CFA Level I flashcards

The spread over the reference rate that equates a floating-rate note's discounted cash flows to its market price; compared to the quoted margin to determine premium/discount pricing.

• Quoted margin = fixed spread stated at issuance
• Discount margin > quoted margin → bond priced at a discount
• Discount margin < quoted margin → bond priced at a premium

Memory trick: 'Higher required margin, lower price — risk demands a discount'

Members must disclose all actual and potential conflicts of interest to employers, clients, and prospective clients in a manner that ensures transparency.

• Board memberships in covered companies are classic conflicts
• Disclosure must be prominent and in plain language
• Conflicts should be disclosed before, not after, providing advice

Memory trick: Sunlight is the best disinfectant for conflicts.

Portfolio standard deviation ranges between |wAσA − wBσB| (at ρ = −1) and wAσA + wBσB (at ρ = +1), illustrating the maximum diversification benefit at perfect negative correlation.

• ρ = +1: no diversification benefit, SD = weighted average
• ρ = −1: maximum diversification benefit, SD = |difference of weighted SDs|
• ρ = 0: partial diversification benefit, SD < weighted average

Memory trick: Opposites cancel: at ρ=−1, risks fight and shrink to their difference.

Members and candidates must not undertake conduct that compromises the integrity or reputation of the CFA designation or the CFA Program, including disclosing exam content.

• Confidentiality of exam content is permanent
• Includes cheating, sharing questions, and violating Candidate Pledge
• Also covers actions like exam impersonation and copyright violations

Memory trick: What happens in the exam room stays confidential forever.

The cost of preferred stock equals the fixed preferred dividend divided by the net issuance price (market price minus flotation costs).

• Formula: rp = Dp / Net proceeds per share
• Flotation costs reduce net proceeds, increasing effective cost
• Preferred dividends are not tax-deductible, unlike interest on debt

Memory trick: Divide the dividend by what you actually pocket after fees.

The expected value of a discrete random variable is the probability-weighted average of all possible outcomes.

• E(X) = sum of [P(X_i) x X_i]
• Probabilities across all scenarios must sum to 1.0
• Used as the basis for calculating variance and standard deviation of returns

Memory trick: Weight, multiply, then add — that's expectation's trade.

CFO is computed by starting with net income and adjusting for noncash items and changes in operating working capital accounts.

• Add back noncash expenses like depreciation
• Increase in operating asset = cash outflow (subtract)
• Decrease in operating liability = cash outflow (subtract)

Memory trick: Assets up = cash down; Liabilities down = cash down

Progressive/proportional taxes reduce the size of the fiscal multiplier because a portion of additional income is taxed away, lowering the marginal propensity to spend out of GDP.

• Multiplier = 1/[1-MPC(1-t)]
• Higher tax rate t reduces multiplier size
• Automatic stabilizers smooth business cycle swings without new legislation

Memory trick: Taxes act like a shock absorber, softening every spending bump.

A high-water mark ensures a hedge fund manager only earns incentive fees on new profits that exceed the fund's previous highest NAV, preventing fees on recovered losses.

• Protects investors from paying twice for the same gains
• Fee only applies to NAV growth above the prior peak
• Common alongside incentive fees in hedge fund structures

Memory trick: No fee for climbing back to where you already were — only for new heights.

The primary market is where new securities are issued directly by companies to raise capital; in firm commitment underwriting, the investment bank buys the entire issue and assumes the risk of reselling it.

• Primary market = new issuance; proceeds go to issuer
• Secondary market = trading among investors, no new capital raised
• Firm commitment shifts unsold-share risk to underwriter; best-efforts does not

Memory trick: Primary pays the company; secondary just swaps shares.

Roll yield is the return earned (or lost) when an investor rolls a futures position from an expiring contract into a new one; it is positive in backwardation and negative in contango.

• Backwardation: near price > far price → positive roll yield
• Contango: near price < far price → negative roll yield
• Roll yield is a key driver of returns for commodity index investors

Memory trick: Back-warders sell high, buy low — contango costs you dough.

In a plain vanilla interest rate swap, only the net difference between the fixed and floating payments is exchanged at each settlement date.

• Net payment = (Fixed rate - Floating rate) × Notional
• Fixed-rate payer pays when fixed > floating
• Only the net amount is exchanged, not gross payments

Memory trick: Swap streams net out — only the difference crosses the table.

A t-test on a regression slope coefficient tests whether the estimated coefficient differs significantly from a hypothesized value, using the coefficient's standard error.

