Nice Novel

[Jason Whitlock]

Call is the right to buy-bullish
put is right to sale-bearish
option is "in the money" when intrinsic value>0
Premium = int value + time value
effects of div and int rates on premium
higher div rate: lower call premiums,higher put premiums
higher int rate:higher call prem,lower put prem
long call option for buyer: price rises from 85 to 90, premium is 1: profit is 4
short call option for writer: price rises to 41 from 30, premium is 5: loss is 6
long put for buyer: orig price is 45, price falls to 35, premium is 5 profit is 5
short put for writer: orig price is 30, falls to 24, premium of 6: loss of 4
BE for call = strike plus premium
BE for put=strike plus premium
Buy Call: Max gain-unlimited,max loss is premium
Sell Call: Max gain-premium, max loss unlim
Buy Put: Max Gain-strike-premium, max loss is premium
Sell Put: Max gain-premium, max loss-strike minus premium

[Jason Whitlock]

A customer sells 1 ABC feb 50 call@ 7 when mkt price is 52. Mkt value falls to 48, what does cust gain or lose?

Mkt price<strike price so dont exercise, just earn 700 premium
Breakeven = 50+7
Max loss is unlimited-premium. mkt price could keep rising, theyd have to sell for 48 and pay more


Customer buys 2 ABC Jan 60 Puts @ $4 when the market price of ABC is $59.

The maximum potential loss is?

Maximum loss for a put buyer is the premium paid.

B.E Point
The breakeven point for puts (buyers or writers) is Strike Price Less Premium = 60-4 = 56

(same prob)ABC stock falls to $40 and the customer buys the stock in the market and exercises the put. The gain is?
Market price of $40 is less than the Strike Price of $60. The put buyer exercises and gains a profit on the exercise of $20 *200 (two contracts) options = $4000
The expense of buying the call $4*200 (two contracts) = $800 offsets the $4000 profit from exercise. Total profit = $3200

If ABC stock rises to $62 and the customer closes the positions at $1, the gain or loss is?

Put buyer bought the put contracts for $4 *200 (two contracts) = $800 (the outflow)
Put buyer cal sell the contracts for $1* 200 (two contracts) = $200 (inflow)
Net expense or loss = $600

[Jason Whitlock]

4. A customer sells 1 ABC Jul 40 Put at $6 when the market price of ABC is $38

ABC stock rises to $60 and stays there until July. What is the gain or loss?

Market Price of $60 exceeds the Strike Price of $40 so the put buyer never exercises on our investor here (the put is said to be ‘out of the money’). So the investor just gets the premium of $6 *100 = $600

The customer’s break even is?

The breakeven point for puts (buyers or writers) is Strike Price Less Premium = $40 - $6 =$34

At Market Price of $34, the put buyer exercises on the put writer.

The put writer has to buy at the Strike Price of $40 (since the put buyer has the right to sells at $40) and sell at the Market Price of $34, resulting in a $6 loss.

The loss is offset by what the writer earned on the premium or $6

Net loss is 0

The customer’s maximum potential gain is ?

The put writers maximum gain is the premium. This is earned when Market Price exceeds the Strike Price and the writer is not exercised upon.



The market falls to $25 and the customer is exercised upon. The customer sells the stock in the market. The loss to the put writer is?

The put writer has to buy at the Strike Price of $40 (since the put buyer has the right to sell at the Strike Price of $40) and sells in the market for $25 for a loss of $15 *100 = $1500

This is offset by the premium earned by the put writer of $6 * 100 - $600

Net Loss is $1500 -$600 = $900


The maximum potential loss to the writer?

The maximum loss for a put writer is the Strike Price less Premium.

If the Market Price of the stock falls to zero, the put buyer will exercise his right to sell at the Strike Price which means that the writer has to buy at the Strike Price of $40 and buy at Zero. The loss on exercise for the put writer is $40 * 100 = $4000

The loss is offset by what the put writer earned on selling the put or $6 * 100 = $600

Net loss is $40 - $6 = $3,400

This is also the maximum gain to the put buyer.

