Explanation
As the compounding frequency increases, the nominal rate needs to decrease to produce the same amount of dollars at the end of a given time period. A continuously compounded rate of return has an infinite number of discrete compounding periods, and therefore the nominal rate expressed as a continuously compounded rate will always be nominally lower than any other rate.
Refer to the tutorial on interest rates for more details on continuously compounded rates work.

Explanation
Theta measures time decay, ie the change in value of the option with the passage of time. When the option is close to expiry, theta is very low as the value of the option is driven by intrinsic value rather than the time value. Therefore theta approaches zero as the option comes closer to expiry.

Explanation
The loss to the fund manager is $20*100 = $2,000. The initial margin placed was $5,000. After the loss is charged to his account, the margin balance is only $3,000 ($5,000 - $2,000). The margin to be maintained is
$5,000. Therefore the margin call is $2,000.
Note that there would have been no margin call till the balance in the margin account had reduced to the
'maintenance' level of $4,000. So if the price had fallen by $5, and the loss had been $500, there would have been no margin call. But when the margin call would be made, it would require the balance to be brought up to the initial margin of $5,000 (and not the maintenance margin of $4,000).

Explanation
The no-arbitrage futures price for the stock is the current spot price plus the carrying cost for one year, which in this case is $100 * 10% =$10. Therefore the no-arbitrage futures price for the stock is $110.
($100*(1+10%), or $100 + $10.)

Explanation
A total return swap allows an investor or a financial institution to gain exposure to an asset or a portfolio without actually having to go long in those positions. The counterparty provides the return from the exposure and receives LIBOR plus a spread in exchange. Effectively, the counterparty has funded the investor's position for a fixed interest rate, therefore a TRS is essentially a funding arrangement. However, the structure of a TRS may also have other consequences that are relevant for tax and accounting - the assets under a TRS are not held on the balance sheet of the investor receiving the total return. Statement I is correct as the TRS helps gain an exposure without having to fund the position with cash.
Repos are useful for shorting corporate bonds. The investor desirous of shorting a corporate bond would sell the bond in the market, and immediately borrow the bond from someone else using a repo to deliver to the party he has sold the bond to. Repos are used extensively to cover short bond positions, and therefore statement II is correct.
Statement III is not correct as counterparty risk continues to exist with a TRS. The counterparty may fail to provide the agreed returns, and the risk exists.
Statement IV is correct as the bank that borrows funds using a repo continues to hold the underlying assets on its balance sheet. Therefore Choice 'd' is the correct answer.