• t = (b1 - hypothesized value) / standard error of b1
• Degrees of freedom = n - k - 1, where k is the number of independent variables
• Fail to reject H0 if |t-statistic| is less than the critical t-value

Memory trick: Subtract the hypothesis, divide by the error, compare to the fence.

Under IFRS, an asset is impaired when its carrying amount exceeds its recoverable amount, defined as the higher of fair value less costs to sell and value in use.

• Recoverable amount = higher of FV less costs to sell and value in use
• Impairment loss = Carrying amount − Recoverable amount
• IFRS impairments can be reversed (except for goodwill); US GAAP impairments generally cannot

Memory trick: Recover the HIGHER value, then subtract from carrying amount

A perfectly competitive firm should shut down in the short run if price falls below average variable cost, since it cannot cover variable costs.

• Shutdown point: P < AVC
• Firm operates at a loss if AVC < P < ATC
• Long-run exit occurs when P < ATC persistently

Memory trick: 'AVC or bust' — if price can't cover variable cost, shut the doors.

GIPS requires all fee-paying, discretionary portfolios meeting a composite's definition to be included; discretion is judged by actual investment authority, not by administrative relabeling by the firm.

• Asset-weighted composite return: sum(weight × return) across portfolios
• Reclassifying a portfolio to avoid inclusion without genuine change in authority violates GIPS
• Substance-over-form governs discretionary status determinations

Memory trick: "Relabeling a loser doesn't make it non-discretionary."

Appraisal-based real estate indices tend to understate true volatility and correlation with other asset classes because appraisals are infrequent and appraisers partially anchor to prior valuations, smoothing reported returns.

• Smoothing biases volatility estimates downward
• Repeat-sales/transaction-based indices better reflect true market volatility
• This affects real estate's apparent diversification benefit in portfolio analysis

Memory trick: Appraisals lag reality — smoothing hides the true bumps.

Measures the responsiveness of quantity demanded of one good to a price change in another good.

• Positive value = substitutes
• Negative value = complements
• Zero value = unrelated (independent) goods

Memory trick: Positive sign = Partners in substitution; Negative sign = Necessary complement.

Members must disclose the basic format and general principles of investment processes, distinguish fact from opinion, and communicate on an ongoing basis with clients about material changes.

• Reports must separate factual data from analyst opinion/estimates
• Must maintain records supporting recommendations
• Applies to written and oral communications

Memory trick: Facts are proven; opinions are labeled.

A cross rate is an exchange rate between two currencies derived from their common relationship to a third currency (often USD).

• Cross rate = (quote/base for currency A) ÷ (quote/base for currency B) when both are quoted vs same currency
• Ensure consistent quotation convention before dividing
• Reciprocal of a cross rate reverses the currency pair

Memory trick: Cancel the common currency like canceling units in a fraction.

A no-arbitrage relationship linking the prices of European calls and puts with the same strike and expiration: c + PV(X) = p + S0.

• p = c - S0 + PV(X)
• c = p + S0 - PV(X)
• Assumes European-style options and no dividends

Memory trick: Fiduciary call equals protective put — balance the equation to isolate the missing price.

The required return on equity based on the risk-free rate plus a risk premium proportional to systematic risk (beta).

• re = Rf + β(Rm − Rf)
• Beta measures sensitivity to market movements
• Higher beta implies higher required equity return

Memory trick: Risk-Free plus Beta times Market Premium equals required Return

Covered interest rate parity states that the forward exchange rate must adjust for the interest rate differential between two currencies to prevent arbitrage.

• F = S × (1+r_domestic)/(1+r_foreign)
• Higher domestic rate implies forward premium on foreign currency
• Prevents riskless arbitrage between money markets and FX forwards

Memory trick: Higher rate currency's counterpart trades at a forward premium — quote domestic over foreign.

A market order executes immediately at the best available prices, potentially filling across multiple price levels of the order book if the order size exceeds the volume available at the best price, resulting in an average execution price different from the quoted best price.

• Market orders prioritize speed over price certainty
• Large orders may 'walk the book,' filling at successively worse prices
• Average execution price is a quantity-weighted average across fill levels

Memory trick: Big orders climb the ladder of asks.

In an equal-weighted index, each constituent receives the same dollar weight, so the index return equals the simple (arithmetic) average of the individual stock returns.

• Weight per stock = 1/n regardless of price or market cap
• Index return = simple average of constituent returns
• Requires periodic rebalancing to maintain equal weights

Memory trick: Equal weight, equal voice — just average the returns.

