CFA- Risk and Return(Portfolio Management).pdf, Study notes of Finance

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Forward commitment and

contingent claims features and

instruments

Types of derivatives

- Forward commitment and

contingent claims features

and instruments

• Margin is cash or other collaterals that both the buyer and seller must deposit.
• Initial margin is the amount that must be deposited in a futures account before a trade may be made.
• Mark-to-market – Daily adjustment of margin balance for any gains and losses in the value of the futures position based on the new settlement price on that day
• Maintenance margin is the minimum amount that must be maintained in a futures account based on daily Mark-to-market. If actual margin is below the maintenance margin, the account holder must deposit additional funds
• price limits - exchange-imposed limits on how much each day’s settlement price can change from the previous day’s settlement price. Exchange members are prohibited from executing trades at prices outside these limits.
• circuit breakers - when a futures price reaches a limit price, trading is suspended

Elements of Futures / Future Exchanges

Contract for 100g of gold with initial margin of $5,000 + maintenance margin of $4,700.

• On Day 0:
  • Buyer and seller make a trade at a price of $1,950 per gram
  • both parties deposit the initial margin of $5,000 into their accounts.
• On Day 1: the settlement price falls to $1,947.50.
• On Day 2: the settlement price falls to $1,945.
• Question 1: What will happen to the buyer and sellers margin accounts on day 1 close
• Question 2: What will happen to the buyer and sellers margin accounts on day 2 close

Example: How exchanges handle trades

• Swaps are netted off, i.e. at each settlement date, all payments are netted so that only one net payment is made.
• Swaps are exposed to counterparty credit risk, unless the market has a central counterparty structure to reduce counterparty risk.
• Example of a simple swap
  • a fixed-for-floating interest rate swap for two years with quarterly interest payments based on a notional principal amount of $10 million.
  • One party makes quarterly payments at a fixed rate of interest (the swap rate)
  • The other makes quarterly payments based on a floating market reference rate.
  • Over time, the value of the swap can become positive for one party and negative for the other party.

2. Types of derivatives – Swaps

agreements to exchange a series of payments on multiple settlement dates over a specified time period (e.g., quarterly over 2 years)

• Consider an interest rate swap with a notional principal amount of $10 million, a fixed rate of 2%, and a floating rate of the 90 - day secured overnight financing rate (SOFR).
• At each settlement date, the fixed-rate payment will be $10 million × 0.02/4 = $50,000.
• The floating-rate payment at the end of the first quarter will be based on 90 - day SOFR at the initiation of the swap, so that both payments are known at the inception of the swap.
• If, at the end of the first quarter, 90 - day SOFR is 1.6%, the floating-rate payment at the second quarterly settlement date will be $10 million × 0.016 / 4 = $40,000. The fixed-rate payment is again $50,000, so at the end of the second quarter the fixed-rate payer will pay the net amount of $10,000 to the other party.

Example:

3. Types of derivatives – Options

• Can be of two types based on an underlying Put option (buyer sells)
• gives the buyer the right (but not the obligation) to sell X shares at a specified price (the exercise price or the strike price) for specified period of time (the time to expiration).
• The put seller (also called the writer of the option) takes on the obligation to purchase the X shares at the price specified in the option, if the put buyer exercises the option. Call option (buyer buys)
• gives the buyer the right (but not the obligation) to buy X shares at a specified price (the exercise price) for a specified period of time.
• The call seller (writer) takes on the obligation to sell the 100 shares at the exercise price, if the call buyer exercises the option.

• Lets assume
  • X = the exercise price of a put = $25 at the expiration of the option.
  • S = Current trader price of the underlying
• If S is at or above $25, the put holder will not exercise the option.
  • There is no reason to exercise the put and sell shares at $25 when they can be sold for more than $25 in the market.
  • So the put buyer lets the option expire, and the put seller keeps the proceeds from the sale.
  • This is the outcome for any put option where market price is higher than put option,
• If S is below $25, the put buyer will exercise the option.
  • the put seller must purchase shares for $25 from the put buyer.
  • On net, the put buyer essentially receives the difference between the stock price at expiration and $25 (times number of shares).

Example: How a simple one-way put option works

• Consider a call option with a premium of $5 and an exercise price of $50. This means the buyer pays $5 to the writer.
• At expiration, if
  • the price of the stock is less than or equal to the $50 exercise price, the option has zero value, the buyer of the option is out $5, and the writer of the option is ahead $5.
  • When the stock’s price exceeds $50, the option starts to gain (breakeven will come at $55, when the value of the stock equals the exercise price plus the option premium.
  • Conversely, as the price of the stock moves upward, the seller of the option starts to lose (negative figures will start at $55, when the value of the stock equals the exercise price plus the option premium).
• The sum of the profits between buyer and seller is always zero; thus, trading options is a zero-sum game.

Call example

Visually: Writer (short call), buyer (long call)

The breakeven for both is X

• the premium (i.e S = $55). The maximum loss for the buyer of a call is the $ premium (at any S ≤ $50). The call holder will exercise the option whenever the stock’s price exceeds X The writer makes the $ premium (at any S ≤ $50). Unlimited loss for writer (S > $55) Unlimited profit for buyer (S > $55)

Visually: Writer (short put), buyer (long put)

The breakeven is X - the premium (i.e. S = $45). The maximum loss for the buyer is the $5 premium (at any S ≤ $50). The maximum profit for the writer is the $5 premium (for S ≥ $50) Loss for writer is = Profit for buyer Maximum profit for buyer is X – premium ($50 - $5 = $45)

• Suppose that both a call option and a put option have been written on a stock with an exercise price of $40. The current stock price is $42, and the call and put premiums are $ and $0.75, respectively.
• Question: With an expiration day stock price of $35 and with a price at expiration of $43.

1. Calculate the profit to the long and short positions for the put
2. Calculate the profit to the long and short positions for the call

Exercise

• Profit will be computed as ending option value – initial option cost.
• Stock at $35:
  • Long put: $5 – $0.75 = $4.25. The buyer paid $0.75 for an option that is now worth $5.
  • Short put: $0.75 – $5 = – $4.25. The seller received $0.75 for writing the option, but the option will be exercised so the seller will lose $5 at expiration.
• Stock at $43:
  • Long put: – $0.75 – $0 = – $0.75. The buyer paid $0.75 for the put option and the option now has no value.
  • Short put: $0.75 – $0 = $0.75. The seller received $0.75 for writing the option and it has zero value at expiration.

Solution: Put

Moneyness

Call Optio n Stock Price > Strike Price S – X >0 In the Money Stock Price = Strike Price S = X At the Money Stock Price < Strike Price S – X < 0 Out of the Money Put Option Stock Price < Strike Price S – X < 0 In the Money Stock Price = Strike Price S = X At the Money Stock Price > Strike Price S – X > 0 Out of the Money www.proschoolonline.com Copyright©-IMS Proschool Pvt..Ltd