To increase beta from 0.30 to 1.00, the manager must add positive market exposure through futures.

The number of contracts is:

$$N = (\beta_T - \beta_P)\frac{V_p}{V_f}$$

where:

• $\beta_T - \beta_P = 1.0 - 0.30 = 0.70$
• $V_p = 10{,}000{,}000$
• $V_f = 250 \times 1380 = 345{,}000$

So:

$$N = 0.70 \times \frac{10{,}000{,}000}{345{,}000} \approx 20.29$$

Rounding to the nearest whole number gives long 20 S&P 500 futures contracts.