FRM Part I Cheat Sheet: Risk, Statistics and Valuation
Review original FRM Part I formula reminders and key distinctions for probability, portfolio risk, bond sensitivity, options and loss measures.
Check the convention before the formula
Record the rate’s compounding convention, time unit, cash-flow date and currency. A correct formula with inconsistent units still gives a wrong result. These reminders support study; use the question’s stated assumptions and the official curriculum for fuller treatment.
Quantitative tools
| Relationship | Reminder |
|---|---|
| Conditional probability | \(P(A\mid B)=P(A\cap B)/P(B)\), for \(P(B)>0\). |
| Expected value | \(E[X]=\sum_i p_i x_i\) for a discrete variable. |
| Variance | \(\operatorname{Var}(X)=E[X^2]-(E[X])^2\). |
| Covariance and correlation | \(\operatorname{Cov}(X,Y)=\rho_{XY}\sigma_X\sigma_Y\). |
| Standard error of an independent sample mean | \(\sigma/\sqrt{n}\) when population standard deviation is known; estimation and dependence change the treatment. |
A p-value is a probability of results at least as extreme as those observed under the specified null model. It is not the probability that the null hypothesis is true. Statistical significance does not by itself establish economic importance or causation.
Portfolio risk
For two assets:
\[ \sigma_p^2=w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2\rho_{12}\sigma_1\sigma_2. \]Diversification depends on joint behavior as well as individual volatility. A historical correlation estimate is not a guarantee of future crisis behavior. Distinguish total risk from the market-related risk summarized by beta.
Bonds and rate sensitivity
For annual cash flows discounted at a single annual yield:
\[ P=\sum_{t=1}^{T}\frac{CF_t}{(1+y)^t}. \]For a small parallel yield change under consistent yield units:
\[ \frac{\Delta P}{P}\approx-D_{\mathrm{mod}}\Delta y. \]Money sensitivity and percentage sensitivity are different. For a one-basis-point shift, first-order dollar DV01 is approximately \(P D_{\mathrm{mod}}\times0.0001\). Divide dollar DV01 by price before comparing relative sensitivity. Convexity becomes more relevant for larger changes; embedded options can change the cash flows and invalidate a simple fixed-cash-flow interpretation.
Options and cash-flow timing
At expiration, a long call pays \(\max(S_T-K,0)\) and a long put pays \(\max(K-S_T,0)\). Payoff excludes the initial premium; profit must account for it and any applicable funding convention.
For European options with the same strike and expiry, known cash dividends, consistent funding and the usual frictionless assumptions:
\[ C+PV(K)+PV(D)=P_{\mathrm{put}}+S_0. \]Here \(P_{\mathrm{put}}\) is the put price, not a bond price, and \(PV(D)\) is the present value of dividends before expiry. Prove a proposed arbitrage with dated cash flows: initial funding, dividends or other interim payments, and terminal payoffs. A positive initial receipt alone is insufficient.
Risk-measure distinctions
| Distinction | What to remember |
|---|---|
| VaR vs expected shortfall | VaR is a loss quantile; expected shortfall summarizes the tail beyond the chosen quantile under the specified definition. State confidence, horizon and loss convention. |
| Market vs credit vs liquidity risk | Price changes, counterparty performance and the ability to transact or fund obligations are related but distinct exposures. |
| Model fit vs predictive evidence | Good in-sample fit does not establish out-of-sample performance. Consider validation design, leakage and changing relationships. |
| Risk limits vs guarantees | A limit guides decisions and escalation; it does not eliminate uncertainty or losses. |
Use topic practice to apply a distinction in context, and return to the official materials when you cannot explain why it matters.