TO 36 RELATE TO DERIVATIVES STEPHEN MULLER, CFA, CASE SCE...
Questions 31 to 36 relate to Derivatives
Stephen Muller, CFA, Case Scenario
Stephen Muller, CFA, is a derivatives specialist at Winstar Associates, a derivatives
dealer firm. He is analyzing two transactions – i) establishment of an interest rate collar
on a floating rate loan undertaken by Top-Tech, a client of WA, and ii) sale of equity call
options to a client.
Interest Rate Collar
Top-Tech arranged a floating rate loan on June 15, 2013 to finance the construction of
one of its factories. Top-Tech’s CEO made a request to Muller to reduce the firm’s
exposure to the risk of rising interest rates. Muller responded by purchasing caplets and
selling floorlets to establish a zero-cost position. Details concerning the loan transaction
and hedging transaction are summarized in Exhibit 1. Exhibit 2 summarizes LIBOR rates
and the number of days falling within each settlement period.
Exhibit 1:
Details Concerning Loan and Hedging Transaction
Loan amount
$50 million
Frequency of interest payments
Semi-annually (June 15 and December 15)
Term of loan
2 years
Cap rate
10.20%
Floor rate
9.40%
Interest rate on loan
Libor + 100 basis points
Exhibit 2:
Loan Settlement Dates and LIBOR Rates
Number of
LIBOR
Settlement Date
Days in Period
(%)
June 15, 2013
8.50
December 15, 2013
183
9.00
June 15, 2014
182
9.20
December 15, 2014
183
9.95
June 15, 2015
182
11.30
Muller shares the results of the transaction to his recently hired junior analyst, Tyron
Bolt. After a preliminary review, Bolt poses the following questions to his supervisor:
Question 1: “At which rates will Top-Tech’s exposure to interest rate risk be highest?”
Question 2: “Effective interest payments can differ even if the LIBOR rate is the same for
each settlement date. Is this because some options are expiring when they
are in-the-money?”
Delta Hedged Position
Next, Muller analyzes the short call position taken by WA. The firm sold 1,000 call
options, priced at $85.60, to its client so that the latter could hedge his stock holding. To
delta hedge the firm’s short call position, a senior derivatives trader at WA purchased
shares of the underlying stock when the market price was $3,000. The exercise price of
each call option was $2,250 while the shares were purchased using available funds and
carry a zero dividend yield.
Muller notes that a frequent issue with delta hedging is the need to dynamically rebalance
the hedge with the passage of time and change in price. Muller would like to analyze the
impact of an instantaneous price change on the delta hedged position. He uses the Black-
Scholes-Merton (BSM) model to calculate new deltas for each change in the underlying
price as well as estimates the new call price. He summarizes the results in Exhibit 3
assuming time to be a constant factor in his analysis.
Exhibit 3:
Results of the BSM Model and
Delta-Estimated Call Prices
New Price of
Delta-Estimated
Underlying
Call Price ($)
($)
New Delta
2,980
?
0.5980
2,990
79.48
0.6123
3,000
85.60
0.6545
3,010
92.61
0.7010
31. Using the data in Exhibit 1, the effective interest due on June 15, 2014 is closest
to:
A.
$2.427 million.
B.
$2.440 million.
C.
$2.629 million.
32. The most appropriate response to Question 1 and 2, respectively, is:
Question 1:
Question 2:
A.
any rate exceeding 10.20%
a no.
B.
any rate below 9.40%
a yes.
C.
any rate between 9.40% and 10.20%
a yes.
33. Using the data in Exhibits 1 and 2, the caplet payoff on June 15, 2015 is closest
A.
$0.
B.
$63,200.
C.
$278,100.
34. Using the data in Exhibit 3 as well as on the delta hedged position, the transaction
required to reestablish the hedge when the underlying declines to $2,990 will
involve:
A.
selling 42 shares.
B.
selling 57 shares.
C.
purchasing 57 more shares.
35. Using the data in Exhibit 3 and the information provided on the delta hedged
position, compared to the delta-estimated price of $92.17, an increase in the
underlying price to $3,010 will result in the actual call price calculated from the
BSM model being:
A.
equal.
B.
lower.
36. Using the data in Exhibit 3 and the information provided on the delta hedged
position, when the underlying declines to $2,980 the delta-estimated call price is
closest to:
A.
$72.51.
B.
$73.64.
C.
$85.03.