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.