Archive / Mutual Fund Distributors / Risk, Return & Performance of Funds

nism-series-va-modified-duration-bond-price-sensitivity-formula[ MUTUAL FUND DISTRIBUTORS ]

A debt mutual fund scheme has a Modified Duration of 4.5 years. If market interest rates rise by 50 basis points (+0.50%), what is the approximate percentage change in the scheme's Net Asset Value (NAV)?

[ A ]+2.25% (NAV increases by 2.25%)

[ B ]-0.50%

[ C ]-2.25% (NAV declines by 2.25% due to inverse price-yield relationship: % Δ Price ≈ - Modified Duration * Δ Yield)[ CORRECT ]

[ D ]+4.50%

Takeaway

Option C is correct: -2.25% (NAV declines by 2.25% due to inverse price-yield relationship: % Δ Price ≈ - Modified Duration * Δ Yield)

Derivation

Modified Duration measures the approximate percentage price change for a 1% move in yield, in the opposite direction. With Modified Duration = 4.5 years and a yield rise of Δy = +0.50% = +0.0050, the estimated NAV change is % Δ NAV ≈ −(4.5 × 0.0050) = −0.0225, or −2.25%. The negative sign is not optional — it reflects the fundamental inverse relationship between bond prices and yields: when rates rise, the present value of a bond's fixed future coupons and principal falls. A higher-duration scheme carries a larger multiplier on any given yield move, which is exactly why long-duration debt funds see sharper NAV swings than short-duration ones when the rate cycle turns.

Why the others fail

A — +2.25% (NAV increases by 2.25%)

Bond prices move inversely to interest rates; a rise in yields depresses NAV, so a positive NAV change in this direction is directionally impossible.

B — -0.50%

Assumes the NAV change equals the raw yield shift of 0.50% one-for-one, ignoring that Modified Duration of 4.5 years amplifies the price impact well beyond the yield move itself.

D — +4.50%

States the Modified Duration figure of 4.5 directly as if it were the percentage NAV change, rather than the multiplier applied to the yield shift.