| Course | FIN-3210 Security Analysis and Portfolio Management |
|---|---|
| Module | Module 5 |
| Paper type | Written assignment 5: derivative markets |
| Length | About 685 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | B.S.B.A. in Finance |
| Updated | October 2026 |
Free sample paper for FIN 3210 Module 5
Floors, Ceilings and a Hedge: Options and Futures for a Trenton Household's Portfolio
Student Name
B.S.B.A. in Finance, Thomas Edison State University
FIN-3210: Security Analysis and Portfolio Management
Mentor Name
Month Day, Year
Floors, Ceilings and a Hedge: Options and Futures for a Trenton Household's Portfolio
Problem 1: Options Basics
A call option gives the holder the right to buy an asset at a set strike price before or at expiration; a put gives the right to sell. The buyer pays a premium; the seller, or writer, receives it and takes on the obligation. At expiration, a call is worth max(S − K, 0) and a put max(K − S, 0), where S is the stock price and K the strike (Bodie et al., 2017). Sharpe (1964) showed that only systematic risk, measured by beta, is priced, which is why the futures hedge below is sized by the portfolio's beta.
Problem 2: A Protective Put
The couple owns 100 shares of the utility at $52. To protect against a fall before a planned sale in three months, they could buy a three-month put with a $50 strike for $2.10 a share.
The put sets a floor: whatever happens, the position is worth at least $50, so the maximum loss is $4.10 a share, the $2 drop to the strike plus the premium. The cost is the premium, which lowers every gain by $2.10. A protective put works like insurance on the shares.
| Stock price at expiration | Stock value | Put value | Total value | Profit per share |
|---|---|---|---|---|
| $40 | $40 | $10 | $50 | −$4.10 |
| $50 | $50 | $0 | $50 | −$4.10 |
| $60 | $60 | $0 | $60 | +$5.90 |
Problem 3: A Covered Call
Alternatively, they could write a three-month call with a $55 strike and collect $1.80 a share.
The covered call sets a ceiling: the most the couple can earn is $4.80 a share, because any rise above $55 goes to the call buyer. In exchange, the premium cushions small losses. It suits an investor who expects little movement and would be content to sell at $55.
| Stock price at expiration | Stock value | Call obligation | Total value | Profit per share |
|---|---|---|---|---|
| $40 | $40 | $0 | $40 | −$10.20 |
| $50 | $50 | $0 | $50 | −$0.20 |
| $60 | $60 | −$5 | $55 | +$4.80 |
Problem 4: Put-Call Parity
For European options on a non-dividend-paying stock, put-call parity requires C − P = S − K / (1 + r)^T. Consider a $50-strike call priced at $4.40 and the $50 put at $2.10, with three months to expiration and a 4 percent annual risk-free rate. The right side is $52 − $50 / 1.04^0.25 = $52 − $49.51 = $2.49. The left side is $4.40 − $2.10 = $2.30. The call is cheap relative to the put by about $0.19. In principle, a trader could buy the call, sell the put and short the stock to lock in a small riskless profit, although transaction costs and the utility's dividend, which the simple formula ignores, would likely absorb it. Black and Scholes (1973) built their option pricing model on the same idea, that an option's price must be consistent with a riskless hedge.
Problem 5: Hedging With Index Futures
The couple's taxable portfolio of $500,000 has a beta of 1.1 relative to a stock index. If they fear a market decline over the next three months but do not want to sell and pay capital gains taxes, they can sell index futures. With the index at 5,000 and a contract multiplier of $50, one contract controls $250,000 of index value. The number of contracts to sell is beta × portfolio value / contract value = 1.1 × $500,000 / $250,000 = 2.2 contracts. Since contracts are indivisible, they would sell two and accept a small unhedged amount. If the market fell 10 percent, the portfolio would lose about 11 percent, or $55,000, and the two short contracts would gain about $50,000, offsetting most of the loss. If the market rose, the futures loss would offset the portfolio's gain: a hedge removes upside as well as downside.
What the Problems Show
Derivatives let investors reshape risk. A protective put buys a floor at the cost of a premium, a covered call sells upside for income and a futures hedge locks in a value at the cost of giving up gains. None creates return without giving something up.
References
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654. https://doi.org/10.1086/260062
Bodie, Z., Kane, A., & Marcus, A. J. (2017). Essentials of investments (10th ed.). McGraw-Hill Education.
Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x
Reading the FIN 3210 Module 5 assignment instructions
Derivative Markets is the fifth module's topic. Expect problems on option payoffs and profits, strategies such as protective puts, covered calls and spreads, put-call parity and the use of futures to hedge or speculate, including the number of contracts needed to hedge a portfolio with beta. The futures hedge uses beta from the CAPM framework Sharpe developed, which ties this module to the portfolio theory before it. The household, prices and index level here are illustrative composites. Expect payoff diagrams for option strategies, a put-call parity check and a futures hedge for a stated exposure. Many versions use exchange-traded option prices supplied in the assignment.
How the FIN 3210 Module 5 example is put together
Problem 1 defines calls and puts and their payoffs. Problems 2 and 3 tabulate a protective put and a covered call at the same three expiration prices and explain the floor and ceiling each creates. Problem 4 checks put-call parity with stated prices, finds a small mispricing and explains why it may not be exploitable, citing Black and Scholes. Problem 5 computes the number of index futures contracts to hedge a portfolio with beta and shows the hedge's effect in a falling and a rising market. Each strategy is shown with its payoff at several prices so its risk is visible. The hedge section shows the result under a rise and a fall in the futures price.
FIN 3210 Module 5 rubric: what earns full marks
Payoff tables and a beta-sized hedge drive the derivatives grade. Mentors look for correct payoff and profit calculations, accurate use of put-call parity and a correct hedge ratio, along with clear explanations of what each strategy gains and gives up. Distinguishing payoff from profit, by including the premium, and recognizing practical limits, such as dividends or indivisible contracts, demonstrate the understanding the module aims for. Mentors check that payoffs include the premium paid and that the hedge ratio matches the exposure being hedged. Explaining when each strategy suits an investor's view shows judgment. Options answers need payoffs across several prices, and the futures answer needs a hedge sized with beta; interpret each.
FIN 3210 Module 5 help from the desk
Derivatives problems lose points for confusing payoff with profit, for forgetting that the option writer receives the premium and for computing a futures hedge without adjusting for beta. Build a payoff table at several prices, then subtract the premium for profit. Check signs carefully for written options. Discount the strike in put-call parity. Multiply by beta in the hedge ratio and round to whole contracts. Label each payoff table with the stock price range you tested. A free first sample of your own FIN-3210 Module 5 problems is available on request. Tabulate profit at five or six terminal prices before drawing conclusions about a strategy. Explain in words what each strategy is betting on.
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FIN 3210 Module 5 questions, answered
Where can I find a free FIN 3210 Module 5 sample paper?
Above: a protective put, a covered call, a parity check and a beta-weighted index futures hedge for the Trenton couple.
What is a protective put?
Buying a put on a stock you own, which sets a minimum value for the position in exchange for the premium.
What is put-call parity?
The relationship that a call minus a put with the same strike and expiration equals the stock price minus the present value of the strike.
How many futures contracts hedge a portfolio?
Beta times the portfolio value divided by the value controlled by one contract, the index level times the multiplier.
What is the difference between an option's payoff and its profit?
Payoff is its value at expiration; profit subtracts the premium paid or adds the premium received.