A dynamic bond fund expects rate cuts and must choose between a 10-year callable bond with modified duration 7.1 and effective duration 4.2, and a 7-year bullet with duration 5.6, at similar yields. Which gains more from a 100 basis point fall, and what allocation would you run today?

The bullet gains more: about 5.8% on a 100 basis point fall against about 3.6% for the callable, despite the callable's higher modified duration. Effective duration measures the bet because the issuer will call the bond if rates fall. The callable's extra 30 basis points of yield wins only if rates do not fall. With a cut-leaning view, run about 75% bullet and 25% callable: expected return 9.01%, and less to lose if the view is wrong.

A home loan borrower refinances when rates fall, so the bank that lent at 10% does not get to enjoy 10% for long when market rates drop. An issuer will call its bond when rates fall, so the bondholder's gain is capped near the call price, and only effective durationPrice sensitivity measured by revaluing the bond, option included, at yields slightly up and slightly down; it allows the cash flows to change when the option is exercised. captures that. Modified duration of 7.1 assumes the cash flows run to maturity. Effective duration of 4.2 reprices the bond with the call option, so it is the number that measures the rate bet.

Add convexity. The bullet has positive convexity, about 38, so it gains slightly more than duration says when yields fall and loses slightly less when they rise. The callable has negative convexityPrice gains shrink as yields fall and losses grow as yields rise, because the embedded call shortens the bond when that hurts the holder., about -120, because the call becomes more likely as yields fall. For a 100 basis point fall the bullet gains about 5.6 plus 0.2, 5.8%; the callable about 4.2 less 0.6, 3.6%; and modified duration would have promised 7.1%.

Add the yield to the price change. On a cut, the bullet earns about 12.89% and the callable 11.00%. With no change, the callable's higher yield wins, 7.40% against 7.10%. On a rise, the callable's lower effective duration loses less, 2.60% against 1.69%. The callable is a carry trade: it pays 30 basis points more for selling the issuer the right to refinance, and it wins in every scenario except the one the fund expects.

Weight the scenarios: 50% cut, 35% no change, 15% rise. The bullet's expected return is 9.18% and the callable's 8.48%, so the view favours the bullet. Run about 75% bullet and 25% callable: expected return 9.01%, most of the cut payoff, and about 7.5 basis points of extra carry if the cuts do not come. The callable slice is a hedge on the view, not a rate bet. If the fund's conviction rose, it would shift toward the bullet; if cuts looked fully priced in today's yields, toward the callable.

State the limits. Effective duration and convexity come from a model whose volatility assumption drives the call value, so ask what volatility was used. The scenario numbers are second-order approximations that work for 100 basis point moves and drift for larger ones. And the callable's issuer credit matters: a lender's bond may carry spread risk that the government-like bullet does not.