value: expected revenue at the end of the horizon times a price-to-sales (P/S) terminal value multiple taken from later-stage peers, discounted at the investor's target return.

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

The price-to-sales ratio (P/S) divides the share price by annual net sales per share, where net sales are total sales minus returns and customer discounts.

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

Graphically, modified duration is the slope of the price–yield curve at today's yield, scaled by the price. The curve bends, so the straight tangent line is exact only at the point where it touches.

Modified duration Fixed Income

The price/earnings-to-growth (PEG) ratio divides the P/E by expected EPS growth. Enter growth as a percentage number, so 20% growth is 20.

Valuing with multiples: comparables and forecasted fundamentals Equities

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

A pricing model describes how customers are billed for units of a product or service. Many exist because "a unit" can be defined in many ways, and prices can vary by quality, units sold, channel, customer size and type, or unit cost.

Pricing and revenue models Corporate Finance

Pricing power is a company's ability to freely set prices and other terms for its products without hurting demand.

Revenue drivers and pricing power Equities

In the primary bond markets an issuer sells new bonds to raise money. In the secondary bond markets investors trade existing bonds with each other.

Primary and secondary bond markets vs equity markets Fixed Income

A primary dealer is a financial intermediary the government designates to take part in every auction with competitive bids.

Government bond auctions and trading vs corporate bonds Fixed Income

The primary equity market is where an issuer lists and sells a new equity security to raise ownership capital, or where existing private stakes become publicly traded shares.

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

A hedge fund usually borrows from a prime broker. In margin financing, the broker lends the fund the securities or cash, and the fund deposits cash or other collateral in a margin account, based on set fractions of its positions.

Leverage, redemptions, lockups and gates Alternative Investments

In the US, lenders separate prime loans from subprime loans. Prime borrowers have strong employment and credit histories, a low DTI, substantial equity and a first lien.

Residential mortgage loans: the features that matter Fixed Income

The principal (also par value or face value) is the amount the issuer agrees to repay. Some debt repays principal in pieces, as a mortgage does, rather than as one lump sum at maturity.

The features of a bond Fixed Income

A principal vs agent test asks who controls the good or service before it goes to the customer. The one that does, and bears the inventory and price risk, reports the full price.

Revenue recognition: the five-step model Financial Statement Analysis

The issuer's managers accept it because the first-day jump raises the value of their own shares, while the lost proceeds are a cost to the firm. That is a principal-agent problem: shareholders are the principals, managers the agents (see stakeholder conflicts).

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

A principal-agent relationship exists when one party (the principal) hires another (the agent) to perform a task.

Principal-agent problems and stakeholder conflicts Corporate Finance

A principal-only (PO) security receives only principal. Its holder gets par, so a faster return of principal raises its value: when rates fall and prepayments rise, a PO gains.

Mortgage pass-throughs and CMOs Fixed Income

The logic is the principle of no arbitrage: similar assets should trade at similar prices. No two firms are identical, but if investors see two firms as close substitutes, their multiples should be close too.

Valuing with multiples: comparables and forecasted fundamentals Equities

Start with the prior probability, your view of the event before the news; it is also called the a priori or ex ante probability.

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

A prior-firm record may be shown if it is clearly identified as the record of a prior entity, and fair, accurate and complete.

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

Lenders hold a priority claim: they are paid before shareholders, both in operations and if the company is wound up.

Debt vs equity: lenders and shareholders Corporate Finance

The most senior debt has the first claim on the issuer's cash flows and assets, and the level of seniority drives how much an investor gets back. That order is the priority of claims.

Seniority, recovery rates and notching Fixed Income

Under priority of transactions, trades for clients and the employer must come before trades in any account where you hold beneficial ownership.

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

Private capital is funding for companies that comes from neither the public equity nor the public debt market.

What makes an investment alternative: features and categories Alternative Investments

A public (listed) company has some or all of its shares listed and traded on a stock exchange, a rules-based, open market where prices and volumes are visible. A private company has no listed shares.

Public vs private companies, going public and going private Corporate Finance

Lenders and investors write loan covenants and reporting requirements and so monitor the reports closely. The limit is the incentive it creates: a covenant that depends on reported numbers gives managers a reason to manage them.

Why managers misreport, and what stops them Financial Statement Analysis

Private debt is debt that investors provide directly to private entities. It grew quickly in the years after the 2008 financial crisis, when tighter regulation reduced lending by traditional lenders and private lending funds filled the gap between what borrowers wanted and what banks would supply.

Private debt: direct lending, mezzanine, venture and distressed debt Alternative Investments

Private debtholders are banks and other institutions that provide loans, credit lines and leases. They often hold to maturity and typically have direct access to management and non-public information, so they know more about the borrower.

