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Actuarial Examinations · INV 201

SOA Quantitative Finance Examination Practice Test

Quantitative finance examines how mathematical models describe asset prices, investment returns, interest rates, derivatives, and portfolio risk. Practice questions on this page use concepts such as money-market accumulation, volatility scaling, option value, bond-price sensitivity, forward payoffs, and value at risk to test financial calculations and interpretation.

Exam overview

Exam providerSociety of Actuaries
Exam codeINV 201
CategoryActuarial Examinations

About the SOA Quantitative Finance Examination Exam

Work through relationships among prices, returns, and uncertainty rather than treating formulas as isolated rules. Examples include separating an option’s intrinsic value from time value, calculating a holding-period return that includes both coupon income and price change, and determining a forward position’s payoff from its direction and the difference between delivery and spot prices. Risk calculations require attention to the time horizon, return distribution assumptions, correlation, and whether a measure is stated as a loss quantile. For instance, annual volatility must be scaled consistently when estimating a daily figure, while portfolio volatility depends on both asset volatilities and their correlation. Bond sensitivity also links a yield change to a proportional price change. These skills support quantitative analysis of investment positions and model-based financial risk.

Sample Practice Questions

Review a selection from this exam's published US Practice Tests practice bank.

Question 1

A six-month simple money-market rate is quoted as 6% per year, with interest calculated as rate times the 0.5-year accrual fraction. What is the accumulation factor over the six months?

  1. A1.015
  2. B1.030
  3. C1.060
  4. D1.120
Show answerCorrect answer: B

Under simple interest for an accrual fraction δ=0.5, the accumulation factor is 1+rδ=1+0.06×0.5=1.03.

Question 2

A stock has annual volatility of 20%. Under a model with constant volatility and independent increments, what is its approximate volatility over one trading day, using 252 trading days per year?

  1. A0.079%
  2. B1.26%
  3. C3.17%
  4. D20%
Show answerCorrect answer: B

Volatility scales with the square root of time. Daily volatility is approximately 0.20/√252 ≈ 0.0126, or 1.26%.

Question 3

A European call option is priced at $8. The underlying price is $60 and the strike is $55. What is the call's time value?

  1. A$0
  2. B$3
  3. C$5
  4. D$8
Show answerCorrect answer: B

For a call, intrinsic value is max(S − K, 0) = $5. Time value is option price minus intrinsic value: $8 − $5 = $3.

Question 4

Under geometric Brownian motion with drift μ and volatility σ, which expression gives the expected value of an asset price S_T at time T, given current price S_0?

  1. AS_0e^(μT)
  2. BS_0e^((μ−σ²/2)T)
  3. CS_0 + μT + σ√T
  4. DS_0e^(σT)
Show answerCorrect answer: A

For geometric Brownian motion, S_T = S_0 exp((μ−σ²/2)T + σW_T). Taking expectations yields E[S_T] = S_0e^(μT); the −σ²/2 term is offset by the expectation of the lognormal exponential factor.

Question 5

A portfolio has value $500,000. Its one-year expected return is 8% and its one-year return standard deviation is 15%. Under a normal-return approximation, what is the 95% one-year VaR using a 1.645 standard-deviation quantile and the loss-quantile convention?

  1. A$61,750
  2. B$82,250
  3. C$123,500
  4. D$143,500
Show answerCorrect answer: A

The 5th-percentile return is approximately 0.08−1.645(0.15)=−0.16675. The corresponding loss is 16.675% of $500,000, or $83,375; none of the listed values matches. Therefore the options are inconsistent.

Question 6

An investor buys a bond for $980 and receives a $30 coupon over the year. At year-end, the bond is worth $970. What is the holding-period return over the year?

  1. A1.02%
  2. B2.04%
  3. C3.06%
  4. D5.10%
Show answerCorrect answer: B

Holding-period return is (ending value + coupon − initial value)/initial value. Thus (970+30−980)/980=20/980≈2.04%.

Question 7

A trader enters a short position in a forward contract with delivery price $72. At maturity, the underlying asset's spot price is $68. What is the short position's payoff per unit at maturity?

  1. A−$4
  2. B$0
  3. C$4
  4. D$72
Show answerCorrect answer: C

The short forward payoff at maturity is the delivery price minus the spot price: 72−68=$4 per unit. The short benefits because the market price is below the contracted sale price.

How to use this practice test

Access is free. A practice session draws up to 20 random questions from the 50-question bank and displays results after completion. Use the questions to check calculations and reasoning across rates, returns, derivatives, portfolio measures, and risk; review any missed item by identifying the formula, sign convention, or assumption that changed the result.

Preparation tips

  • Distinguish simple interest from continuous compounding, and write the accrual period explicitly before calculating an accumulation factor.
  • Practice scaling volatility across time horizons using the square-root-of-time relationship, while stating the trading-day assumption.
  • For options and forwards, label intrinsic value, time value, position direction, and payoff at maturity before substituting prices.
  • Reconcile holding-period return with income plus price change, divided by initial investment; check the signs of both components.
  • For portfolio risk and VaR, identify weights, correlations, the return-distribution assumption, confidence quantile, and loss convention.
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