Bond assignment homework assignment

Business Finance

Harvard University

Question Description

Please complete the attached investment homework assignment. I will also include chap 15-17 powerpoints for review if needed.

Unformatted Attachment Preview

FIN 327: Chapters 15 and 16 Readings Chapter 15.1, 15.2, 15.3 p. 474-490 Chapter 16.1 p.508-510 Chapter 16.3 p.517-527 Chapter 16.4 p. 527-529 Exercises Chapter 15: 1, 3, 4, 6, 7.a.b., 8, 12, 13, 14, 15 a.b. Chapter 16: 1, 5a.b.c.d., 12 1 OUTLINE 1. Basics 2. Pricing 3. Strategies 2 1. Options vs. Futures Similarity with futures: Options allow for leveraged investments (can be used for speculation, hedging, or synthetic). Difference with futures: • Options have asymmetric payoffs • Options are more common than futures for individual stocks 1. Call and Put Definitions • A call option gives its holder the right to purchase an asset for a specified price, called the exercise or strike price, on or before some expiration date. • A put option gives its holder the right to sell an asset for a specified exercise price or strike price. • The purchase price of the options is called the premium. 1. Underlying securities • Options are available on most major stocks, ETFs, indexes, interest rates, exchange rates, and commodities. • Most option contracts trade during regular market hours, from 9:30 ET to 4:00 pm. Some index options trade until 4:15 pm. 1. Payoffs and Profits • Some notation: – 𝑆𝑇 = 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑎𝑡 𝑒𝑥𝑝𝑖𝑟𝑎𝑡𝑖𝑜𝑛 – 𝑋 = 𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 – 𝐶0 = 𝐶𝑎𝑙𝑙 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 – 𝑃0 = 𝑃𝑢𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 1. Payoffs and Profits • When describing the profitability of option strategies at maturity either graphically or with equations, two approaches can be used: Payoffs → always positive Profits → can be negative For calls: Difference between the stock price (𝑆𝑇 ) and exercise price (𝑋), if positive For puts: Difference between exercise price (𝑋) and the stock price (𝑆𝑇 ), if positive = Payoffs – Option Premium 1. Payoffs and Profits Payoff Profit Call option (long position) 𝑆𝑇 − 𝑋 𝑆𝑇 − 𝑋 − 𝐶0 if 𝑆𝑇 ≥ 𝑋 0 −𝐶0 Put option (long position) 0 −𝑃0 X − 𝑆𝑇 X − 𝑆𝑇 − 𝑃0 bullish move, make money when prices go up if 𝑆𝑇 < 𝑋 if 𝑆𝑇 ≥ 𝑋 if 𝑆𝑇 < 𝑋 bearish move, make money when prices go down 1. Payoffs and Profits • It is also possible to take a short position in options. In that case, the payoffs will be “-” those of the long position. In other words, if the option buyer makes $10, it must be that the option seller loses $10. • The party that sells the contract (takes the short position) is called the option writer. 1. Payoffs and Profits Options give you different ways to make the same bet: Long position in securities Bullish or or Long position in calls Short position in puts Short position in securities Bearish or or Long position in puts Short position in calls 1. Payoffs and Profits • What’s the maximum loss you can have if you take a long position in calls? Answer: The premium 𝐶0 . • What’s the maximum that you can lose if you take a short position in calls? Answer: Unlimited 1. Payoffs and Profits • Example: Call option with exercise price of 𝑋 = $80. Call premium is 𝐶0 = $14. 1. Payoffs and Profits • With the call option on the previous slide (exercise price 𝑋 = $80 and premium 𝐶0 = $14), compute the option’s payoffs and profits for the scenarios in the table below. 𝑺𝑻 65 75 80 Payoff $0 $0 $0 Profit / Loss -$14 -$14 -$14 90 $90-$80 = $10 $10-$14 = -$4 100 $100-$80 = $20 $20-$14 = $6 1. Payoffs and Profits • What is the breakeven price 𝑆𝑇 that the stock must reach to make a profit of $0? Profit = 𝑆𝑇 − 𝑋 − 𝐶0 = 𝑆𝑇 − $80 − $14 = 0 → 𝑆𝑇 = $94 • Keep in mind that making a profit is not just a matter of having the stock price being above the exercise price, it must also make up for the premium. 1. Payoffs and Profits • Example: Put option with exercise price of 𝑋 = $80. Premium is 𝑃0 = $10 -$10 1. Payoffs and Profits • With the put option on the previous slide (exercise price 𝑋 = $80 and premium 𝑃0 = $10), compute the option’s payoffs and profits for the scenarios in the table below. 𝑺𝑻 65 75 80 Payoff $80-$65 = $15 $80-$75 = $5 $0 Profit / Loss $15-$10 = $5 $5-$10 = -$5 -$10 90 $0 -$10 100 $0 -$10 1. Contract sizes • Contract sizes typically call for the delivery of 100 shares. In the last years, “mini” contracts with sizes of 10 have also been introduced on a few names. (Quotes are always based on 1 share.) • For example, if a call option is quoted for $2, you would pay $2 x 100 = $200 for the option. The payoffs are also multiplied by 100. If the exercise price is $80 and the stock price is $85, the payoff of the call option would be 100 x ($85 - $80) = $500. The profit would be $500-$200=$300. 