The Triple-Leveraged Fund's Nightly Trade

You run the hedging desk for an exchange-traded product that promises $3 \times$ the **daily** return of a crude oil index. At last night's close the fund had $\$200$ million of investor equity, so it held $\$600$ million of index exposure via swaps and futures.

(a) Today the index rises $4\%$. What trade must the fund do into today's close to be correctly positioned for tomorrow, and in which direction?

(b) Suppose instead the index had fallen $4\%$. What trade then?

(c) The index goes up $10\%$ one day and down $10\%$ the next. The index is then down $1\%$ over the two days. Where is the $3 \times$ fund? Explain the gap to a client who expected $-3\%$.