5. For a covered call –
Break even and also Max Loss = Cost of the stock less Premium received
Max Gain = Premium net of the difference between the Cost of the stock and the Strike Price

For a protective put –
Break even = Cost of the stock plus Premium paid;
Max Gain UL;
Max Loss = Premium net of difference between the Cost of the stock and the Strike Price

1. A customer buys 100 shares of ABC stock at $40 and buys 1 ABC Oct 40 put at $4

ABC stock falls to $36 and just prior to expiration, the customer exercises the put. What is the gain or loss?

Buys 100 shares at $40 – outflow $4000
Buys 1 ABC Oct 40 put at $4 – outflow $400

Cash flow from the exercise. Customer has the right to sell her shares at the Strike Price of $40*100 = $4000 inflow.

Loss $400


2. A customer buys 100 shares of XYZ at $49 and buys 1 XYZ Jan 50 Put @$5

The stock falls to $32 and the customer exercises the put. The gain or loss is?

Buys 100 shares at $49 – outflow $4900
Buys 1 XYZ Jan 50 put at $5 – outflow $500

Cash flow from the exercise. Customer has the right to sell the shares at the Strike Price of $50*100 = $5000 inflow. $100 Gain on Exercise but customer paid $500 for the right to sell his 100 shares of XYZ at $50.

Net loss = $400

The break even point is?

Cost of stock plus premium = Cost of Stock was $49 plus $5 Premium Paid = $54

Buys 100 shares at $49 – outflow $4900
Buys 1 XYZ Jan 50 put at $5 – outflow $500
Total outflow = $5400

The maximum potential gain is?

Unlimited. The put protects the downside of the owned stock. On the upside, if the stock continues to increase, the investor has unlimited gain (less the cost of the put).

The maximum potential loss is?

Max loss on a protective put is the premium net of any difference between the stock cost and the strike price.

Premium is $5, difference between the stock cost and the strike is 50-49= 1 so the maximum loss is $4 or $400 for the contract

Exercising at 50 when the investor bought the stock at $49 will result in a $1 gain. However the premium of $5 is lost.

Even if the stock falls to 0, the investor can exercise at $50 and earn $1 on the stock he purchased for $49. This is offset by $5 expense of buying the put.

Net loss is $4*100 =$400

Just prior to expiration, the stock is trading at $49. The customer closes the option position at a premium of $2. One week later the stock moves to $55 and the customer sells the stock in the market. The net gain or loss on all transactions is?

Buys 100 shares at $49 – outflow $4900
Buys 1 XYZ Jan 50 put at $5 – outflow $500
Total outflow = $5400

Sells the put for $2 – inflow $200
Sells the stock for $55 – inflow $5500
Total inflow = $5700

Net gain = 300



4. A customer buys 200 shares of BBB at $72 and sells 2 BBB 70 Calls @$6

The market rises to $80 and the calls are exercised, The customer gain or loss is?

Purchase 200 shares at $72 = 14,400 outflow
Sell 2 calls for $6 = 1,200 inflow
Net initial outflow = 13,200

The call writer is exercised upon (because market price of $80 exceeds strike price of $70)) and has to sell at the Strike Price of $70.

But he bought the shares for $72 so the loss on the 200 shares is $2*200 = $400. The call writer also received the call premium of $1,200. Net profit is $800

Sell the shares at $70 - $14,000 inflow

Net gain = $800

Net gain = $4 *200 (2 contracts) = $800


The break even point is?

Cost of stock less premium received. = $72 - $6 = $66

At a Market Price of $66, Market Price is less than Strike Price.
The call buyer does not exercise. The call writer is not exercised upon.

The call writer can sell the stock he bought at $72 for $66, resulting in a loss of $6 *200 = $1,200. This is offset by the premium earned on the saleof the call option of $6*200 = gain of $1,200.

Net gain/loss = 0


Maximum potential loss is?

Cost of stock less premium received. = $72 - $6 = $66 *200 (2 contracts) = 13,200
maximum loss

If the Market Price goes to zero, the call writer is not exercised upon.

However, he now has to sell the stock he bought for $72*200 shares =$14,400 for 0 resulting in a loss of $72*200 shares or $14,400. This loss is offset by the gain on the sale of the call option of $6*200 or $1,200 for a net loss of $13,200.


