Overview of Equity-linked Securities (also referred to as Structured Equity Products):

This project assignment builds on Chapter 7 Advanced Option Strategies, by demonstrating how to construct complex payoffs to match a forecast, by combining options together with the underlying stock or stock portfolio. The project will use the Black-Scholes-Merton option pricing spreadsheet and the Option Strategy Analyzer spreadsheet.

Equity-linked securities (ELS) (also referred to as `equity-linked notes or `structured equity products) are structured products with returns that are tied to the price movements of an underlying listed equity index, a specific stock, or a particular basket of stocks. They are designed to address a more diverse range of investment objectives and with a greater amount of flexibility than traditional equity products. For our purposes, you may think of an ELS as a combination of the underlying stock or stock-index plus options on the underlying that yields a set of future cash flows that better match a given belief, given desire, or specific investment strategy.

Note that for a typical ELS:

1. Dividends: You miss out on the dividends of actually owning the underlying stock or stock index.

2. Liquidity risk: ELS are designed to be bought and held to maturity. The secondary market is

   usually small or nonexistent. Thus, investors face liquidity risk.

3. Counterparty credit risk: Investors are exposed to the risk of default by the issuing institution.

4. See the posted article The Dark Side of Financial Innovation: A Case Study of the Pricing of a

   Retail Financial Products, 2011, by Henderson and Pearson, for a case study on real-life ELSs.

Data:

Assume the following hypothetical values: Starting value for SPY ETF: 460; Dividend yield: 1.30% (contin. compounded, annualized rate); risk-free interest rate over the life of the option: 0.55% (contin. compounded, annualized rate). Assume that 80-day European-style call and put options on the SPY can be bought or written at any desired strike price, with the Black-Scholes-Merton model providing the fair value for the options. Assume that the implied volatility of the index for pricing the options is a 20% annualized standard deviation. Ignore any considerations of margin requirements for the derivative contracts.

Consider the following possible ELS. The terminal cash flows for the ELS would occur in 80 days and depend upon the terminal value of the SPY in 80 days from now. Assume that the options and SPY ETF can be transacted in any integer amount (so not restricted by option-contract convention), and that the ELS has a scaling of 100 times the SPY price (which means the scaling would be 100 SPY units).

You will need to figure out the underlying holdings and price to offer the following ELS:

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ELS Payoff Description: -For no price movement: 1) If the SPY ends up at 460 in 80 days, then the ELS pays off at 460 per unit at expiration (or $46,000 with the 100 multiplier). -On the Downside:

2) On the downside, for SPY declines down to a closing SPY of 430, the ELS payoff would lose on a 1 to 1 basis. So, if the SPY price ended up at 430 in 80 days, then the ELS payoff would be $43,000 at expiration. 3) For further SPY declines between 430 down to 400, the ELS payoff will decline only 0.50 to 1 basis for every additional 1 unit of SPY decline (or, limited protection). So, for example, if the SPY ended up at 400, the ELS payoff would be $41,500.

4) For SPY declines below 400, then the ELS payoff does not decline further. So, if the SPY ended up at 350, then the ELS payoff would still be $41,500. -On the Upside 4) On the upside up to a SPY increase to 470, the ELS will payoff $1 more for every $1 increase in the SPY. So, if the SPY ended up at 470 in 80 days, the ELS payoff would be $47,000 at expiration.

5) For SPY outcomes between 470 and 520, the ELS payoff will increase on a 2:1 basis for every $1 increase in the SPY price. So, if the SPY ended up at 520 in 80 days, the ELS payoff would be $57,000 at expiration. 6) If the SPY price goes up beyond 520, then the ELS payoff does not increase further. So, for example, if the SPY ends up at 550 in 80 days, then the ELS payoff is still $57,000 at expiration.

To make sure that you understand the ELS Payoffs, below is a graph of the PAYOFFS at ELS EXPIRATION only, over a range of possible terminal SPY prices in 80 days from now. Note that this is NOT THE SAME as the Profit, because the Profit is the Payoff minus the Initial Cost of the ELS.

60,000 58,000 56,000 54,000 52,000 50,000 48,000 46,000 44,000 42,000 40,000

Asset Price at Expiration ($)

Future Payoff from Strategy at Expiration

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373 380 387 394 401 408 415 422 429 436 443 450 457 464 471 478 485 492 499 506 513 520 527 534 541

Payoff

For this ELS:

1. If you are the issuer of this ELS, what should be your holdings of options and the SPY ETF to generate

   the future cash flows for the above ELS. For simplicity, assume that the issuer keeps the dividends from the underlying index over the life of the contract as the spread, so that the ELS can be offered at a price based on the current fair values of the options and ETF.

2. What do you estimate as an initial market price for the ELS above, given the assumptions in A. above and assuming that we can use the Black-Scholes-Merton model to value the options? (Round all individual option prices from the spreadsheet to the penny, $0.01, in your downstream calculations). Paste in a copy of the input cells and output price from the BlackScholes-Binomial option pricing spreadsheet for one of the options as an appendix in your report, so I can check that your inputs into the spreadsheet are correct.

3. Provide a graph using the Option Strategy Analyzer spreadsheet that shows the profit from buying the ELS at your initial price in B, over a range of possible terminal SPY values from 372.5 to 544, if the position is held to maturity. What is the breakeven terminal SPY value for this ELS investment, assuming that the ELS is initially priced as in B. above? What is the profit in dollars and the corresponding percentage return if the SPY ended up at 520, based on the initial price in B. above? Include a copy of this Option Strategy Analyzer Excel spreadsheet that contains your profit graph as a separate file for your deliverables for this assignment.

Deliverables: You should prepare a written report on this project. This report should be in MS Word or some other similar word-processing package. Your report should include:

1) Header Information: Project title, class, date, and YOUR NAME. 2) A summary written report, in the spirt of an Executive Summary, that concisely summarizes the problem assignment and your work and findings and the graph requested in Part C above. The summary report should also answer the questions in the above instructions, items A to C above. (See http://en.wikipedia.org/wiki/Executive_summary for a review of Executive Summaries). 3) The requested Option Strategy Analyzer spreadsheet (per item C above) should be submitted as a second separate file.