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

(i)

Value of a long put option = Max[X-S, 0]

S = underlying price at expiry,

X = exercise price.  

(ii)

Value of portfolio = Value of put option + value of stock

(iii)

Return on investment = (Value of portfolio at expiration - value of portfolio today) / value of portfolio today

value of portfolio today = purchase price of stock + purchase price of put option

value of portfolio today = $100 + $5 = $105

А в Spot price at Value of Value of Return on expiration put option portfolio investment $85 $23 $108 2.86% $90 $18 $108 2.86% $95 $108 2.86% $100 $108 2.86% $105 $108 2.86% $110 $110 4.76% $115 $115 9.52% $120 $120 14.29% $125 $125 19.05% $130 $130 23.81%

The formulas are below :

Spot price at Value of put option Value of portfolio Return on investment 1 expiration 2 85 3 90 4 95 5 100 6 105 7 110 8 115 9 120 10 125 =MAX(108-A2,0) =MAX(108-A3,0) =MAX(108-A4,0) =MAX(108-A5,0) =MAX(108-A6,0) =MAX(108-A7,0) =MAX(108-A8,0) =MAX(108-A9,0) =MAX(108-A10,0) =MAX(108-A11,0) =A2+B2 =A3+B3 =A4+B4 =A5+B5 =A6+B6 =A7+B7 =A8+B8 =A9+B9 =A10+B10 =A11+B11 = (C2-105)/105 =(C3-105)/105 =(C4-105)/105 =(C5-105)/105 =(C6-105)/105 =(C7-105)/105 =(C8-105)/105 =(09-105)/105 =(C10-105)/105 =(C11-105)/105 11 130

(iv)

The put option gains in value if the stock price at expiration is below the option exercise price. Thus, if the stock price falls, the gains on the put option offset the losses on the stock. In this way, the put option is helping you to reduce the downside risk of your investment.

Value of value of portfolio Return on investment Spot price at put expiration option $85 $15 $90 $10 $95 $100 $105 $110 $115 $120 $125 $130 $100 $100 $100 $100 $105 $110 $115 $120 $125 $130 -4.76% -4.76% -4.76% -4.76% 0.00% 4.76% 9.52% 14.29% 19.05% 23.81%

Value of put option Spot price at 1 expiration 2 85 3 90 4 95 5 100 6 105 7 110 8 115 9 120 10 125 11 130 =MAX(100-A2,0) =MAX(100-A3,0) =MAX(100-A4,0) =MAX(100-A5,0) =MAX(100-A6,0) =MAX(100-A7,0) =MAX(100-A8,0) =MAX(100-A9,0) =MAX(100-A10,0) =MAX(100-A11,0) Value of portfolio =A2+B2 =A3+B3 =A4+B4 =A5+B5 =A6+B6 =A7+B7 =A8+B8 =A9+B9 =A10+B10 =A11+B11 Return on investment =(C2-105)/105 =(C3-105)/105 =(C4-105)/105 = (C5-105)/105 = (C6-105)/105 =(C7-105)/105 = (C8-105)/105 =(C9-105)/105 =(C10-105)/105 =(C11-105)/105