FRM Part I key terms

A firm-wide process for identifying, measuring, and managing all material risks together rather than in isolated silos, so that aggregate risk stays within the organization's stated appetite.

The amount and type of risk an organization is willing to accept in pursuit of its objectives, usually expressed through limits, targets, and qualitative statements approved by senior management or the board.

The tendency for one party to take greater risks or behave less carefully because another party bears the consequences, often arising when information is hidden after a contract is signed.

A market failure in which one side of a transaction has information the other lacks before contracting, causing higher-risk participants to be selected disproportionately and potentially driving safer participants out of the market.

A conflict of interest that arises when managers or agents act in their own interest rather than in the interest of the principals-owners or shareholders-who delegated decision-making authority to them.

A model that prices an asset using its sensitivity to the overall market, stating that expected excess return equals beta multiplied by the market's expected excess return.

A measure of how much an asset's return tends to move with the market portfolio; a beta above one indicates amplified market sensitivity, while a beta below one indicates dampened sensitivity.

A performance measure equal to the portfolio's average excess return over the risk-free rate divided by the standard deviation of its returns, capturing reward per unit of total risk.

A result stating that the sum or average of many independent random variables tends toward a normal distribution as the sample grows, regardless of the shape of the underlying distribution.

A range constructed from sample data that is expected to contain the true population parameter in a stated proportion of repeated samples, such as 95% of the time.

The probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one computed from the sample; small values suggest the null is unlikely.

Rejecting a true null hypothesis, which is equivalent to a false positive; the probability of this error equals the significance level chosen for the test.

A regression estimation method that chooses coefficients minimizing the sum of squared differences between observed values and the values predicted by the fitted linear model.

The proportion of the total variation in the dependent variable explained by the regression, ranging from zero to one, with higher values indicating a better-fitting model.

A condition in which two or more independent variables in a regression are highly correlated, making individual coefficient estimates imprecise even if the overall model fits well.

A measure of the asymmetry of a distribution: positive skew means a longer right tail and negative skew a longer left tail, relative to a symmetric normal distribution.

A measure of how heavy the tails of a distribution are compared with the normal distribution; excess kurtosis above zero signals more frequent extreme outcomes than normal.

A family of models in which current conditional variance depends on past squared shocks and past variances, commonly used to capture volatility clustering in financial return series.

A private agreement to buy or sell an asset at a specified price on a future date, with terms negotiated between two parties and no exchange or clearinghouse involved.

A standardized, exchange-traded agreement to buy or sell an asset at a set price on a future date, marked to market daily and guaranteed by a clearinghouse.

An agreement between two parties to exchange interest payments, typically one fixed and one floating, calculated on a specified notional principal over a set term.

A contract in which one party pays periodic premiums and receives compensation if a specified reference entity experiences a credit event, effectively transferring default risk.

A no-arbitrage relationship linking European call and put prices with the same strike and maturity: the call minus the put equals the stock price minus the present value of the strike.

A short-term secured borrowing in which one party sells securities and agrees to buy them back later at a higher price, with the difference reflecting the implied interest rate.

The difference between the spot price of an asset and its futures price, or between two related prices; it narrows toward zero as the futures contract approaches maturity.

The non-monetary benefit of holding a physical commodity rather than a futures position, such as avoiding supply disruptions, which reduces the cost of carrying the commodity forward.

The particular bond or asset that a short futures position holder finds most economical to deliver against the contract, typically the one with the lowest net purchase-and-delivery cost.

An entity that interposes itself between trade counterparties, becoming buyer to every seller and seller to every buyer, and manages default risk through margin and a default fund.

A loss threshold that, over a specified horizon and confidence level, is expected to be exceeded only with a stated small probability, summarizing downside risk in a single number.

The average loss conditional on losses exceeding the value at risk threshold, also called conditional VaR; it captures tail severity and is more sensitive to extreme outcomes.

The rate of change of an option's price with respect to a small change in the underlying asset's price, often interpreted as the equivalent number of underlying shares.

The rate of change of an option's delta with respect to the underlying price; high gamma means delta shifts quickly, making hedges unstable for large price moves.

The sensitivity of an option's price to a change in the volatility assumption, measuring how much value is added or lost when implied volatility rises or falls.

A closed-form option pricing framework assuming lognormal stock prices, constant volatility and rates, and no arbitrage, which values European options from replicating portfolio arguments.

A valuation approach that computes expected payoffs using probabilities adjusted so all assets earn the risk-free rate, then discounts at that rate to obtain arbitrage-free prices.

A measure of a bond's price sensitivity to interest rate changes, often expressed as the weighted average time until cash flows are received; modified duration gives percentage price change per rate change.

A second-order measure of how a bond's duration changes as yields change, capturing the curvature of the price-yield relationship and improving estimates of price changes for larger rate moves.

The change in a bond or portfolio's value for a one-basis-point parallel shift in interest rates, providing a simple cash measure of interest rate exposure.

The volatility input that, when inserted into an option pricing model, makes the model's value equal the observed market price; it reflects the market's current volatility expectation.

A structural credit risk model treating a firm's equity as a call option on its assets, so default occurs when asset value falls below debt at maturity.