UNIVERSITY OF THE WESTERN CAPE

2018

Semester Test 1

MODULE NAME : INVESTMENT ANALYSIS

MODULE CODE : MAN308

DURATION: 90 minutes MARKS: 45

LECTURER: Mr Samuel Enow

Question One [20]

a. An investor purchases a stock for R38 and a put for R.50 with a strike price of
R35. The investor sells a call for R.50 with a strike price of R40. What is the
maximum profit and loss for this position? Draw the profit and loss diagram
for this strategy as a function of the stock price at expiration. /10/

MEMO
Position ST < 35 35  ST  40 40 < ST

Buy stock ST ST
X2X2XX 2X2 ST
X2X2X2
Write call ($40) 0 0 40 - ST

Buy put ($35) 35- ST 0 0

Total $35 ST $40

Profit

$2

$35 $40
-$3

Award full 10 marks if the diagram and figures are correct. Otherwise,
allocate 5 marks for profit and loss table and 5 marks for diagram. Mark
linently
 b. Donna Donie, CFA, has a client who believes the common stock price of TRT
Materials (currently R58 per share) could move substantially in either
direction in reaction to an expected court decision involving the company. The
client currently owns no TRT shares, but asks Donie for advice about
implementing a strangle strategy to capitalize on the possible stock price
movement. A strangle is a portfolio of a put and a call with a higher exercise
price but the same expiration date. Donie gathers the TRT option-pricing data:

characteristics Call option Put option

Price R5 R4
Strike price R 60 R 55
Time to expiration 90 days from now90 days from now

Recommend whether Donie should choose a long strangle strategy or a short

strangle strategy to achieve the client’s objective and briefly motivate your answer
/4/
Memo
Donie should choose the long strangle strategy (1 mark). A long strangle option
strategy consists of buying a put and a call with the same expiration date and the
same underlying asset, but different exercise prices (1 mark). In a strangle strategy,
the call has an exercise price above the stock price and the put has an exercise price
below the stock price. An investor who buys (goes long) a strangle expects that the
price of the underlying asset (TRT Materials in this case) will either move
substantially below the exercise price on the put or above the exercise price on the
call. (2 marks). (Accept any reasonable answer)

Calculate, at expiration for the appropriate strangle strategy using the data above, the:
i. Maximum possible loss per share. /2/

The maximum possible loss per share is R9.00, which is the total cost of the two
options (R5.00 + R4.00). (Award 1 mark for each correct answer)

ii. Maximum possible gain per share. /2/

The maximum possible gain is unlimited if the stock price moves outside the
breakeven range of prices.

iii. Break-even stock price(s). /2/

The breakeven prices are R46.00 and R69.00. The put will just cover costs if the
stock price finishes R9.00 below the put exercise price
(i.e., R55 − R9 = R46), and the call will just cover costs if the stock price finishes
R9.00 above the call exercise price (i.e., R60 + R9 = R69).
Question Two [15]

A stock index is currently trading at R50. Joel, wants to value 1-year index options
using the binomial model. The stock will either increase in value by 20% or fall in
value by 20%. The annual risk-free interest rate is 6%. No dividends are paid on any
of the underlying securities in the index.

a. Calculate the value of a European call option on the index with an exercise
price of 60.

The two possible values of the index in the first period are:
uS0= 1.20 × 50 = 60

dS = 0.8 × 50 = 40

The value of call is 0 (5 marks)

b. Calculate the value of a European put option on the index with an exercise
price of 60.

60- 40 = 20 * 0.35 = 7 /1.06 = R6.60 (5 marks)

c. Confirm that your solutions for the values of the call and the put satisfy put-
call parity.
0 + 60/1.06 = 60 + 6.6 (3 marks), Therefore it doesn’t satisfy the
equation (2 marks)

Question Three [10]

i. Joel Franklin is a portfolio manager responsible for derivatives. Franklin observes

an American style option and a European-style option with the same strike price,
expiration, and underlying stock. Franklin believes that the European-style option
will have a higher premium than the American-style option. Critique (criticise)
Franklin’s belief that the European-style option will have a higher premium. /4/

Memo
American options should cost more (have a higher premium). American options
give the investor greater flexibility than European options since the investor can
choose whether to exercise early. When the stock pays a dividend, the option to
exercise a call early can be valuable. But regardless of the dividend, a European
option (put or call) never sells for more than an otherwise-identical American
option. (Accept any reasonable answer)
ii. State the effect, if any, of each of the following three variables on the value of a
call option.
(No calculations required.)
a. An increase in short-term interest rate. /2/
b. An increase in stock price volatility. /2/
c. A decrease in time to option expiration. /2/

Factor Call (C0) Put (P0)

Volatility of Underlying Asset Returns () (+) (+)

The higher the volatility of the underlying asset returns, the higher the upside profit potential for both
Call and Put, while the downside risk is limited to their upfront premiums.

Positive correlation between S0 and C0; Positive correlation between S0 and P0

Time to Expiration of the Option (T) (+) (+)

Time value is a version of volatility value

The longer the time to expiration, the more chances are there for Call / Put options to move deeper in-the-money,
while the downside risk is limited to the upfront premiums paid.

Positive correlation between S0 and C0; Positive correlation between S0 and P0

Risk-Free Rate (r) (+) (-)

LC: right to buy at X [i.e. –X]; LP: right to sell at X [i.e. +X]
The higher the risk-free discount rate, the lower the present value of future payment for Call [i.e. PV(-X)];
The higher the risk-free discount rate, the lower the present value of future receipt for Put [i.e. PV(+X)]