• 40 questions

FRM Practice Exam

Forty Part I questions in the four topics GARP lists, with the arithmetic worked in each explanation.

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A fund returned 10.0% against a target return of 4.0%. Its downside deviation, measured below that target, is 8.0%. What is the Sortino ratio?

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Unofficial practice questions, not affiliated with GARP. Bank checked October 12, 2026.

The real exam, as GARP describes it

Questions
100
Time limit
240 minutes
Question kinds
Multiple-choice, equally weighted.
Topics
Foundations, quantitative analysis, markets and products, valuation and risk models.
Result
Pass or fail, with quartiles. No pass mark is published.
Part II
80 questions in four hours.
Official practice
Two full-length exams for registered candidates.

Checked October 12, 2026 against GARP's FRM Program and Exams page and FRM Study Materials page. Rules change, so confirm with the agency itself before your test.

GARP's FRM Program and Exams page

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All 40 questions with answers

Foundations of risk management 10

  • A fund returned 10.0% against a target return of 4.0%. Its downside deviation, measured below that target, is 8.0%. What is the Sortino ratio? Answer: 0.75. Source: Own question; the answer is worked out again. Formula: Wikipedia, Sortino ratio. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • A fund returned 10.0% with a standard deviation of 16.0% while the risk-free rate was 2.0%. What is its Sharpe ratio? Answer: 0.50. Source: Own question; the answer is worked out again. Formula: Wikipedia, Sharpe ratio. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • A manager returned 11.0% against a benchmark return of 9.0%, with a tracking error of 4.0%. What is the information ratio? Answer: 0.50. Source: Own question; the answer is worked out again. Formula: Wikipedia, Information ratio. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
Show all 40 questions (37 more)

Foundations of risk management, continued

  • A portfolio is split equally between two assets with volatilities of 20% and 10%. Their returns are uncorrelated. What is the portfolio's volatility? Answer: 11.2%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Modern portfolio theory. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • A portfolio returned 10.0%, the risk-free rate was 2.0% and the portfolio's beta is 1.25. What is its Treynor ratio? Answer: 6.4%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Treynor ratio. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • A portfolio with a beta of 1.1 returned 12.0% in a year when the market returned 9.0% and the risk-free rate was 3.0%. What is its Jensen's alpha? Answer: 2.4%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Jensen's alpha. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • The covariance between a stock's returns and the market's returns is 0.018. The variance of the market's returns is 0.015. What is the stock's beta? Answer: 1.20. Source: Own question; the answer is worked out again. Formula: Wikipedia, Beta (finance). Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • In a two-factor arbitrage pricing model the risk-free rate is 2.0%. A stock has a sensitivity of 1.0 to a factor with a 3.0% risk premium and 0.5 to a factor with a 4.0% premium. What return does the model expect? Answer: 7.0%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Arbitrage pricing theory. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • The risk-free rate is 3.0%, the expected return on the market is 8.0% and a stock has a beta of 1.2. What return does the capital asset pricing model expect from the stock? Answer: 9.0%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Capital asset pricing model. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).
  • Which risk do the Basel II and Basel III frameworks define as the chance of loss from internal processes, people and systems that are inadequate or fail, or from external events? Answer: Operational risk. Source: Basel definition as given in Wikipedia, Operational risk. Topic: FRM Exam Part I, Foundations of Risk Management (GARP, FRM Program and Exams).