$6 – $72 = $66 *200 (2 contacts) - $13,200

The maximum potential gain is?

Premium net of the difference between the purchase price of the stock (the stock cost) and the Strike Price.

When the investor is exercised upon the call writer has to sell at the Strike Price (since the call buyer has the right to buy at the Strike Price).


Net gain = $4 *200 = $800

[Jason Whitlock]

B. Determinants of Option Values

1. Stock price--an increase in the price of the stock increases the value of a call option and decreases the value of a put option

2. Exercise price--an increase in the exercise price decreases the value of a call option and increases the value of a put option

3. Stock price volatility--an increase in the volatility of the stock increases the value of both a call and a put option

4. Time to expiration--an increase in the time to expiration increases the value of a call option while it may increase or decrease the value of a put option

5. Interest rate--an increase in interest rates increases the value of a call option and decreases the value of a put option

6. Stock dividend--a higher dividend payout lowers the value of a call option and raises the value of a put option

Stock Price, Interest Rate, Volatility, Time – Directly related to value of Call Premium

Exercise Price and Dividend Payout – Indirectly related to value of Call Premium

SERVD T




H = (Cu- Cd) (/uSo – dSo); (12.50-0)/(65-40) = 1/2

Thus we can create a risk free hedge portfolio be selling two options and buying one share of stock.

1/n is called the hedge ratio.
Remember that the hedge ratio is 1/n or number of shares per option so 1/2 shares per option. Multiply both side equally by two = 1 share per 2 options


Portfolio hedge ratio:

Consider two portfolios. Which has more dollar exposure to IBM price movements? Use hedge ratio H

Portfolio 1:
750 IBM Calls + 200 shares of IBM Portfolio 2:
800 IBM shares

Each option changes in value by H dollars for each dollar change in stock price. So if H=0.6 then the 750 IBM calls are equivalent to (750*.6 = 450) 450 IBM shares in terms of their response to the market value of IBM stock. Thus the first portfolio which has the equivalent of 450 +200 = 650shares of IBM has less dollar sensitivity to price movement.


•Option elasticity

[Jason Whitlock]

B. The Basics of Futures Contracts

• Long position: Commits to purchasing (buy) the commodity on a delivery date

o The person that will purchase the good (take delivery)
o Profits from futures price increases (can sell in the future at a higher price)

• Short position: Commits to deliver (sell) the commodity on the delivery date

o The person that will sell the good (deliver or called ‘make delivery’)
o Profits from futures price declines (can buy back at a lower price)

• Short position loss equal long positions gain

• No money changes hands immediately but margin is posted

• Futures market (price predicted at a future date) and spot market (price today


• Profit to long = Spot at Maturity less Original futures price

• Buyer must buy the commodity at the contracted future price (take delivery) but then could sell that the spot price at maturity.

• If spot is higher than the contracted future price at maturity, the long investor makes money.

• If spot is lower than the contracted future price at maturity, the long investor loses money. (Paid too much)

• Profit to short = Original futures price less Spot at Maturity

• Seller must deliver the commodity at the contracted future price (make delivery) but then could buy that the spot price at maturity.

• If spot is higher than the contracted future price at maturity, the short investor loses money.

• If spot is lower than the contracted future price at maturity, the short investor makes money.

[Jason Whitlock]

Probs

Leverage

Example: The initial margin requirement on a 5,000 bushel corn contract at $2.1275 per bushel is 10%. What is the dollar amount of the margin requirement?

If the initial margin on corn is 10% of contract value, then the trader must post 0.1*(2.1275*5000) = $1,063.75

If corn prices go up by $0.02 per bushel, what is the percent return on the investment compared to the percent change in the price of corn?

Gain = $0.02*5000 = $100 on and investment of $1,063.75 = 9.4% return (10x greater than the increase in the price of corn of 02/2.1275 =
0.94%)


Lev:
Example: Suppose a speculator buys 1 June T-bond futures contract (100,000 par value at delivery) at a listed future price of 103-29 (remember T-bonds are quoted in 32nds).

