Macaulay’s duration is less than modified duration except for: a. Zero-coupon bonds. b. Premium bonds. c. Bonds selling at par value. d. None of the above.

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Macaulay's duration is a measure of the weighted average time until a bond's cash flows are received, taking into account both the timing and amount of each cash flow. It is calculated by dividing the present value of each cash flow by the bond's price and summing them.

Modified duration, on the other hand, is a measure of the price sensitivity of a bond to changes in its yield. It is a modified version of Macaulay's duration that incorporates the percentage change in yield.

For zero-coupon bonds, Macaulay's duration and modified duration are equal since there is only one cash flow at maturity.

For premium bonds (bonds selling above par value), Macaulay's duration is greater than modified duration because the higher coupon payments received earlier in the bond's life reduce the weighted average time until the bond's cash flows are received.

For bonds selling at par value (bonds selling at their face value), Macaulay's duration and modified duration are equal since the bond's coupon rate is equal to its yield, and there are no premium or discount effects.