Corporate stakeholders and their interests Corporate Finance

Private capital is funding for companies that comes from neither the public equity nor the public debt market. Equity is private equity; loans and other debt are private debt.

What makes an investment alternative: features and categories Alternative Investments

A private equity fund buys, improves and sells portfolio companies; a venture capital fund does this for young companies.

Mutual funds, ETFs and other pooled investment products Portfolio Construction

Private equity securities are issued mainly to institutional investors through a private placement, a sale to selected buyers instead of the general public.

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

A private investment in public equity (PIPE) belongs here. A listed company facing a restructuring must raise equity quickly, so it sells new shares privately to a small group of investors.

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

A private limited company (a limited liability company, or LLC, in the United States, a GmbH in Germany or a société à responsabilité limitée, or SARL, in France) caps the number of owners and restricts share transfers, and in many places it is taxed as a pass-through business.

Organizational forms of businesses Corporate Finance

A sale can be a public offering, open to anyone, or a private placement.

Primary and secondary bond markets vs equity markets Fixed Income

Private placements. Strict limits and supervisory review. They can be offered as an enticement for continued business, and holders have a reason to push the investment to clients later.

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

A government sells all or part of a state-owned company to the public, called a privatization.

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

The pro forma balance sheet picks up every result, and it must balance.

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

Then net income, depreciation, the working capital change, capex and the financing plan give the pro forma cash flow statement.

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

Other names are pro forma earnings, non-IFRS measures and alternative performance measures.

Non-GAAP measures and other presentation choices Financial Statement Analysis

The pro forma income statement is built top down in four steps: revenue, operating costs (cost of sales, then selling, general, and administrative expenses, or SG&A), operating profit, and finally the non-operating items (interest, tax and the share count).

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

Build pro forma statements from these. Companies use pro forma statements internally for budgets and in presentations to lenders, and a full model is covered in the financial modeling module.

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

When demand exceeds supply, an oversubscribed issue must be allocated pro rata: each eligible order receives the same fill ratio, at the same price, on a round-lot basis to avoid odd lots.

Standard III(B): Fair Dealing Ethical and Professional Standards

How likely an outcome is.

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

For a continuous variable, probability is the area under the probability density function (PDF) between two points.

Random variables and distribution functions Quantitative Methods

The mean looks forward: it is a forecast built from a probability distribution, a list of outcomes with the probability of each, summing to 1.

Unconditional expected value, variance and standard deviation Quantitative Methods

For a discrete variable, the probability mass function (PMF) lists P(X = x) for every outcome. The probabilities add to 1, and the probability of a range is the sum over the outcomes in it.

Random variables and distribution functions Quantitative Methods

The first is the probability of default (POD), usually stated for one year. The second is the loss given default (LGD).

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

The better route is to make the probability of distress explicit. Weight the going-concern value and the distress sale value by their probabilities.

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

Probability sampling gives every member an equal chance of being picked, so the result can be representative and the error can be measured.

Sampling methods and sampling error Quantitative Methods

A probability tree (also called a decision tree) shows an uncertainty that plays out in stages. Each point where the uncertainty resolves is a node.

Probability trees, conditional expectations and conditional variance Quantitative Methods

Value each scenario, weight each value by its probability and add them up. That gives the probability-weighted equity value.

Scenario analysis with probability weights Equities

It is better modeled as an explicit scenario with a probability. The result is a probability-weighted scenario value.

Where DCF and growth models break down Equities

These proceeds from sale of equipment are an inflow in cash flow from investing activities. The gain or loss is not cash: it only tells you how the price compares to book value.

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

Inventory is recorded at the cost of getting the goods to where they are sold, in the condition they are sold. These product costs sit on the balance sheet until the goods are sold.

FIFO, LIFO and weighted average when prices rise or fall Financial Statement Analysis

Product differentiation is what gives the firm that pricing power: quality, features, brand, location or service that buyers will pay for.

Monopolistic competition: price, output and the long run Economics

Product mix. If a low-margin product, segment or region is forecast to grow faster than the rest, the overall margin should fall, even if you do not know each margin precisely.

Expense models: margins, itemization and operating leverage Equities

With a production flexibility option, it changes output when demand differs from the forecast, for instance by adding overtime or extra shifts.

Real options Corporate Finance

A profession is an occupational community with specific education, expert knowledge and a framework of practice and behavior that supports trust, respect and recognition.

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

A professional body is the organization that sets and maintains those standards. Employers, regulators, trade associations and not-for-profit groups can all support an industry, but they generally do not exist to set and police professional standards, so they are not professional bodies.

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

Maintain and improve your own competence, and strive to help other investment professionals improve theirs.

