Question

You Just  a TD stock at $100 and a put option on the TD stock at $5. The put has exercise price of $108 and expiration date is 6 months from now. Assume that the spot price of the TD stock on expiration date turned to as follows (consider each case separately):
Spot price at expiration
$85
$90
$95
$100
$105
$110
$115
$120
$125
$130
i. What will be value of put option expiration date under each scenario.
ii. What will be the value of your portfolio (a stock and a put option) at expiration under each case?
iii. What will be your return on investment (a stock and a put)? Compute holding period return for each case.
iv. Discuss how put option is helping you to reduce the downside risk of your investment.
Now assume that you rather short the TD stock today and buy a call option with a strike price of $105
v. What will be value of call option expiration date under each scenario.
vi. Discuss how call option is helping to reduce the upside risk of your investment strategy.

Answer 1

Purchase Price of Stock	100
Option Exercise Price	108
Option Premium	5
Spot Price at Expiration	Payoff of Option i.e. Value of Option at expiration [Higher of (Option Exercise Price-Spot Price at Expiration) & 0]	Profit/Loss on Option [Payoff-Premium]	Profit/Loss on Stock [Spot Price at Expiration-Purchase Price]	Value of Portfolio [Spot Price at Expiration+ Profit/Loss on Option]	Return on Investment i.e. Holding Period Return [((Value of Portfolio-Purchase Price of Stock)/Value of Portfolio]
85	23	18	-15	103	0.03 = 3%
90	18	13	-10	103	0.03 = 3%
95	13	8	-5	103	0.03 = 3%
100	8	3	0	103	0.03 = 3%
105	3	-2	5	103	0.03 = 3%
110	0	-5	10	105	0.05 = 5%
115	0	-5	15	110	0.1 = 10%
120	0	-5	20	115	0.15 = 15%
125	0	-5	25	120	0.2 = 20%
130	0	-5	30	125	0.25 = 25%

From above table,

Put Option has COMPLETELY ELEMINATED the downside risk of the Investment. Although such scenarios are rare. This is clearly an Arbitrage Opportunity, there is NO DOWNSIDE RISK AT ALL. Put Option gives RIGHT to Sell the stock at Exercise Price. Therefore, no matter what, we will be able to sell the stock for AT LEAST 108, and to avail that Option, Cost is just $5. Therefore, there is a RISKLESS PROFIT of $3.

Note: As per Guidelines, we are supposed to answer ONLY 4 Sub-Questions.