The table gives information about the assets and liabilities of three companies.

	Assets			Liabilities
Company	Present Value	Modified Duration	Convexity	Present Value	Modified Duration	Convexity
U	200,000	10.2	150	200,000	9.3	148
V	300,000	8.6	85	300,000	8.6	80
W	400,000	15.8	300	400,000	15.8	305

(I) Company U’s position is immunized against small interest rate changes.

(II) Company V’s position is immunized against small interest rate changes.

(III) Company W’s position is immunized against small interest rate changes.

• I only
• II only
• III only
• I, II, and III
• The correct answer is not given by (A), (B), (C), or (D).

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

Besides present values of assets and liabilities matching, 1) their modified durations must also match, and 2) the convexity of the assets must exceed the convexity of the liabilities, in order for the company’s position to be immunized against small changes in interest rate. Only company V satisfies all these conditions.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.