Quick question see bold highlighted part.

Question 1 Pension fund XY has a large investment portfolio comprising bonds and equity. The trustees are concerned about a fall in value over the next year as economies worldwide emerge from the Covid-19 pandemic crisis. The trustees are considering two main strategies: Reduce equity price risk by lowering the beta of the equity portfolio. Purchase Credit Default Swaps (CDSs) to reduce credit risk in the bond portfolio.

a) The equity portfolio is currently valued at $500 million and the S&P 500 index futures contract is trading at $445,000. The trustees have asked for the equity portfolio beta to be reduced from 1.45 to 0.90.

Required: Calculate the number of S&P index futures required to change the equity portfolio beta from 1.45 to 0.90 and explain the rationale behind the formula and approach you use in this calculation.

-hi i need help with the rationale of the formula. other than the beta of futures contract being 1 and buying sand selling futures based on sign from ai) which i got -.618 (selling futures) i don't know what else to write for bold part.