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 sts_t is the annual effective yield on a zero-coupon investment from time 0 to time tt. It represents the rate at which a single cash flow at time tt 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=1Pd2Pdy2>0C = \frac{1}{P} \frac{d^2P}{dy^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
C is correct.

Cash flows: 80 at times 1 through 4, and 1080 at time 5. Yield i=6%i = 6\%.

Compute present values:
PV1=80/1.06=75.472PV_1 = 80/1.06 = 75.472
PV2=80/1.062=71.200PV_2 = 80/1.06^2 = 71.200
PV3=80/1.063=67.170PV_3 = 80/1.06^3 = 67.170
PV4=80/1.064=63.368PV_4 = 80/1.06^4 = 63.368
PV5=1080/1.065=807.072PV_5 = 1080/1.06^5 = 807.072

Price P=1084.28P = 1084.28.

Convexity formula: C=∑t(t+1)⋅PVt(1+i)2×PC = \frac{\sum t(t+1) \cdot PV_t}{(1+i)^2 \times P}.

Compute ∑t(t+1)⋅PVt\sum t(t+1) \cdot PV_t:
1(2)(75.472)=150.941(2)(75.472) = 150.94
2(3)(71.200)=427.202(3)(71.200) = 427.20
3(4)(67.170)=806.043(4)(67.170) = 806.04
4(5)(63.368)=1267.364(5)(63.368) = 1267.36
5(6)(807.072)=24212.165(6)(807.072) = 24212.16

Sum =26863.70= 26863.70.

C=26863.70(1.06)2×1084.28=26863.701.1236×1084.28=26863.701218.30=22.05C = \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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