The binomial model prices an option by computing a risk-neutral probability of an up move, then discounting the expected payoff at the risk-free rate.

• Risk-neutral probability π = (1+r-d)/(u-d)
• Call value = [π×Cu + (1-π)×Cd]/(1+r)
• No investor risk preferences are needed under risk-neutral valuation

Memory trick: Climb the tree with risk-neutral odds, then discount the branch payoffs home.

Values a stock when dividend growth declines linearly from a high initial rate to a stable long-term rate over a specified transition period, using a half-life adjustment (H).

• H = one-half of the transition period in years
• Formula: V0 = D0/(r-gL) × [(1+gL)+H(gS-gL)]
• Approximates a more complex multistage model with a single closed-form expression

Memory trick: Growth glides down like a ramp — take the midpoint (H) to capture the slope.

A deferred tax liability arises when tax depreciation exceeds book depreciation, causing taxable income to be temporarily lower than pretax financial income; it represents taxes that will be paid in future periods.

• DTL = Temporary difference × Tax rate
• Accelerated tax depreciation vs. straight-line book depreciation is a common source of DTLs
• The temporary difference reverses over the asset's life as book depreciation eventually exceeds tax depreciation

Memory trick: Tax deducts fast, liability grows last.

The full approximation for a bond's percentage price change combines the linear duration effect and the curvature convexity effect: %ΔP ≈ −ModDur×Δy + 0.5×Convexity×(Δy)².

• Convexity term is always added, improving accuracy for large yield changes
• Positive convexity benefits bondholders in both rising and falling yield scenarios
• Duration-only estimates understate price increases and overstate price decreases

Memory trick: Duration is the line, convexity is the curve that saves you.

A long straddle combines a long call and a long put at the same strike, profiting from large price moves in either direction once the combined premium is exceeded.

• Total cost = call premium + put premium
• Profit = combined payoff − total premium paid
• Breakeven points are Strike ± total premium

Memory trick: Straddle the strike — big moves either way pay off once premiums are covered.

The total probability rule calculates the unconditional probability of an event by summing the probabilities of that event occurring within each mutually exclusive and exhaustive scenario, weighted by the scenario's probability.

• P(A) = sum of P(S_i) x P(A|S_i) across all scenarios S_i
• Scenarios must be mutually exclusive and exhaustive
• Widely used to combine conditional probabilities into an overall probability

Memory trick: Weight each conditional outcome by its scenario's chance, then add.

The amount by which a convertible bond's market price exceeds its conversion value (the value if immediately converted into shares).

• Conversion value = conversion ratio × current stock price
• Premium reflects the value of the option to convert later at a potentially higher stock price
• Premium tends to shrink as the stock price rises well above the conversion price

Memory trick: 'Bond price minus stock-swap value equals the premium you're paying for optionality'

The J-curve describes the typical pattern of PE fund IRR over time: negative returns in early years due to fees and unrealized investments, followed by rising positive returns as investments mature and are exited.

• Named for the shape of the return curve over time
• Driven by front-loaded fees and slow early value creation
• Returns typically improve as portfolio companies are exited in later fund years

Memory trick: Dip like a J before you rise — fees first, fortune later.

DOL measures the sensitivity of EBIT to changes in sales, driven by the proportion of fixed operating costs in the cost structure.

• DOL = Contribution Margin / EBIT
• Higher fixed costs relative to variable costs increase DOL
• Higher DOL means greater EBIT volatility for a given change in sales

Memory trick: Fixed costs act like a lever — small sales moves, big EBIT swings.

DOH measures the average number of days a company holds inventory before selling it, calculated as 365 divided by inventory turnover.

• Inventory turnover = COGS / Average inventory
• DOH = 365 / Inventory turnover
• Lower DOH generally indicates more efficient inventory management

Memory trick: Turn inventory into turnover, then flip turnover into days.

The price at which a short seller's account equity falls to the maintenance margin level, triggering a margin call, calculated using P0 × (1+IM)/(1+MM).

• Short sellers face margin calls when price rises, not falls
• Formula: Pmc = P0 × (1+initial margin)/(1+maintenance margin)
• Proceeds from the short sale plus margin deposit form the initial equity base

Memory trick: For shorts, rising prices erode equity — flip the long formula's signs.

Members must act for the benefit of their employer and not misappropriate confidential information, trade secrets, or client lists for personal or competitive use.

• General industry knowledge and skills may be taken to a new job
• Confidential records, client lists, and proprietary models may not be taken
• Violation occurs at the time of misappropriation, not at resignation

Memory trick: Take your skills, leave the files.

