### CFA Practice Question

An investor has \$10,000 in cash and a stock is selling for 100 per share. Calls on that stock are selling for a premium of \$2.04. If the investor wishes to create a fiduciary call position, she should ______
A. buy 10,000 worth of stock and sell 4,902 calls.
B. buy 5,000 worth of calls and use the rest to buy stock at 50% margin.
C. buy 98 calls and invest the remainder in Treasury bills.
Explanation: A fiduciary call is an indirect way of owning the upside potential of a stock without buying the stock. In this case, 98 calls would cost a total of \$200 (= 98 x \$2.04), and the balance amount of \$9,800 will be invested in a risk-free security. If the stock price falls, the calls will expire worthless and the investor will get the future value of the risk-free security (which includes interest); if the stock price rises, the calls can be exercised and the investor will earn a profit along with the future value of the risk-free security. The net cost of this strategy is the premium paid on the calls, i.e., \$200.

User Comment
eddeb okay with the solution, but why exactly 98 calls?
chuong We concern only fiduciary call including buying call and buying bond
n9845705 98 x 2.04 x 100 = 19,992
Doesn't this mean he can only buy half of 98?
julamo you don't multiply by 100. If you buy some call options you pay only the premium, not the price of the underlying stock.
coolpassion 100n + 2.04n = 10000
n = 98
Tomcat82 calls are selling for \$2.04. Each contract is for 100 shares. So in fact you do pay \$204 per contract.
pepper hi coolpassion, where did you get the formula?
alallstar apparently they are pretending each call option is for a single share, priced at \$2.04, rather than the standard 100 option contract that would cost \$204.
Mikehuynh Fiduciary = protective
long call + long bonds = sale of put + possess underlying asset
RAustin Wow I want in on this strategy, buying options for \$2 when the underlying stock is \$100; to the moon baby!!
petervinh18 Don't make sense to me...
1 call (contract) = 100 shares; so
98 calls (contracts) = 9,800 shares, then muliply premium
9800 x \$2.04 = \$19,992...which it more than \$10k cash in hand.

Per Julamo posted...not multiply price of stock but I think we are multiplying contract persective.
mbuenafe Pass...
santibanez Mikehuynh, fiduciary call ( long call + long risk free asset ) = protective put (LONG put + long risky asset )
cfastudypl Thanks coolpassion, you nailed it. As the formula, clearly shows a clear strategy of what smart investors and traders would do under the circumstance. It is assume though, from the formula, that the risk free rate will be higher than the call premium for the formula to be valid. Thanks, all the same. For, others, it is important to keep in perspective the fundamental, buying a call is not the same as buying a share.