Triple-leveraged ETFs

Underlying unlevered ETF demonstrated the following path over a four day period:

Day	0	1	2	3	4
Price	100	110	100	90	100

Assuming risk-free rate of interest of zero for both lending and borrowing.

a. You are managing a 3X leverage ETF that targets 3 times the daily return of the underlying index. If the starting with a price of 100, what is the daily price?

Day	0	1	2	3	4
Price	100

b. You are managing a 3X leverage ETF that targets 3 times the daily return of the underlying index. If the starting with a price of 100, what is the daily position in the un-levered ETF and cash?

Day	0	1	2	3	4
Position in unlevered ETF	300
Position in cash	-200

c. You are managing a -3X leverage ETF that targets 3 times the opposite daily return of the underlying index. If the starting with a price of 100, what is the daily rebalancing decision in the un-levered ETF and cash?

Day	0	1	2	3	4
Position in unlevered ETF	-300
Position in cash	400
Rebalancing Trade in ETF	NA