If the price of the T-bonds is 104-29 at the time the contract expires, what is the speculator's return on her investment? Assume a margin requirement of 10%.

$103,906.25*10% = $10,390.625 investment

Gain at expiration = 104-29-103-29 = $104,906.25 - $103,906.25 = $1000
So gain =$1,000 / 10,390.625 = 9.62%

If the speculator had purchased T-bonds instead of T-bond futures contract, what would have been the return on investment?
1000/103906.25 = 0.962%


Basis

• Basis Risk exists if contract and asset are to be liquidated earlier than maturity

• Spot (cash) less Futures Price = Basis (we’ll use this; this is used by Series 3 exams)
• Basis consists of carrying charges and cost of transport for the commodity to the exchange approved delivery point
• The cash price should be less than the futures price on any one day (called the discount basis in a Normal Market).because of expected price inflation. If so, Basis is negative; Basis approaches zero at maturity approaches

• A short hedge (trader sold the future to protect any potential decline in the cash price) means that the trader is “long the basis”

Cash Short Future Basis
Time zero 3.94 4.03 -.09
Time t * 3.97 3.98 -.01
Basis +0.03 +0.05 -.01 less-.09=+.08
*Time t here is before maturity
Here the basis strengthened (+.08), so the short hedger profits

The basis strengthens when
• the futures price declines more than the cash price
• the future price rises less than the cash price
• the future price declines while the cash price rises



• A long hedge (trader bought the future) means that the trader is “short the basis”

Cash Long Future Basis
Time zero 3.94 3.77 +0.17
Time t * 3.97 3.98 -.01
Basis -0.03 +0.21 -.01 less.17=-.18

Long hedge trader made money on the future of +0.18

Here the basis weakened (-.18), so the long hedger profits

The basis weakens when

• the futures price increases more than the cash price
• the future price declines less than the cash price
• the future price rises while the cash price declines


Here’s how the book looks at Basis: Some speculators try to profit from movement in basis by betting on the changes in the differences between spot and future prices


Book Example:

Position Today Tomorrow Profit/Loss

Long 100 ounces Spot Price Spot Price $ 300 profit
of gold = $391 = $394.00 ($ 3.00 x 100)

Short 100 ounces June price June price -$250 loss
futures contract = $396 = $398.50 ($ 2.50 x 100)

Basis $ 500 -$ 450 $ 50 profit
($ 5.00 x 100) ($ 4.50 x 100) ($ 0.50 x 100)

Net gain is the decrease in basis or $0.50 an ounce

[Jason Whitlock]

IV. The Determination of Futures Prices

A. The Spot-Futures Parity Theorem (or cost of carry relationship)

Stock price is equal to the present value of the futures price

S0=f0/(1+r)^t
F0=S0(1=Rf)^t

Example: Suppose gold currently sells for $280 an ounce. If the risk free rate is 0.5% per month, a six month maturity future contract should have a price of?
Fo = So(1+rf)T

Fo = 280*(1.005)6= 288.51


put call parity

. Put-Call Parity Relationship


Buy a call and write a put (same exercise price and expiration). Payoff depend on stock price at time t called St. Instead of M as the market price, we will use St

St< or = X St > X
Pay off of Call Held 0 St - X
Minus the Pay off to Written Put -(X-St) -0
St -X St - X

Use numbers Buy a call and write a put with an exercise price of 50 and a stock price of 45. The call would not be exercised but the buyer of the put would exercise meaning that this investor would be obligated to buy stock that is worth 45 at 50 for a loss of 5 (thus 50 – 45 or X-St). If the stock price had been 56, then the call pays off 56-50 ( St –X) and the put writer is not exercised upon. Pay off of the call minus the payoff of the written put is the same.

C-P=S0-X/(1+rf)^t


The difference between the call and put values is equal to the difference between the stock price and the present value of the exercise price.

Example: What is the approximate put premium when the exercise price is $50, the stock price is $52 and the call premium is $4? Assume that the short term interest rate on debt is 10% and the time to expiration is three months.


4 – P = 52- (50/(1.1)0.25)

4 – P = 52 – 48.82

4 – P = 3.18, P=0.82