Hedged Position Gain/Loss

I don’t get why the Beta is used in the loss to portfolio calc. Is it assuming that the index that decreases 7% has a beta of 1 whereas the beta of the equity prtu is 1.25?

Consider an investor who hedges a \$75,000,000 equity portfolio using S&P 500 futures contracts. The S&P 500 futures contract stands at 1080.00 and one contract is worth 225 times the index. The beta of the portfolio is 1.25. Assuming the index decreases by 7%, which of the following is closest to the net profit, in dollars, of the overall (hedged) position? – No. of contracts sold to hedge position = \$75,000,000 / (1080 x 225) x 1.25 = 386 contracts

Loss to portfolio = \$75,000,000 x 0.07 x 1.25 = \$6,562,500

Gain to futures = 386 contracts x (1080 x 225) x 0.07 = \$6,565,860

Overall gain = \$6,565,860 - \$6,562,500 = +\$3360

In which reading did you find this?

I ask because I want to read the original text. It sounds as though they’re misusing beta; i.e., they’re treating it as a comparison of _ values _, not a comparison of returns. It’s a common mistake that finance people make (the same problem occurs in reading 30 on Trading), and I wish that the curriculum authors would understand that (and avoid it).

It’s a sample question from a prep provider