You have $10,000 to invest and decide to invest in a combination of a riskless asset (f), a stock index fund (S), and a long-term bond fund (B), with the following properties:

• Asset: E(r) / Standard Deviation / Beta

• Riskless Asset (f): 0.04 (4%) / 0.00 / 0
• Stock index fund (S): 0.10 / 0.25 / 1.2
• Long-term bond fund (B): 0.06 / 0.15 / 0.4

The correlation of the returns between the long-term bond fund and the stock index fund equals 0.3. The market portfolio is defined as 66% of stock S and 34% of the bond B.

(b) What dollar amount should you invest in asset S if you would like to achieve an expected return of 7% with the lowest possible standard deviation?