Members must ensure that performance information communicated to clients or prospects is fair, accurate, and complete, avoiding selective or misleading presentations.

• Cannot cherry-pick best-performing accounts
• Must disclose relevant time periods and methodology
• GIPS compliance is one way to satisfy this Standard

Memory trick: Show the whole orchard, not just the best apples.

For preferred stock or any perpetuity with a constant, non-growing dividend, intrinsic value equals the dividend divided by the required rate of return: V = D / r.

• Applies when dividend growth rate is zero
• Formula is a special case of the Gordon Growth Model with g=0
• Commonly used for valuing perpetual preferred shares

Memory trick: No growth, just divide dividend by required return.

Relative PPP predicts that the exchange rate will adjust so that the currency of the higher-inflation country depreciates by approximately the inflation rate differential relative to the lower-inflation country.

• S1 = S0 × (1+π_price currency)/(1+π_base currency)
• High-inflation currency depreciates
• Long-run FX forecasting tool, imperfect in short run

Memory trick: High inflation, low currency value — PPP evens out purchasing power.

The multiplier effect by which an initial change in government spending leads to a larger change in aggregate output, driven by the marginal propensity to consume.

• Multiplier = 1/(1-MPC) = 1/MPS
• Higher MPC leads to a larger multiplier
• Assumes no crowding out, taxes, or import leakages in simplest form

Memory trick: The bigger the MPC, the bigger the bounce-back spending ripple.

Money duration converts modified duration into a dollar sensitivity measure by multiplying by market value; PVBP is the dollar price change for a 1 bp yield shift.

• Money Duration = Modified Duration × Market Value (or Full Price).
• PVBP = Money Duration × 0.0001.
• Useful for hedging and comparing dollar exposure across bonds of different sizes.

Memory trick: Money duration turns 'percent sensitivity' into 'dollar sensitivity' — then shrink by 0.0001 for PVBP.

Hedge funds typically charge a management fee (percentage of AUM) plus an incentive fee (percentage of profits), often stacked so the incentive fee is calculated on profit after the management fee is deducted.

• Management fee is usually charged regardless of performance
• Incentive fee is typically 15–20% of profits
• Order of fee calculation (before/after management fee) affects investor returns

Memory trick: Manage first, then reward the win — fees stack before the incentive fee begins.

FCFF is the cash flow available to all capital providers (debt and equity) after accounting for operating expenses, taxes, and investments in fixed and working capital.

• FCFF = NI + NCC + Int(1−t) − FCInv − WCInv
• Represents cash available to all suppliers of capital
• Used in firm-level DCF valuation

Memory trick: Start with NI, add back non-cash and after-tax interest, subtract investments.

A technique for estimating the required yield or price of an illiquid or newly issued bond by interpolating yields of comparable, actively traded bonds.

• Commonly used for private placements or infrequently traded bonds
• Interpolates by maturity (or duration) between benchmark bonds
• Assumes credit quality and other risk factors are similar

Memory trick: 'Straight line between two known yields finds the missing one'

A private equity performance multiple equal to (cumulative distributions + residual NAV) divided by paid-in capital, showing total value generated relative to invested capital.

• TVPI = DPI + RVPI
• DPI reflects only realized distributions
• A TVPI above 1.0x means the fund has created value above capital contributed

Memory trick: Total value = cash back PLUS what's still on the table.

A valuation approach combining explicit dividend forecasts with a terminal sale price estimated by applying a market multiple (e.g., P/E) to a forecasted future fundamental (e.g., EPS).

• Terminal value = Multiple × Forecasted fundamental in the terminal year.
• All cash flows, including terminal value, must be discounted back to present at the required return.
• This hybrid approach blends fundamental (DDM) and relative (multiples) valuation.

Memory trick: Discount each dividend, then discount the final selling price too — nothing skips the time machine.

In a PE distribution waterfall, after LPs receive their preferred return, a GP catch-up clause allocates profits fully to the GP until the GP's cumulative share equals the target carried interest percentage of total profits, after which remaining profits split per the carry ratio.

• Catch-up ensures GP reaches full target carry (e.g., 20%) despite preferred return to LPs
• Catch-up amount solved via X/(preferred+X) = target carry %
• After catch-up, remaining profit splits per agreed ratio (e.g., 80/20)

Memory trick: LPs get their preferred slice, then GP catches up to their full 20% before sharing the rest.

A method of deriving zero-coupon (spot) rates sequentially from the par yield curve by using previously solved spot rates to price successive coupon bonds.

