To hedge a stock portfolio using index futures, the optimal number of futures contracts to short is calculated using the formula:

$N = \beta \times \left( \frac{V_P}{V_F} \right)$

Where:

• $\beta$ is the beta of the portfolio = $0.98$
• $V_P$ is the current value of the portfolio = \`633`,000,000$
• $V_F$ is the value of one futures contract = Futures Price $\times$ Multiplier = $2,906 \times 250 = `$726`,500$

$N = 0.98 \times \left( \frac{633,000,000}{726,500} \right)$ $N = 0.98 \times 871.3007$ $N = 853.87$

The number of contracts Lange should short is closest to 854.