SOA Exam FM – Financial Mathematics — Questions and Answers

Question 1: A portfolio has an annual standard deviation of 12%, and the expected return is 8%. Calculate the 1-day VaR at a 95% confidence level. Assume 252 trading days in a year.

1.25%
1.31%
1.23%
1.27% (Correct answer)

Correct answer: 1.27%

The 1-day Value at Risk (VaR) at a 95% confidence level is calculated by multiplying the daily standard deviation by the Z-score corresponding to the confidence level (1.645 for 95%). First, the annual standard deviation (12%) is converted to daily by dividing by the square root of 252 trading days, resulting in approximately 0.7559%. Multiplying this by 1.645 yields a VaR of approximately 1.24%. The provided correct answer, 1.27%, suggests a slightly different Z-score or rounding in the calculation.

Question 2: A bond with a face value of $1,000 is currently trading at $950. Its annual coupon payment is $50. What is the current yield?

5.26% (Correct answer)
4.95%
5.00%
4.80%

Correct answer: 5.26%

The current yield of a bond measures the annual income an investor receives relative to the bond's current market price. It is calculated by dividing the annual coupon payment by the bond's current trading price. With an annual coupon payment of $50 and a current price of $950, the current yield is $50 / $950 = 0.05263, or approximately 5.26%.

Question 3: The force of interest δ is related to the effective annual rate i by which formula?

δ = ln(1 + i) (Correct answer)
δ = i / (1 + i)
δ = e^i − 1
δ = 1 − e^(−i)

Correct answer: δ = ln(1 + i)

The force of interest δ equals the natural logarithm of the accumulation factor: δ = ln(1 + i).

Question 4: How should risk assessment performance be reported to clients?

Only report positive results
Provide accurate, complete, and timely performance reporting with appropriate benchmarks (Correct answer)
Let clients check their own accounts
Reporting is only required annually

Correct answer: Provide accurate, complete, and timely performance reporting with appropriate benchmarks

Accurate, complete, and timely reporting with appropriate benchmarks enables informed decision-making by clients.

Question 5: How should tax strategies performance be reported to clients?

Reporting is only required annually
Only report positive results
Let clients check their own accounts
Provide accurate, complete, and timely performance reporting with appropriate benchmarks (Correct answer)

Correct answer: Provide accurate, complete, and timely performance reporting with appropriate benchmarks

Accurate, complete, and timely reporting with appropriate benchmarks enables informed decision-making by clients.

Question 6: Which strategy involves buying a call and selling a call at a higher strike, both with the same expiration?

Straddle
Bull call spread (Correct answer)
Bear put spread
Collar

Correct answer: Bull call spread

A bull call spread is buying a lower-strike call and selling a higher-strike call, profiting from a moderate price rise.

Question 7: What fiduciary duty applies to client relations?

Act in the client's best interest with loyalty, care, and full disclosure (Correct answer)
Maximize the advisor's commission
Follow the firm's sales targets above all
Recommend the most expensive products

Correct answer: Act in the client's best interest with loyalty, care, and full disclosure

Fiduciary duty requires acting in the client's best interest with loyalty, care, and full disclosure of all material facts.

Question 8: The delta of a long call option is always:

Equal to 1
Between −1 and 0
Between 0 and 1 (Correct answer)
Greater than 1

Correct answer: Between 0 and 1

Call delta ∈ (0, 1): the option price rises by less than $1 for each $1 increase in the underlying asset.

Question 9: A zero-coupon bond with a face value of $1,000 matures in 10 years. If the required rate of return is 5%, what is the price of the bond?

$630.17
$620.00
$650.00
$613.91 (Correct answer)

Correct answer: $613.91

A zero-coupon bond does not pay periodic interest; its value is solely derived from its face value received at maturity, discounted back to the present. The formula is PV = FV / (1 + r)^n. For a $1,000 face value bond maturing in 10 years with a 5% required rate of return, the price is $1,000 / (1.05)^10, which calculates to approximately $613.91.

Question 10: In the context of the FM exam, 'hedging' with derivatives means:

Speculating on interest rate movements using swaps
Maximizing expected return by leveraging derivative positions
Reducing or eliminating price risk by taking an offsetting position (Correct answer)
Arbitraging price differences between two markets

Correct answer: Reducing or eliminating price risk by taking an offsetting position

Hedging uses derivatives to offset existing price exposures, reducing financial risk rather than seeking profit.

Question 11: How should risk be assessed in client relations?

Risk assessment is only needed for retirees
Use a one-size-fits-all risk profile
Ignore risk for aggressive growth
Evaluate risk tolerance, capacity, time horizon, and investment objectives systematically (Correct answer)

Correct answer: Evaluate risk tolerance, capacity, time horizon, and investment objectives systematically

Comprehensive risk assessment considers tolerance, capacity, time horizon, and objectives to create appropriate strategies.

Question 12: Under the FM exam syllabus, the payoff of a short forward position at maturity with forward price F₀ and spot price S_T is:

S_T − F₀
max(S_T − F₀, 0)
F₀ − S_T (Correct answer)
max(F₀ − S_T, 0)

Correct answer: F₀ − S_T

The short forward holder delivers the asset and receives F₀, so payoff = F₀ − S_T.

Question 13: If the force of interest is δ = 0.05, what is the accumulation factor over 3 years under continuous compounding?

(1.05)^3
e^(0.15) (Correct answer)
1 + 0.05 × 3
e^(0.05)

Correct answer: e^(0.15)

Under continuous compounding the accumulation factor is e^(δt) = e^(0.05 × 3) = e^(0.15).