Quantitative analysis 10

  • A regression estimates a slope coefficient of 0.80 with a standard error of 0.25. What is the t-statistic for the test that the true slope is zero? Answer: 3.2. Source: Own question; the answer is worked out again. Formula: Wikipedia, t-statistic. Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • A regression has a total sum of squares of 80 and a residual sum of squares of 20. What is its coefficient of determination, R²? Answer: 0.75. Source: Own question; the answer is worked out again. Formula: Wikipedia, Coefficient of determination. Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • A sample of 36 monthly returns has a standard deviation of 12.0%. What is the standard error of the sample mean? Answer: 2.0%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Standard error. Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • A series of daily returns has a kurtosis of 5. What is its excess kurtosis, and what does that say about its tails? Answer: 2, so its tails are fatter than a normal distribution's. Source: Wikipedia, Kurtosis (excess kurtosis). Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • A trade gains $10 with probability 0.6 and loses $5 with probability 0.4. What is the standard deviation of its profit? Answer: $7.35. Source: Own question; the answer is worked out again. Arithmetic on the figures in the question (mean and variance of a discrete variable). Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • An exponentially weighted model updates variance as 0.94 × yesterday's variance + 0.06 × yesterday's squared return. Yesterday's volatility estimate was 1.00% and the return was 2%. What is today's volatility estimate? Answer: 1.09%. Source: Own question; the answer is worked out again. The update rule is stated in the question; weighting idea: Wikipedia, Exponential smoothing. Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • Of 1,000 borrowers, 50 default. A warning model flags 40 of the 50 defaulters and 95 of the 950 borrowers who repay. What share of the flagged borrowers default? Answer: 29.6%. Source: Own question; the answer is worked out again. Arithmetic on the counts in the question (conditional probability). Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • Operational loss events at a bank arrive as a Poisson process averaging 2 a month. What is the probability of a month with no events? Answer: 13.5%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Poisson distribution. Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • Three loans each have a 10% chance of default, independently of one another. What is the probability that exactly one of them defaults? Answer: 24.3%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Binomial distribution. Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).
  • Two assets have return volatilities of 20% and 15%, and the covariance of their returns is 0.006. What is their correlation? Answer: 0.20. Source: Own question; the answer is worked out again. Formula: Wikipedia, Correlation (Pearson coefficient). Topic: FRM Exam Part I, Quantitative Analysis (GARP, FRM Program and Exams).

Financial markets and products 10

  • A futures account has an initial margin of $5,000 and a maintenance margin of $3,750. A fall below maintenance must be topped back up to the initial margin. After losses the balance is $3,500. How much must the trader deposit? Answer: $1,500. Source: Own question; the answer is worked out again. The rule is stated in the question; terms: Wikipedia, Margin (finance). Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • A one-year European call with a $50 strike costs $5.00. The stock, which pays no dividend, is at $52 and the continuously compounded rate is 5%. By put–call parity, what is the European put with the same strike and expiry worth? Answer: $0.56. Source: Own question; the answer is worked out again. Formula: Wikipedia, Put–call parity. Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • A stock that pays no dividend trades at $50. The continuously compounded risk-free rate is 4%. What is the no-arbitrage price of a one-year forward on the stock? Answer: $52.04. Source: Own question; the answer is worked out again. Formula: Wikipedia, Forward price. Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • A two-year bond pays a 5% annual coupon on a face value of 100. Its yield to maturity is 4%. What is its price? Answer: 101.89. Source: Own question; the answer is worked out again. Discounted cash flows: Wikipedia, Present value. Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • An investor buys a call with a $40 strike for $3. At expiry the stock is at $48. What is the investor's profit per share? Answer: $5. Source: Own question; the answer is worked out again. Arithmetic on the figures in the question (payoff of a call at expiry). Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • In an interest rate swap on $10,000,000, a firm pays a fixed 5.0% a year and receives a floating rate set at 4.2% for this period. Payments are netted every six months. What does the firm pay this period? Answer: $40,000. Source: Own question; the answer is worked out again. Fixed for floating swap: Wikipedia, Swap (finance). Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • The minimum-variance hedge ratio is the correlation between spot and futures price changes times the ratio of the spot volatility to the futures volatility. With a correlation of 0.9, a spot volatility of 4% and a futures volatility of 5%, what is it? Answer: 0.72. Source: Own question; the answer is worked out again. The formula is stated in the question. Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • The spot rate is 1.2000 US dollars per euro. One-year interest rates are 5% in dollars and 3% in euros, compounded annually. What one-year forward rate does covered interest rate parity give? Answer: 1.2233. Source: Own question; the answer is worked out again. Formula: Wikipedia, Interest rate parity. Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • Two clearing members agree a trade and it is accepted for clearing by a central counterparty (CCP). What happens to the trade? Answer: It becomes two trades, each member facing the CCP. Source: Wikipedia, Central counterparty clearing (novation). Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).
  • With annual compounding, the one-year spot rate is 2.00% and the two-year spot rate is 3.50%. What one-year rate, one year forward, do they imply? Answer: 5.02%. Source: Own question; the answer is worked out again. Formula: Wikipedia, Forward rate. Topic: FRM Exam Part I, Financial Markets and Products (GARP, FRM Program and Exams).

