Free SOA Exam FM General Cash Flows, Portfolios, and Asset-Liability Management Practice Questions (2026)

Free SOA Exam FM (Financial Mathematics) General Cash Flows, Portfolios, and Asset-Liability Management Practice Questions

General cash flow analysis on SOA Exam FM integrates time value of money, annuities, and bond concepts into portfolio immunization, asset-liability management, and real-world financial decision-making scenarios.

309 questions 144 easy 106 medium 59 hard 2026 syllabus

Sample Questions

Question 1 Easy

Which of the following best describes a spot rate?

Solution

D is correct.

A spot rate

s_{t}

is the annual effective yield on a zero-coupon investment from time 0 to time

t

. It represents the rate at which a single cash flow at time

t

is discounted to the present.

Question 2 Medium

Which of the following statements about convexity is NOT correct?

Solution

C is correct.

The statement that convexity is always negative for a standard fixed-coupon bond is NOT correct. Convexity for standard fixed-coupon bonds is always **positive** because the second derivative of the price with respect to yield is positive:

C = \frac{1}{P} \frac{d ^{2} P}{d y ^{2}} > 0

Positive convexity means the price-yield curve bows upward, which benefits the bondholder: prices rise more than duration predicts when yields fall, and fall less when yields rise. Negative convexity only occurs for callable bonds or mortgage-backed securities where cash flows change with interest rates.

Question 3 Hard

A 5-year bond pays annual coupons of 8% on a face value of $1,000 at an annual effective yield of 6%. Calculate the convexity of this bond.

Solution

A is correct.

Cash flows: 80 at times 1 through 4, and 1080 at time 5. Yield

i = 6%

.

Compute present values:

P V_{1} = 80/1.06 = 75.472

P V_{2} = 80/1.0 6^{2} = 71.200

P V_{3} = 80/1.0 6^{3} = 67.170

P V_{4} = 80/1.0 6^{4} = 63.368

P V_{5} = 1080/1.0 6^{5} = 807.072

Price

P = 1084.28

.

Convexity formula:

C = \frac{\sum t ( t + 1 ) \cdot P V _{t}}{( 1 + i ) ^{2} \times P}

.

Compute

\sum t (t + 1) \cdot P V_{t}

1 (2) (75.472) = 150.94

2 (3) (71.200) = 427.20

3 (4) (67.170) = 806.04

4 (5) (63.368) = 1267.36

5 (6) (807.072) = 24212.16

Sum

= 26863.70

C = \frac{26863.70}{( 1.06 ) ^{2} \times 1084.28} = \frac{26863.70}{1.1236 \times 1084.28} = \frac{26863.70}{1218.30} = 22.05

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