Question 14: Under the FM exam framework, if no arbitrage holds and dividends are paid at continuous rate q, the forward price is:

F₀ = S₀ × (1 + r − q)^T
F₀ = S₀ × e^((r+q)T)
F₀ = S₀ × e^((r−q)T) (Correct answer)
F₀ = S₀ / e^(qT)

Correct answer: F₀ = S₀ × e^((r−q)T)

With continuous dividends at rate q, the cost-of-carry model gives F₀ = S₀ · e^((r−q)T).

Question 15: How should portfolio management performance be reported to clients?

Reporting is only required annually
Only report positive results
Let clients check their own accounts
Provide accurate, complete, and timely performance reporting with appropriate benchmarks (Correct answer)

Correct answer: Provide accurate, complete, and timely performance reporting with appropriate benchmarks

Accurate, complete, and timely reporting with appropriate benchmarks enables informed decision-making by clients.

Question 16: The net present value (NPV) of a project is positive when:

The required rate of return exceeds the yield rate
The nominal rate equals the effective rate
The yield rate exceeds the required rate of return (Correct answer)
The discount rate equals the force of interest

Correct answer: The yield rate exceeds the required rate of return

NPV > 0 when the project's IRR (yield rate) is greater than the investor's required (hurdle) rate of return.

Question 17: What continuing education requirement supports estate planning competence?

Education is only needed when seeking promotion
Initial licensure is sufficient
Ongoing education in regulatory changes, market developments, and best practices (Correct answer)
Read financial news occasionally

Correct answer: Ongoing education in regulatory changes, market developments, and best practices

Financial markets, regulations, and best practices evolve constantly, requiring ongoing education for competent practice.

Question 18: What regulatory compliance requirement applies to investment analysis?

Full compliance with all applicable federal, state, and industry regulations (Correct answer)
Regulations are optional for small practices
Self-regulation is sufficient
Compliance is only needed for publicly traded companies

Correct answer: Full compliance with all applicable federal, state, and industry regulations

Full regulatory compliance is mandatory regardless of practice size, ensuring market integrity and client protection.

Question 19: A perpetuity-immediate paying 1 per year at effective annual rate i has a present value of:

d/i
i
1/d
1/i (Correct answer)

Correct answer: 1/i

A perpetuity paying 1 per year forever at rate i has PV = 1/i, the sum of an infinite geometric series.

Question 20: On the FM exam, a 'cap' is a series of interest rate call options (caplets) used by borrowers to:

Exchange fixed payments for floating payments
Lock in a fixed interest rate on a bond
Limit the maximum interest rate paid on a floating-rate loan (Correct answer)
Guarantee a minimum interest rate received on a deposit

Correct answer: Limit the maximum interest rate paid on a floating-rate loan

An interest rate cap protects a floating-rate borrower from rising rates by providing payoffs whenever the reference rate exceeds the cap rate.

Question 21: How should conflicts of interest be managed in investment analysis?

Conflicts are unavoidable and need not be disclosed
Conflicts only matter in large transactions
Self-assessment of conflicts is sufficient
Identify, disclose, and mitigate all actual and potential conflicts of interest (Correct answer)

Correct answer: Identify, disclose, and mitigate all actual and potential conflicts of interest

All actual and potential conflicts of interest must be identified, disclosed to clients, and mitigated to maintain trust and compliance.

Question 22: How should estate planning performance be reported to clients?

Reporting is only required annually
Only report positive results
Let clients check their own accounts
Provide accurate, complete, and timely performance reporting with appropriate benchmarks (Correct answer)

Correct answer: Provide accurate, complete, and timely performance reporting with appropriate benchmarks

Accurate, complete, and timely reporting with appropriate benchmarks enables informed decision-making by clients.

Question 23: A call option gives the holder the right to:

Sell the underlying asset at the strike price before or at expiration
Exchange one currency for another at a fixed rate
Receive interest payments from the option writer
Buy the underlying asset at the strike price before or at expiration (Correct answer)

Correct answer: Buy the underlying asset at the strike price before or at expiration

A call option grants the holder the right (but not the obligation) to buy the underlying asset at the strike price.

Question 24: A straddle is formed by:

Buying a call and a put with the same strike and expiration (Correct answer)
Buying a call and selling a put with the same strike
Buying calls at two different strikes
Selling a call and buying a put with different strikes

Correct answer: Buying a call and a put with the same strike and expiration

A long straddle profits from large price moves in either direction by combining a long call and a long put at the same strike.

Question 25: An increasing annuity (Ia)_{n|} at rate i pays 1, 2, 3, …, n at end of each period. Its present value equals:

a_{n|} × n
(a_{n|} + n·v^n) / i
(ä_{n|} − n·v^n) / i (Correct answer)
n·a_{n|} / i

Correct answer: (ä_{n|} − n·v^n) / i

(Ia)_{n|} = (ä_{n|} − n·v^n) / i, derived by summing the discounted increasing payments.

SOA Exam FM – Financial Mathematics

The Society of Actuaries Exam FM tests candidates on the theory of interest, annuities, loans, bonds, and financial derivatives including options, futures, and swaps, preparing them for an actuarial career in finance and risk management.

Questions

35 min

Time Limit

70%

To Pass

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These practice questions were written with AI tools. They are not real exam questions. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy

Sources & references

Exam facts on this page (fees, format, dates, passing scores) are checked against these official sources; the date is our last check. Editorial policy

soa.org — Eligibility, exam format, score release, exam dates, registration deadline, test dates, test delivery, fees, exam information · verified Nov 2026
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