1. Expiration • Expirations tend to be fairly short, ranging up to only several months. LEAPS offer longer maturities, up to 3 years. • Until a few years ago, options were offered only with monthly expirations on the third Friday of the month. (Unusual price movements common on those days.) • In the last years, the market for “Weeklys” has grown in importance: options on major stocks/ETFs now typically have expirations every Friday. 1. American vs. European • An American option allows its holder to exercise the right to purchase (if a call) or sell (if a put) the underlying asset on or before the expiration date. • European options allow for exercise of the option only on the expiration date. 1. Clearinghouse • Similarly to what we had with futures, there is a clearinghouse (the Options Clearing Corporation) that becomes the effective buyer of the option from the writer and the effective writer of the option to the buyer. Buyer Options Clearing Corporation Seller 1. Margins • Because the OCC guarantees contract performance, it requires option writers to post margin to guarantee that they can fulfill their contract obligation (unless they own the security). Margin calls are possible if the required margin exceeds the posted margin. • The option buyer does not need to post margin because after purchasing the option, no further money is at risk. 1. Assignment for Option Writers • Once you sell an option (put or call), you have the potential for being assigned to fulfill your obligation to receive (and pay for) or deliver (and get paid for) shares of stock on any business day. [Most of the time, this occurs on expiration.] Assignment can be avoided by closing the contract before expiration. • OCC utilizes a random procedure to assign exercise notices to the accounts maintained with OCC by each Clearing Member. 1. Moneyness The “moneyness” of an option describes whether immediate exercise of the option would be profitable. In-themoney 𝑆𝑡 > 𝑋 𝐶𝑎𝑙𝑙𝑠 𝑆𝑡 < 𝑋 𝑃𝑢𝑡𝑠 At-themoney 𝑆𝑡 = 𝑋 Out-ofthe-money 𝑆𝑡 < 𝑋 𝐶𝑎𝑙𝑙𝑠 𝑆𝑡 > 𝑋 𝑃𝑢𝑡𝑠 1. Moneyness • The more an option is in-the-money, the more expensive it is. The more an option is out-of-themoney, the least expensive it is. Deep-out-of-themoney options are similar to lottery tickets. • When you follow stock prices, there is only one number to follow. For options, there are several numbers (call vs puts, by maturity, by exercise price). Typically, all these prices are presented together in an option chain. Example: Option Chain for TSLA Current price Call prices are on the left Exercise prices are in the middle Put prices are on the right Prices are listed by maturity Example: To purchase the May 2 220 call, you would pay $715 Within a maturity, different strike prices are presented 2. Intrinsic vs. Time Value • Why would someone pay for an out-of-the-money option? • Even though immediate exercise would be unprofitable, the option retains a positive value because there is always a chance the stock price will move sufficiently by the expiration date to allow for profitable exercise. 2. Intrinsic vs. Time Value • The price of an option can be divided into an intrinsic value component that represents the payoff from immediate exercise and a time value component that represents the difference between the price and the intrinsic value. • Options are wasting assets in the sense that the time value declines over time, especially when close to maturity. If you buy calls or puts and the stock price does not change over time, you will lose money. 2. Intrinsic vs. Time Value 2. Time Decay Time decay as expiration approaches Example TSLA call options, current price 218.14 Expiration Exercise price 210 April 25, 2014 May 2, 2014 May 9, 2014 Exercise price 217.5 April 25, 2014 May 2, 2014 May 9, 2014 Price Intrinsic value Time value 10.00 12.70 19.60 8.14 8.14 8.14 1.86 4.56 11.46 5.25 8.00 15.50 0.64 0.64 0.64 4.61 7.36 14.86 2. Pricing • The Black-Scholes formula provides an equation to price European call options. (It is in the textbook, you don’t have to memorize it for the exam.) These notes give the main pricing implications of the BS formula, without going through the math. 2. Pricing • Option prices are proportional to current stock prices: Higher share price (relative to other stocks) Higher Option Prices for Calls and Puts • For example, GOOGL is a relatively expensive stock at $546 vs. Citigroup at $48. The at-the-money call option for GOOGL for May 2014 is $13.25 vs. $1.14 for Citigroup. 2. Pricing • Are options on cheaper stocks necessarily a better thing? Of course, an option that is too expensive may simply not fit in a budget. • Options that are too cheap can also be a problem if you need to buy many contracts. When buying options, there is usually a contract fee of $0.75 per contract in addition to the commission. For example, if you buy 10 contracts, that represents an additional $7.50 transaction cost on top of the commission. 