FRM Part I common mistakes
FRM Part I · Understand the traps and how to avoid them.
Computing the Sharpe ratio as (Rp − Rf)/βp and the Treynor measure as (Rp − Rf)/σp - the two denominators get swapped.
Both ratios put an excess return in the numerator, so the denominators are recalled as a pair of symbols rather than as two distinct definitions of risk; under time pressure the more familiar symbol is written first.
What to do instead
Anchor each ratio to the question it answers before calculating. Sharpe uses total risk σ and answers 'excess return per unit of total variability' - use it to rank portfolios when the portfolio is the investor's entire holding. Treynor uses β and answers 'excess return per unit of non-diversifiable risk' - use it to rank portfolios that will be blended into an already diversified fund. Write the word 'total' or 'systematic' above the denominator first, then fill in the symbol.
Discounting probability-weighted (real-world) expected cash flows at the risk-free rate on the grounds that the cash flows 'already contain the risk'.
Real-world probabilities and risk-free discounting look like a matched pair, and the two legitimate combinations are visually symmetric on the page, so the mismatch is invisible in the algebra.
What to do instead
Commit to one consistent pairing: real-world expected cash flows discounted at a risk-adjusted rate, or risk-neutral expected cash flows (built from risk-neutral probabilities with expected growth at the risk-free rate) discounted at the risk-free rate. Diagnostic: if the probabilities in the question are described as historical or subjective and no risk-neutral wording appears, the discount rate must exceed the risk-free rate.
Dividing by n instead of n−1 when computing the standard deviation of a series of historical returns or of a sample of observations.
The descriptive-statistics formula is learned first and is the one that surfaces automatically; the estimator version appears later in the syllabus and looks like a rounding detail that will not be tested.
What to do instead
Classify the data before computing. A complete population uses n; any sample used to estimate an unknown population parameter uses n−1. In FRM questions, a series of historical returns is almost always treated as a sample. Mechanical check: the denominator equals the number of squared deviations you summed, minus one, whenever the mean was estimated from the same data.
Building a confidence interval for a mean with 15 observations and unknown population variance using the normal critical value 1.96.
1.96 and 1.645 are over-learned, and the qualifying condition (variance estimated from the same small sample) is a single clause that is easy to skim past in a long stem.
What to do instead
Run a two-branch decision every time: population σ known, or n large → z; σ estimated from the sample and n small (roughly under 30) → t with n−1 degrees of freedom, which widens the interval (for example 2.145 rather than 1.96 at 95% with 14 df). Check the width of your answer against the t value, not the z value.
Testing H0: μ = μ0 against Ha: μ > μ0 and rejecting the null when the test statistic exceeds 1.96 at the 5% level.
1.96 is memorized as 'the 5% number' with no tail direction attached to it, and the alternative hypothesis is read as decoration rather than as the input that selects the critical value.
What to do instead
Write the alternative hypothesis first and let it choose the critical value: a '>' or '<' alternative is one-tailed (1.645 at 5%, 2.326 at 1%); only a '≠' alternative splits 5% into two 2.5% tails and yields 1.96. Where a p-value is given, compare it directly with α and skip critical values entirely.
Answering 'what is the value of the forward contract at initiation?' with the no-arbitrage forward price F0 = S0 × exp(rT).
Both quantities come out of the same formula chain and both are labelled 'forward' in the question stem; the price is the number that gets computed first and the earliest number produced tends to be reported.
What to do instead
Separate the two definitions explicitly. The forward price is the delivery price that makes the contract fair - fixed at initiation, unchanged over the contract's life. The value is what the contract is worth to its holder today and is exactly zero at initiation. For an existing contract the long's value is S0 × exp(−qT) − K × exp(−rT) (with carry adjustments); if the question asks for value, the delivery price K or a current forward price must appear in your expression. If your answer reduces to S0 × exp(rT), you were asked for a price.
Writing the cost-of-carry model as F0 = S0 × exp((r + y − u)T), i.e. adding the convenience yield and subtracting the storage cost.
Storage cost and convenience yield are both quoted as a percentage and both sit under the heading 'carry', so they are treated as interchangeable magnitudes whose signs are guessed rather than derived.
What to do instead
Derive the sign from the cash-and-carry trade every time. Anything that makes holding the physical asset more expensive - storage, insurance, financing - raises the forward price, so add it to r. Anything that makes holding the physical asset more attractive - convenience yield, lease rate, dividend or coupon income - lowers the forward price, so subtract it. Then check the economics: a consumption asset with a high convenience yield should show F0 below S0 × exp(rT).
Using N(d1) as the risk-neutral probability that a call finishes in the money, or using N(d2) as the option's delta.
Black-Scholes is memorized as a string of symbols in which N(d1) appears first, so it inherits whichever interpretation the question happens to ask about.
What to do instead
Attach each term to its job in the formula: N(d2) multiplies the discounted strike and is therefore the risk-neutral probability of exercise; N(d1) multiplies the spot and is therefore the call delta, which is why N(d1) is always the larger of the two. Also verify that the strike enters discounted, K × exp(−rT), not undiscounted - the two errors usually appear together.
Describing a 1-day 95% VaR of $1 million as 'the maximum loss is $1 million' or as 'losses will exceed $1 million on 95% of days'.
VaR is reported as a single number with no tail shown next to it, so the tail probability gets attached to the wrong side of the threshold and the number reads like a worst case.
What to do instead
Read the statement forward and out loud: over a one-day horizon, on roughly 5 days in 100 the loss will be at least $1 million; on the other 95 days the loss will be smaller. It is silent on how large the loss is once the threshold is breached - that is expected shortfall's job. Any option containing 'maximum loss' or 'cannot exceed' is wrong by construction.
Estimating a bond's percentage price change as −D_Macaulay × Δy, and applying that estimate unchanged to a 200 basis point shift in yields.
Only one duration figure appears in the headline sensitivity formula, so the Macaulay number gets used directly as if it were the price sensitivity; convexity is treated as a separate topic rather than as a correction to the same calculation.
What to do instead
Convert before using: modified duration = Macaulay duration / (1 + y/m), then %ΔP ≈ −D_mod × Δy. For yield changes beyond a few dozen basis points add the convexity term ½ × C × (Δy)², which is positive for both directions of move - so a duration-only estimate understates the price gain when yields fall and overstates the price loss when yields rise. If the question supplies convexity, the answer without it is wrong.