The six principles of the Code of Ethics Ethical and Professional Standards

Lying, cheating, stealing and other dishonest acts breach the Standard when they are part of your professional conduct (see the next section).

Standard I(D): Misconduct Ethical and Professional Standards

The Board of Governors keeps oversight and ultimate responsibility for the Professional Conduct Program (PCP).

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

Standard III(E) is not meant to stop you cooperating with a Professional Conduct Program investigation. When permissible under applicable law, treat the Program as an extension of yourself if it asks for client information in an inquiry into your own conduct.

Standard III(E): Preservation of Confidentiality Ethical and Professional Standards

Self-disclosure. Each year members and candidates complete the Professional Conduct Statement and must report anything that questions their conduct, such as civil litigation, a criminal investigation or a written complaint against them.

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

No particular continuing education or professional development plan is mandated. The Standard recommends considering the activities in the tree above: regular professional development, studying for certifications, conferences, employer training, self-study, expert groups and learning new skills when your responsibilities change.

Standard I(E): Competence Ethical and Professional Standards

Practice, and encourage others to practice, in a professional and ethical way that reflects well on you and on the profession.

The six principles of the Code of Ethics Ethical and Professional Standards

You must not engage in professional conduct involving dishonesty, fraud and deceit, and you must not commit any act that reflects adversely on your professional reputation, integrity or competence.

Standard I(D): Misconduct Ethical and Professional Standards

Professionalism is competence plus ethics, applied consistently, with client interests first. A professional uses specialized knowledge in service to others.

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

The payoff is what the option is worth at expiration, before counting what was paid for it. The profit subtracts the premium.

Call and put options: payoff and profit at expiration Derivatives

Strong, stable earnings are the main source of repayment. Analysts focus on recurring operating profit, not one-off gains, and watch for a downturn in a cyclical business or a falling market share.

Assessing corporate creditworthiness Fixed Income

Profitability ratios come in two families: returns on sales (margins) and returns on investment. The margins are the common-size income statement in ratio form.

Profitability ratios: margins and returns on capital Financial Statement Analysis

Makers of large, long-term products such as aircraft may value inventory by program accounting, which looks at the profitability of a whole program rather than the cost of each unit, so deferred production costs can build up in inventory.

Operating profitability and working capital Equities

The SEC also sets prohibited adjustments. A non-GAAP liquidity measure may not exclude charges that need cash settlement, except earnings before interest and taxes (EBIT) and EBITDA.

Non-GAAP measures and other presentation choices Financial Statement Analysis

Projected future multiples put forecasts in the denominator (forward P/E, FY1, FY2) to compare a company with a benchmark on expected rather than past results.

Trailing, current and forward multiples Equities

Since the 2023 revision the Standard spells this out: a prominent plain-language disclosure is placed where the reader will see it, uses everyday words, and communicates the relevant information effectively.

Standard VI(A): Avoid or Disclose Conflicts Ethical and Professional Standards

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

Under proof of stake, selected participants called validators pledge (stake) capital to vouch for a block. A validator proposes a block, a majority of the other validators who have also staked assets must attest that it is valid, and validators are rewarded for both proposing and attesting.

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

Under proof of work, the right to add the next block is decided by a computationally costly lottery. The miners on the network use powerful computers and a great deal of energy to solve a cryptographic puzzle, and the winner locks the block into the chain and earns new cryptocurrency.

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

Proper and improper references are tested by comparing pairs.

Standard VII(B): Reference to CFA Institute, the CFA Designation, and the CFA Program Ethical and Professional Standards

An analyst who visits stores and interviews shoppers is doing proprietary primary research. Industry and peer information put the company's results in perspective, and a consumer-products analyst will usually try the product firsthand.

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

Prospective application means current and future periods only; nothing is restated.

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

The prospectus describes the structure: the priority and amount of payments to the servicer, administrators and each class of securities, and the credit enhancements used.

The securitization process and its parties Fixed Income

In a CDS, the protection buyer pays the protection seller to take on the risk of loss if a third party, the reference entity, defaults.

Credit default swaps Derivatives

In a CDS, the protection buyer pays the protection seller to take on the risk of loss if a third party, the reference entity, defaults.

Credit default swaps Derivatives

Here are the two portfolios. The protective put is a long share plus a long put on it.

Put–call parity: fiduciary call = protective put Derivatives

The usual fix is a proxy: a similar instrument, or a weighted mix of several, stands in for the missing history.

Historical simulation and historical value at risk Quantitative Methods

A manager of a large, diversified portfolio faces thousands of meetings across many markets, so institutions often hire a proxy advisor.

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

In a proxy contest (or proxy fight), a group seeking a board majority persuades shareholders to vote for its nominees.