2. Pricing • Options that are more in-the-money (have more intrinsic value) are more expensive. Higher Stock Price Higher Call Option Price Lower Put Option Price 2. Pricing - Delta • The previous slide relationship implies that both the stock price and the call option price will move up or down together. What’s the difference between investing in the stock vs. the call option? • Leverage: A dollar invested in options will be more sensitive to changes in stock prices than a dollar invested in the stock. For example, if the stock price goes up by 1%, the call option might go up by 10% or 20%. Options closer to maturity have more leverage. 2. Pricing - Delta • To assess price sensitivity, we can use the option’s delta, which measures the dollar change in the option price for a dollar increase in the stock price. • For call options, delta is a number between 0 and 1. The higher the probability that the option ends inthe-money, the higher the delta. • For put options, delta is between -1 and 0. • At-the-money call options have deltas around 0.5 and at-the-money put options have deltas around -0.5. 2. Pricing - Delta • It may sound counterintuitive that the price of an atthe-money call option moves 0.5-to-1 with the stock price. Aren’t options supposed to be more leveraged investments than stock? • Yes. What happens is that option prices are much less expensive than stock prices. When computing returns, the $0.5 increase in the option price is divided by a much smaller number than the $1 increase in the stock price. 2. Pricing - Delta • In practice, you don’t have to compute deltas yourself. Most option trading software can add deltas to the option chain. 2. Pricing - Delta • For example, you buy TSLA’s April 25 call option (strike 217.50) with expiration for $5.30. • The option’s delta is 0.5108. If TSLA’s price goes up by $1, the option’s price will go up by $0.51. • If you invested in the stock directly, the $1 price increase would represent a 1/217.50 = 0.5% return. • By investing in the option, your return is $0.51/$5.30 = 9.6%, almost 20 times higher! (Of course, you would lose 9.6% if the stock price goes down by $1.) 2. Pricing - Delta • If you are investing in options only for a short period of time, e.g. an hour, your option will not lose too much value because of time decay. • In that case, your gain/loss will be approximately 𝐷𝑒𝑙𝑡𝑎 × 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑡𝑜𝑐𝑘 𝑝𝑟𝑖𝑐𝑒. • By contrast with options that are held until maturity, you can make a profit with short-term investments in options even if the option is not in-the-money when you sell it. What matters is to be correct about the price direction. 2. Pricing - Maturity • Options that are closer to expiration lose time value. Option Closer to Expiration Cheaper Option Prices for Calls and Puts Example Prices of GOOGL at-the-money options (strike $545) Expiration April 25, 2014 May 2, 2014 Call 5.70 8.60 Put 4.40 8.90 May 9, 2014 May 16, 2014 May 23, 2014 10.80 13.25 15.00 10.30 12.00 13.60 May 30, 2014 June 20, 2014 16.20 20.50 14.80 18.80 2. Pricing - Volatility • The standard deviation (𝜎) of a stock is used as an input in the Black-Scholes formula. More volatile stocks (higher 𝜎) More expensive option prices for Calls and Puts 2. Pricing - Volatility More volatile stocks are more likely to “hit” the exercise price, especially for out-of-the-money options. 110 105 100 Lower volatility stock Exercise price 110 105 100 95 95 90 90 85 85 80 80 75 75 1 2 3 4 5 6 7 8 9 10 Higher volatility stock Exercise price 1 2 3 4 5 6 7 8 9 10 2. Pricing - Volatility • When pricing options, the implied volatility of a stock is used instead of the historical volatility. • The implied volatility of a stock is computed by asking which standard deviation (𝜎) would make the Black-Scholes equation price equal to market prices. • Example: Tesla (current price $218) vs. SPY (current price $188). The at-the-money call option for May 2014 is 15.5 vs 2.57 for SPY. The implied volatility is 69.4% for TSLA and 11.5% for SPY. 2. Pricing - Volatility • The VIX index tracks the implied 30-day volatility of S&P 500 index options. Historically, the VIX has often spiked in times of crisis and many interpret it as a fear index: 3. Strategies • A strategy of buying or selling options by themselves is called “Naked options”. These are basically purely leveraged strategies, a big bet on up or down price movements. • There are a lot of other strategies that you can pursue either by combining several options together (these are called legs) or by combining the option with a security. Here we cover a few of the main ones. (Beware that combining options can increase transaction costs.) 