• Uses no-arbitrage pricing: bond price = PV of cash flows at spot rates.
• Each new spot rate is solved using the prior year's already-known spot rate(s).
• Spot rates form the basis for valuing off-market bonds and computing forward rates.

Memory trick: Bootstrapping = pulling yourself up rate by rate, using last year's spot rate to solve this year's.

States that firm value increases with leverage due to the tax deductibility of interest, with levered value equal to unlevered value plus the present value of the interest tax shield.

• VL = VU + (t × D)
• Assumes perpetual debt and no bankruptcy costs
• Implies 100% debt financing would maximize value in this simplified model

Memory trick: Taxes turn debt into a value-adding shield

An interval estimate for a population mean when the population standard deviation is known, using the z-distribution critical values.

• CI = sample mean ± z × (σ/√n)
• 95% confidence uses z = 1.96
• Use t-distribution instead if population variance is unknown and n is small

Memory trick: Known sigma? Grab the z! Unknown sigma? Reach for t!

An FRA settles at the beginning of the underlying loan period, so the interest rate differential payoff must be discounted back using the observed reference rate.

• Payoff (undiscounted) = (L - FRA rate) × (days/360) × Notional
• Discount factor = 1 + L × (days/360)
• Long FRA gains when reference rate rises above FRA rate

Memory trick: FRAs pay early, so discount the difference back to settlement day.

VaR estimates the minimum loss expected to be exceeded with a given probability over a specified time period, often assuming a normal distribution of returns.

• Formula: VaR = (μ − zσ) × Portfolio Value (loss magnitude is the negative of this)
• Common confidence levels: 95% (z=1.65) and 99% (z=2.33)
• VaR does not indicate the potential magnitude of losses beyond the threshold

Memory trick: Mean minus z times sigma tells you the danger zone

The direct method calculates CFO by directly computing cash collected from customers and cash paid to suppliers and for operating expenses, using accrual figures adjusted for changes in working capital accounts.

• Cash collections = Revenue − Increase in AR (or + decrease)
• Cash paid to suppliers = COGS + Increase in inventory − Increase in AP
• CFO = Cash collections − Cash paid to suppliers − Cash operating expenses

Memory trick: Adjust each accrual line for its matching balance sheet change to get real cash.

A market condition in which stock prices reflect all information — public and private (insider) — so that no investor can consistently earn abnormal returns.

• Strong form subsumes weak-form and semi-strong-form efficiency.
• Implies insider trading would not generate abnormal profits.
• Empirical studies generally reject strict strong-form efficiency (insiders do earn abnormal returns).

Memory trick: Weak sees past, Semi sees public, Strong sees ALL — even secrets.

Effective duration measures interest rate sensitivity using price shocks and is required for bonds with embedded options, whose cash flows change with yields; callable bonds exhibit negative convexity near the call price, limiting upside price gains.

• Effective duration formula: (V₋−V₊)/(2×V₀×Δy)
• Callable bonds show price compression (negative convexity) as yields fall toward the call price
• Effective duration must be used instead of modified duration for bonds with embedded options

Memory trick: Callable bonds hit a ceiling — upside gets capped.

Members must consider a client's full IPS, including risk tolerance, return objectives, time horizon, and constraints, and reconcile any conflicts through client communication before implementing a strategy.

• Required return formula: (FV/PV)^(1/n) − 1
• Conflicts between risk tolerance and return goals must be discussed with the client
• Suitability decisions must reference the client's total IPS, not a single factor

Memory trick: "When goals and comfort collide, talk before you decide."

Members must obtain written consent from their employer before accepting compensation or benefits from clients or others that could create a conflict with the employer's interest.

• Written consent from employer is required, not just disclosure
• Applies to compensation tied to duties performed for the employer's clients
• Failure to seek consent is a violation even if no actual harm occurs

Memory trick: "Outside pay needs an inside okay."

The proportion of directors who have no material financial, family, or employment relationship with the company, enabling more objective oversight of management.

• Independent directors lack material ties to the company or its executives
• A majority-independent board is generally viewed as stronger governance practice
• CEO/chair duality can further reduce the board's independence from management

Memory trick: More insiders on the board means less outside watchdog power

A bond's annual coupon payment divided by its current market price, ignoring capital gains/losses and time value of money.

• Current yield rises above coupon rate when bond trades at a discount
• Ignores reinvestment and price appreciation to maturity
• Simplest yield measure, least comprehensive

Memory trick: Current yield: coupon over price, nothing nice.