Valuation and risk models 10

  • A $1,000,000 portfolio has a daily return volatility of 1.5%. Returns are normal with a mean of zero, and the 99% one-tailed z-value is 2.326. What is the one-day 99% value at risk? Answer: $34,890. Source: Own question; the answer is worked out again. Parametric method: Wikipedia, Value at risk. Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A $10,000,000 bond position has a modified duration of 5.0. What is its DV01, the change in value for a one basis point change in yield? Answer: $5,000. Source: Own question; the answer is worked out again. Dollar duration and DV01: Wikipedia, Duration (finance). Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A bond has a modified duration of 6.0 and a convexity of 50. With both, what percentage price change is estimated for a 1 percentage point rise in yield? Answer: −5.75%. Source: Own question; the answer is worked out again. Second-order term: Wikipedia, Bond convexity. Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A bond priced at 102.00 has a modified duration of 6.0. Using duration alone, what price is expected if its yield rises by 25 basis points? Answer: 100.47. Source: Own question; the answer is worked out again. Formula: Wikipedia, Duration (finance). Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A bond with annual coupons has a Macaulay duration of 4.2 years and a yield of 5%. What is its modified duration? Answer: 4.00. Source: Own question; the answer is worked out again. Formula: Wikipedia, Duration (finance). Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A desk's one-day value at risk is $10,000. If daily returns are independent and identically distributed, so that risk grows with the square root of time, what is the 10-day value at risk? Answer: $31,623. Source: Own question; the answer is worked out again. The scaling rule is stated in the question. Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A loan has a probability of default of 2%, a loss given default of 40% and an exposure at default of $5,000,000. What is its expected loss? Answer: $40,000. Source: Own question; the answer is worked out again. Formula: Wikipedia, Expected loss. Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A stock at $100 will be worth $110 or $90 in one period, and the risk-free rate for the period is 5%. In a one-step binomial model, what is a call with a $100 strike worth today? Answer: $7.14. Source: Own question; the answer is worked out again. Method: Wikipedia, Binomial options pricing model. Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • A trader has sold calls on 1,000 shares. Each call has a delta of 0.60. What stock position makes the book delta-neutral? Answer: Buy 600 shares. Source: Own question; the answer is worked out again. Delta: Wikipedia, Greeks (finance). Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).
  • In 100 equally likely scenarios, the five worst losses on a portfolio are $20, $16, $14, $12 and $10 million. Taking expected shortfall at the 95% level as the average loss in the worst 5% of cases, what is it? Answer: $14.4 million. Source: Own question; the answer is worked out again. Definition: Wikipedia, Expected shortfall. Topic: FRM Exam Part I, Valuation and Risk Models (GARP, FRM Program and Exams).

How this list was compiled: Our own questions, written to the four topics that GARP's page FRM Program and Exams lists for the FRM Exam Part I (https://www.garp.org/frm/program-exams, read 2026-10-12): Foundations of Risk Management, Quantitative Analysis, Financial Markets and Products, and Valuation and Risk Models. That page gives the format (100 equally weighted multiple-choice questions, four hours, pass or fail) and no weights; the weights are in GARP's FRM Learning Objectives, which GARP sends on request through a form and which was not opened. The bank therefore holds 10 questions in each topic. 37 answers are arithmetic on the numbers the question prints, worked out again; each names the Wikipedia article its formula was read in on 2026-10-12, or says that the question itself states the rule it uses. Three are definitions read in the Wikipedia articles they name. Licence: Questions, choices and explanations are original work of this site.

How it works

This FRM practice exam has 40 questions of our own on the four topics of the FRM Exam Part I, most of them calculations. Unofficial: not affiliated with or endorsed by GARP, and no question comes from the real exam.

Read the full guide

An FRM Exam 1 practice test in four topics

The topics, as the FRM Program and Exams page lists them: Foundations of Risk Management, Quantitative Analysis, Financial Markets and Products, and Valuation and Risk Models. GARP gives the approximate topic weights in its FRM Learning Objectives, not on that page; this bank holds 10 questions in each topic.

How the questions are written

Thirty-seven are calculations: ratios, probabilities, forward and bond prices, value at risk. Each prints every number it needs, and the explanation shows the working.

As an FRM mock exam

Exam mode runs all 40 against a 96-minute clock, the real pace of 100 questions in four hours.

  • Check the compounding a question states: continuous for the forward price and put-call parity here, annual for spot and forward rates.
  • A duration answer is a first estimate; the convexity term adds back a little of the loss.

Questions and answers

How many questions are on the FRM exam?

Part I has 100 equally weighted multiple-choice questions and Part II has 80. Candidates are allotted four hours for each.

What is the passing score for the FRM exam?

None is published. Both exams are scored pass or fail, and results come with quartiles that compare you with other candidates.

Is this FRM practice test from GARP?

No. Registered Part I candidates receive two full-length official practice exams. This FRM practice exam test is separate and unofficial, and copies none of their questions.

Does this cover FRM Part II?

No. Part II covers market, credit, operational and liquidity risk, investment management and current market issues. Every question here is on a Part I topic.

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