Corporate governance mechanisms Corporate Finance

The proxy statement (Form DEF 14A) goes to shareholders before a meeting. It covers proposals to be voted on, ownership by management and principal owners, director biographies and executive compensation.

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

Voting usually happens at the annual meeting, in person or by proxy vote, where another shareholder, a shareholder representative or management votes on the holder's behalf.

Common shares and preference shares Equities

Proxy voting is part of the duty. Proxies have economic value for clients, and you must vote in an informed and responsible way.

Standard III(A): Loyalty, Prudence, and Care Ethical and Professional Standards

You owe every client a duty of loyalty: act for the client's benefit and place the client's interests before your employer's and your own. You must also use prudence and care.

Standard III(A): Loyalty, Prudence, and Care Ethical and Professional Standards

A public (listed) company has some or all of its shares listed and traded on a stock exchange, a rules-based, open market where prices and volumes are visible.

Public vs private companies, going public and going private Corporate Finance

Public censure is a public rebuke. Suspension removes membership and the right to use the designation for a period.

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

Make reasonable efforts to bring about public dissemination, usually by encouraging the issuing company to announce it.

Standard II(A): Material Nonpublic Information Ethical and Professional Standards

A public limited company has no legal cap on owners or on transfers, which suits a company that wants to list its shares.

Organizational forms of businesses Corporate Finance

A sale can be a public offering, open to anyone, or a private placement.

Primary and secondary bond markets vs equity markets Fixed Income

A public–private partnership (PPP) is an agreement for the public and private sectors to finance, build and run public infrastructure.

Ownership structures: general and limited partners Alternative Investments

A public–private partnership (PPP) is a long-term contract under which the private sector delivers a project or service that the public sector traditionally provided.

Infrastructure: economic vs social, greenfield vs brownfield Alternative Investments

Publicly listed equity is shares listed on an exchange. Ownership is spread widely among individuals and institutions, prices are quoted all day, and the company must publish detailed, audited results.

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

A pull on liquidity is a speeding-up of cash outflows, or a limit on trade credit that forces the company to pay out before it has received cash from sales.

Liquidity sources and liquidity ratios Corporate Finance

As maturity approaches, the remaining cash flows shrink in number and the price is pulled to par, provided the issuer does not default. This is the constant yield-price trajectory, and the pull itself is called pull to par.

How price, coupon, maturity and yield are related Fixed Income

Between resets the flat price drifts above or below par if rates have moved, and it is pulled to par as the next reset approaches.

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

Fraud in many forms: scam initial coin offerings (ICOs), market manipulation, theft, phishing for wallet credentials, and schemes such as pump and dump, where early holders talk an asset up, sell into the rush of buyers, and leave the latecomers with steep losses.

Ways to invest in digital assets: direct and indirect Alternative Investments

Besides the standard bond indenture and covenants, two documents matter. The purchase agreement is between the seller and the SPE.

The securitization process and its parties Fixed Income

Accounting standards require the purchase price allocation in three steps.

Goodwill: how it is measured and tested Financial Statement Analysis

The idea behind purchasing power parity (PPP) is that, with identical goods and no frictions, nominal rates would adjust until the same basket costs the same everywhere.

Nominal vs real exchange rates Economics

Putable preference shares give the holder the right, not the obligation, to sell them back at a set price, the put contingency price.

Common shares and preference shares Equities

A call option gives the right, but not the obligation, to buy a share at the exercise price. A put option gives the right, but not the obligation, to sell.

Forward exchange rates and option values by no arbitrage Quantitative Methods

The same way, with the put's payoffs. π depends on the share's moves and r, not on the option, so the same π prices every option on the share. This is put valuation in the tree.

Pricing calls and puts with risk-neutral probabilities Derivatives

Both pay the greater of S_T and X at expiry, so they cost the same. That is put–call forward parity.

Put–call forward parity Derivatives

So their prices today must match. That equality is put–call parity.

Put–call parity: fiduciary call = protective put Derivatives

With put–call parity, which holds for any pair of European options with the same strike and expiry. This is the put–call parity check: S₀ + p₀ = c₀ + X ÷ (1 + r).

Pricing calls and puts with risk-neutral probabilities Derivatives

A putable bond gives the investor the right to sell the bond back to the issuer at a set price, usually par, on set dates.

Callable, putable and convertible bonds Fixed Income

Putable preference shares give the holder the right, not the obligation, to sell them back at a set price, the put contingency price.

Common shares and preference shares Equities

Putable preferred stock: the investor can sell the shares back to the issuer at par or a set price. The investor holds the right, so putable shares carry a lower dividend than similar non-putable ones.

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