A- Suppose that a corporation sets up a pension fund, which invests in a private equity fund (limited partnership), which invests in a leveraged buyout of a family-owned business, which involves transfer of all the shares in the family-owned business to a special purpose vehicle which the private equity fund managers control. According to BlackRock, who is the new owner of the family-owned business: the shareholders of the corporation, the corporation itself, the corporations pension plan, the beneficiaries of the pension plan, the limited partnership, the general partner of the limited partnership, the limited partners, the special purpose vehicle, or some other entity?

B- Consider a leveraged or unleveraged fund which is has exposure of X % to a broad stock market index (S&P 500) and exposure of 100% X % to an approximately risk-free asset (Treasury bills, money market fund, or short-term bond fund). If 0% < X % < 100%, then the fund is long only and unleveraged; if X % > 100%, the fund is leveraged long; and if X % < 0%, the fund is short or leveraged short. Suppose that the market moves down 1%. Replace dots (. . . ) in the table below with actual numbers to answer the following questions: What is the return on the fund (percent)? How much must the fund buy (+) or sell () to re-balance the funds exposure (percent of funds assets)? Is the funds trading stabilizing (buying when market falls, selling when market rises) or destabilizing (selling when market falls, buying when market rises)?

Summarize the results in this table with one sentence and one mathematical formula. Why is the stabilizing or destabilizing effect of rebalancing a 3X levered long ETF different from the stabilizing or destabilizing effect of rebalancing a 3X levered short ETF?

X exposure	return	buy(+) or sell(-)	stabilizing or destabilizing
-300%	...	...	...
-200%	...	...	...
-100%	...	..	...
-50%	...	..	...
+0%	...	..	...
30%	-0.30%	+0.21%	stabilizing
50%	...	..	..
60%	-0.6%	+0.24%	stabilizing
90%	..	...	...
100%	..	...	...
150%	..	...	destabilizing
200%	-2.00%	-2.00%	...
300%	...	...	...

C-If you buy shares in a levered long ETF, is this most similar to buying a call option, selling a call option, buying a put option, or selling a put option? If you buy shares in a levered short ETF, is this most similar to buying a call option, selling a call option, buying a put option, or selling a put option?