SOA Exam FM – Financial Mathematics — Questions and Answers

Question 1: Put-call parity for European options states:

C − P = K·v^T − S₀
C + P = S₀ + K·v^T
C × P = S₀ × K·v^T
C − P = S₀ − K·v^T (Correct answer)

Correct answer: C − P = S₀ − K·v^T

Put-call parity: C − P = S₀ − K·v^T, where C and P are call and put prices, S₀ is spot, K is strike, and v = 1/(1+i).

Question 2: How should risk be assessed in regulatory compliance?

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

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 3: A straddle is formed by:

Buying a call and selling a put with the same strike
Selling a call and buying a put with different strikes
Buying a call and a put with the same strike and expiration (Correct answer)
Buying calls at two 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 4: A bond with a face value of $1,000 has a coupon rate of 6%. What is the annual coupon payment?

$80
$50
$70
$60 (Correct answer)

Correct answer: $60

The annual coupon payment of a bond is determined by multiplying its face value (also known as par value) by its coupon rate. For a bond with a face value of $1,000 and a coupon rate of 6%, the annual coupon payment is calculated as $1,000 * 0.06 = $60. This amount represents the interest income the bondholder receives each year.

Question 5: A forward contract on the FM exam obligates the buyer to:

Sell an asset at any time before expiration
Purchase an asset at a predetermined price on a specified future date (Correct answer)
Exchange interest payments with a counterparty
Pay a premium for the right to buy at market price

Correct answer: Purchase an asset at a predetermined price on a specified future date

A forward contract locks in a purchase price (the forward price) for delivery of the asset at a future date.

Question 6: The swap rate in a plain vanilla interest rate swap is the fixed rate that makes the swap's initial value:

Positive for the fixed-rate payer
Equal to the notional principal
Equal to the floating rate at inception
Equal to zero (fair swap) (Correct answer)

Correct answer: Equal to zero (fair swap)

The fixed swap rate is set so that the present value of fixed payments equals the present value of expected floating payments, making initial value zero.

Question 7: Which strategy involves buying a call and selling a call at a higher strike, both with the same expiration?

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

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 8: In an amortization schedule for a fixed-payment loan, how does the principal component of each payment change over time?

Remains constant each period
Decreases throughout the loan term
Fluctuates based on remaining interest accrued
Increases throughout the loan term (Correct answer)

Correct answer: Increases throughout the loan term

As the outstanding balance decreases, less interest is owed each period, so more of the fixed payment goes toward principal — the principal component increases.

Question 9: What fiduciary duty applies to regulatory compliance?

Follow the firm's sales targets above all
Act in the client's best interest with loyalty, care, and full disclosure (Correct answer)
Maximize the advisor's commission
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 10: The force of interest δ is related to the effective annual rate i by which formula?

δ = 1 − e^(−i)
δ = ln(1 + i) (Correct answer)
δ = e^i − 1
δ = i / (1 + 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 11: A 'floor' is a series of interest rate put options (floorlets) used by investors to:

Convert floating-rate income to fixed-rate income permanently
Limit the maximum interest rate paid on a loan
Guarantee a minimum interest rate received on a floating-rate investment (Correct answer)
Speculate on rising equity prices

Correct answer: Guarantee a minimum interest rate received on a floating-rate investment

An interest rate floor protects a floating-rate investor from falling rates by providing payoffs when the reference rate drops below the floor rate.

Question 12: 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)
5.00%
4.80%
4.95%

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 13: A portfolio holds 1,000 options with a delta of 0.6. How many shares of the underlying stock are required to delta-hedge the portfolio?

1,200 (Correct answer)
1,000
1,500
600

Correct answer: 1,200

Formula: Hedge Shares = Delta × Number of Options Calculation: Hedge Shares = 0.6 × 1,000 = 1,200

Question 14: For a continuously varying interest rate, the present value factor v(t) is:

1 / (1 + i·t)
e^(−i·t)
exp(∫₀ᵗ δ(s) ds)
exp(−∫₀ᵗ δ(s) ds) (Correct answer)

Correct answer: exp(−∫₀ᵗ δ(s) ds)

The present value factor is the reciprocal of the accumulation factor: v(t) = exp(−∫₀ᵗ δ(s) ds).

Question 15: What fiduciary duty applies to portfolio management?

Maximize the advisor's commission
Act in the client's best interest with loyalty, care, and full disclosure (Correct answer)
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 16: How should risk be assessed in tax strategies?

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

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 17: For a continuously payable annuity at a constant force of interest δ, the present value of payments made continuously at rate 1 per year for T years is:

ā(T) = 1 - e^(-Tδ)
ā(T) = T × e^(-δ)
ā(T) = (1 - e^(-δT)) / δ (Correct answer)
ā(T) = (e^(δT) - 1) / δ

Correct answer: ā(T) = (1 - e^(-δT)) / δ

The continuous annuity present value ā(T) = integral of e^(-δt) dt from 0 to T = (1 - e^(-δT))/δ.

Question 18: How should conflicts of interest be managed in tax strategies?

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

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 19: For the following cash flows, calculate the approximate IRR: Year 0: -$10,000 Year 1: $4,000 Year 2: $4,000 Year 3: $5,000

11%
8%
10% (Correct answer)
9%

Correct answer: 10%

Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of a project's cash flows equals zero. For the given cash flows (Year 0: -$10,000; Year 1: $4,000; Year 2: $4,000; Year 3: $5,000), the IRR is found by setting NPV = 0. Through iterative calculation, the IRR is approximately 13.9%. The provided correct answer, 10%, would result in a positive NPV of approximately $698.72, indicating it is not the IRR.

Question 20: What continuing education requirement supports financial planning competence?

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

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 21: On the FM exam, the payoff of a long call option at expiration with strike K and terminal asset price S_T is:

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

Correct answer: max(S_T − K, 0)

The call option payoff is max(S_T − K, 0): positive if the asset exceeds the strike, zero otherwise.

Question 22: An arithmetic increasing annuity-immediate has payments of $100, $200, $300, $400, $500 at the end of years 1 through 5. Which expression gives its present value at 5% annual interest?

100 × (Ia)(5, 5%) (Correct answer)
100 × a(5, 5%)
100 × s(5, 5%)
100 × ä(5, 5%)

Correct answer: 100 × (Ia)(5, 5%)

An arithmetic increasing annuity with first payment P and common difference P uses (Ia)(n,i), so PV = P × (Ia)(5,5%) = 100 × (Ia)(5, 5%).

Question 23: How should conflicts of interest be managed in portfolio management?

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)
Conflicts are unavoidable and need not be disclosed

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 24: What continuing education requirement supports tax strategies competence?

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

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 25: The discount rate d and the interest rate i satisfy which relationship?

d = i × (1 + i)
d = i − 1
d = 1 − i
d = i / (1 + i) (Correct answer)

Correct answer: d = i / (1 + i)

The discount rate d = i / (1 + i), reflecting that d is paid at the beginning of the period while i is paid at the end.

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%

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