Let’s assume the current stock price is $50. Also, suppose a six-month maturity
ID: 2796015 • Letter: L
Question
Let’s assume the current stock price is $50. Also, suppose a six-month maturity call option with exercise price of $50 sells for $4 and the semi-annual interest rate is 3%. Consider the following two strategies for investing a sum of $2,000.
Strategy 1: Invest entirely in at-the-money call options. Buy 500 calls, each selling for $4. (This would require 5 contracts, each for 100 shares.)
Strategy 2: Purchase 200 at-the-money call options for $800. Invest the remaining $1,200 in six-month T-bills, to earn 3% interest.
A). Fill in the table below for each of the investment strategies’ dollar payoff. Show your work below the table.
B). Fill in the table below for each of the investment strategies’ rates of return. Show your work below the table.
Explanation / Answer
Payoff
Strategy1:
45:500*max(45-50,0)=0
50:500*max(50-50,0)=0
55:500*max(55-50,0)=2500
60:500*max(60-50,0)=5000
65:500*max(65-50,0)=7500
Strategy2:
45:200*max(45-50,0)+1200*1.03=1236
50:200*max(50-50,0)+1200*1.03=1236
55:200*max(55-50,0)+1200*1.03=2236
60:200*max(60-50,0)+1200*1.03=3236
65:200*max(65-50,0)+1200*1.03=4236
Return
Strategy1:
45:(0-4*500)/(500*4)=-100%
50:(0-4*500)/(500*4)=-100%
55:(2500-4*500)/(500*4)=25%
60:(5000-4*500)/(500*4)=150%
65:(7500-4*500)/(500*4)=275%
Strategy2:
45:(1200*3%-800)/(800+1200)=-38.2%
50:(1200*3%-800)/(800+1200)=-38.2%
55:(1200*3%+200*5-800)/(800+1200)=11.8%
60:(1200*3%+200*10-800)/(800+1200)=61.8%
65:(1200*3%+200*15-800)/(800+1200)=111.8%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.