An equity fund has a Beta of 1.25 relative to its benchmark index. If the benchmark index declines by 8.0% during a market correction, what is the expected movement in the fund's NAV (holding other factors constant)?

[ A ]Expected increase of 10.0%

[ B ]Expected decline of exactly 8.0%

[ C ]Expected decline of 6.4% (8.0% / 1.25)

[ D ]Expected decline of 10.0% (1.25 * -8.0%)[ CORRECT ]

Takeaway

Option D is correct: Expected decline of 10.0% (1.25 * -8.0%)

Derivation

Beta measures the systematic sensitivity of a scheme's returns relative to movements in its benchmark index (which has a Beta of 1.0). A Beta of 1.25 indicates that the scheme is 25% more volatile than the market on both upsides and downsides. When the market benchmark falls by 8.0%, the expected change in the scheme NAV = Beta * Benchmark Return = 1.25 * (-8.0%) = -10.0% (a 10% decline). This tests the application of Beta under Capital Asset Pricing Model (CAPM) principles. A common error is dividing benchmark return by Beta.

Why the others fail

A — Expected increase of 10.0%

Beta measures directional sensitivity; a positive Beta implies the fund moves in the same negative direction as the falling benchmark.

B — Expected decline of exactly 8.0%

A decline of 8.0% assumes a Beta of 1.00; a Beta of 1.25 amplifies market movements to an expected 10.0% fall.

C — Expected decline of 6.4% (8.0% / 1.25)

6.4% incorrectly divides the benchmark market return by Beta instead of multiplying it to determine portfolio sensitivity.