3. Strategies – Protected Put 3. Strategies – Protected Put Value of a stock Value of a protected put Disadvantage: We are giving up the premium 𝑃 when the stock price does not drop below 𝑋 𝑋−𝑃 Advantage: The protected put will not drop below a floor 𝑋 − 𝑃 when the stock underperforms 𝑋 𝑆𝑇 3. Strategies – Covered Call 3. Strategies – Covered Call Value of a stock Disadvantage: We are giving up the upside potential when the stock price is above 𝑋+C 𝑋 +C Value of a covered call Advantage: We are collecting the premium. If the stock price does not go above 𝑋+C , this increases our return. 𝑋 𝑆𝑇 3. Strategies – Spreads Example • I am moderately bullish about TSLA and I want to buy the May 2 215 call for $975. • My budget is only $500. To afford the option, I can sell the May 2 225 call for $490. My net cost is $975-$490=$485. • Note: Bid-ask spreads can make option combos costly. 3. Strategies – Straddle 3. Strategies - Straddle • If you think that volatility will be limited, you can do the opposite strategy: sell the straddle, i.e. sell a put and a call option. • For example, if you sell the May 2, 2014 TSLA 220 call option for $690 and the 220 put option for $840, your total income is $690+$840=$1,530. You make a profit as long as the stock price ends in the $220 ± $15.30 range. Conclusion • Investing one’s entire portfolio in options is obviously risky because there is a nontrivial chance of losing everything. Smaller short-term option investments have more limited risk. In any case: Investors should have a few years of experience trading regular securities before considering trading options. FIN 327: Chapter 17 Readings Chapter 17 (except “Interest rate futures”, p.566-567) Exercises Chapter 17: 1, 2, 3, 4, 6, 7, 8, 15, 18, 19, 24 a.b., 25 1 OUTLINE 1. 2. 3. 4. 5. 6. 7. Forward vs Futures Payoffs Design Uses of futures Pricing Regulation Swaps 2 1. Forwards vs. Futures • A forward contract is an arrangement calling for future delivery of an asset at an agreed-upon price. • Forward contracts have existed for hundreds of years. Think about a farmer who derives most of his income from selling his crop and worries about fluctuations in the price at which he can sell his crop. A forward arrangement allows him to lock in current prices for his crop. 1. Forwards vs. Futures • These agricultural forward arrangements are at the origin of today’s futures markets. • Futures contracts are basically forward arrangements that: – Have been standardized (for size, quality, maturity) – Can be traded on exchanges • Standardization makes futures contracts highly liquid; transaction costs can be cheaper than for trading the underlying commodities directly. 1. Sample of Futures Contracts Over time, futures markets have evolved to include other commodities and financial instruments: 2. Some Notation Spot price Futures price Current price for immediate delivery Price for future delivery Today: 𝑆0 At time 𝑇: 𝑆𝑇 Today: 𝐹0 Convergence property: At maturity, the futures price and the spot price must converge, i.e. 𝐹𝑇 = 𝑆𝑇 Note: The book also uses the notation 𝑃𝑇 for the spot price at time 𝑇. 2. Payoffs • Long position: Commits to purchasing the commodity on the delivery date (or maturity) for the futures price 𝐹0 . → We say that someone who takes the long position is buying the futures. • Short position: Commits to delivering the commodity on the delivery date ( or maturity) for the futures price 𝐹0 . → We say that someone who takes the short position is selling the futures. 2. Payoffs at Maturity Payoffs for the long position 𝑺𝑻 − 𝑭𝟎 Payoffs for the short position 𝑭𝟎 − 𝑺𝑻 You make money on a long position when the price goes up 𝐹0 𝑆𝑇 𝐹0 You make money on a short position when the price goes down 𝑆𝑇 2. Payoffs Before Maturity • Most traders close their position before the delivery date by entering a reversing trade. In that case (let’s say when the position is exited at time 𝑡 < 𝑇), the profit for the long position is: 𝐹𝑡 𝐹𝑢𝑡𝑢𝑟𝑒𝑠 𝑝𝑟𝑖𝑐𝑒 𝑤ℎ𝑒𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑖𝑠 𝑒𝑥𝑖𝑡𝑒𝑑 − 𝐹0 𝐹𝑢𝑡𝑢𝑟𝑒𝑠 𝑝𝑟𝑖𝑐𝑒 𝑤ℎ𝑒𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑖𝑠 𝑒𝑛𝑡𝑒𝑟𝑒𝑑 →It’s just like buying and selling stocks… … except that payoffs are multiplied by a contract size. 2. Contract Sizes • Each contract has a different size. Many contracts offer an “e-mini” version with a smaller size. Some examples: Contract Standard S&P 500 index Contract size 250 times the index E-mini S&P 500 index Corn Crude oil 50 times the index 5,000 bushels 1,000 barrels • Futures are BIG contracts, think about starting prices around $50,000- ...
Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

This question has not been answered.

Create a free account to get help with this and any other question!

Similar Questions
Related Tags