Question

Your Investment advisor suggests a protective put position: go long the STI index fund and long put options on this fund. The option has an exercise price of $80 and 1 month until expiration. Assume STI index is currently trading at $100. Your best friend Joe recommends you to buy a 1-month call option on the STI index fund with exercise price $90 and buy 1-month risk-free asset with face value of $90.

a) Draw the payoffs to both strategies as a function of the STI index fund value in 1 month' time. Label your graph clearly.

b) Which of these strategies require a greater initial cash flow?

c) Suppose the market prices of the securities are as follows: STI index fund: $100 Riskfree asset: 85 Call: 20 Put: 2 Construct a table of realised profits for each portfolio for the following values of the STI index fund in 1 month: $0, $80, $90, $100, and $120. Plot the profits to each portfolio as a function of STI index fund value on one graph.

d) Which strategy is riskier? Briefly explain.

Answer 1

Strategy 1:  long the STI index fund and long put options

Pay off from Put option = Max( X-S,0)

Pay off from long in index= S

Pay off from Strategy 1 = Max( X-S,0) + (S )

Strategy 2: long in call options + Long in risk free

Pay off from Strategy 2 = Max( S-X,0) + R

Answer A) Pay off table :

Spot	Str1	Str2
0	80=MAX(80-0,0)+0	90=MAX(0-90,0)+90
20	80	90
40	80	90
50	80	90
80	80	90
100	100	100
120	120	120
140	140	140
160	160	160

Pay off graph :

Answer 2) Strategy two required higher initial cash flow,

Answer 3) Now profit from the strategy

Strg. 1: Max( X-S,0)-P + (S-S1 ) =

Strg. 2: Max( S-X,0)-P + R- R1 =

profit table:

Spot	Str1 profit	Str2 Profit
0	-22 =MAX(80-0,0)-2+(0-100)	-17=MAX(0-90,0)-22+(90-85)
80	-22=MAX(80-80,0)-2+(80-100)	-17=MAX(80-90,0)-22+(90-85)
90	-12=MAX(80-90,0)-2+(90-100)	-17=MAX(90-90,0)-22+(90-85)
100	-2=MAX(80-100,0)-2+(100-100)	-7=MAX(100-90,0)-22+(90-85)
120	18=MAX(80-120,0)-2+(120-100)	13=MAX(130-90,0)-22+(90-85)

Graph plot :

Answer 4) As the fluctuation of returns are much higher in strategy 1, so this is consider as riskier than second one.