Derivatives in allocation, rebalancing and market expectations — MCQs

Stonebridge Pension Plan holds a concentrated position in the common stock of a mature technology company. The investment committee remains moderately bullish over the next year but is concerned about the effect of a substantial price decline on the plan's funded status. The committee asks derivatives strategist Priya Nair to evaluate option values and alternative overlays. The stock pays no dividends during the relevant horizons, and all options discussed are European unless otherwise stated. Nair first reviews market prices for a one-year call and put written on the stock. The options have the same exercise price and expiration date. She explains that, in the absence of arbitrage, the price of the put can be inferred from the observed call price, current stock price, and present value of the exercise price. Transaction costs, taxes, bid–ask spreads, and counterparty default risk are ignored. The effective annual risk-free rate applies to all one-year present-value calculations. Nair next values a separate one-period European call using a binomial model. The model assumes that the stock can reach only the up-state or down-state price shown in Exhibit 2. The risk-free return lies between the two possible stock returns, so a no-arbitrage risk-neutral probability exists. Nair notes that the stock's actual expected return and investors' risk preferences are not required because the option can be valued from a replicating portfolio or equivalent risk-neutral valuation. The committee then considers two portfolio objectives. For the first objective, it wants to continue holding the stock, preserve participation if the stock appreciates, and establish a minimum sale value over the one-year horizon. The committee accepts paying an upfront premium to obtain this protection. For the second objective, the committee is willing to surrender gains above a specified price in exchange for current option income. It would implement that objective by selling calls against shares already held rather than by writing uncovered calls. Nair emphasizes that the two overlays alter the return distribution differently. Purchasing a put creates a floor without imposing a ceiling on the stock's gross terminal value, whereas writing a covered call provides premium income and limited downside cushioning but creates an upper bound on the combined position's terminal value. The committee will select an overlay based on the stated objective rather than solely on the amount of premium received or paid.

Silver Pine Advisory manages a concentrated equity position for a client and is evaluating several derivative applications. The firm's investment committee requires all derivative valuations to use no-arbitrage methods. Unless otherwise stated, the options are European, exercise occurs only at expiration, the stock pays no dividends, and markets have no transaction costs, taxes, or restrictions on short selling. The committee begins by comparing a long forward with a long call. A forward requires both counterparties to complete the transaction at maturity, whereas the option buyer decides whether exercise is economically beneficial. The option writer must perform if the buyer exercises. The committee emphasizes that the call premium is distinct from the call's expiration payoff and that a newly initiated forward normally has zero value when its delivery price equals the no-arbitrage forward price. The first valuation assignment uses put–call parity. The call and put have the same underlying stock, exercise price, and expiration date. Interest is compounded annually at the annual effective rate in Exhibit 1. The analyst is instructed to apply c + PV(X) = p + S and to avoid treating the future exercise price as though it were payable immediately. The second valuation assignment uses a one-period binomial model. The stock can take only the up-state or down-state value shown in Exhibit 1. The risk-free return applies over the entire binomial period. The call payoff in each state equals the greater of the stock price less the exercise price or zero. The analyst may value the call by constructing its replicating portfolio or by calculating risk-neutral probabilities and discounting the expected payoff. Silver Pine also considers an overlay for the client's existing shares. The client's objectives are stated in Exhibit 2. The client does not intend to sell the shares and is willing to sacrifice appreciation above a specified level to lower the net premium paid for downside protection. The investment committee instructs the analyst to select an option strategy whose payoff, rather than merely its market outlook, directly satisfies the floor and upside-cap requirements. All option contracts under consideration have a six-month maturity aligned with the client's horizon.

Northbridge Securities advises institutional investors on option valuation and hedging. Analyst Priya Shah is reviewing European calls and puts on non-dividend-paying stocks. All options can be exercised only at expiration, markets are frictionless, and investors can borrow or lend at the stated risk-free rate. Shah first tests whether quoted option premiums are consistent with a portfolio consisting of the underlying stock and a risk-free zero-coupon instrument. For the options in Exhibit 1, the call and put have the same exercise price and expiration date. Shah notes that the relevant exercise-price amount in put–call parity is its present value rather than its undiscounted amount. She is asked to derive the put premium that would prevent arbitrage, assuming the quoted call is correctly priced. Shah then evaluates the call in Exhibit 2 using a one-period binomial model. The stock will have only the two stated end-of-period values. She will first infer the risk-neutral probability from the up factor, down factor, and risk-free gross return. She will then discount the risk-neutral expected call payoff. No subjective estimate of the stock's expected return is required. As a separate check, Shah constructs a stock-and-borrowing portfolio that produces the same payoff as the call in both states. The number of shares is determined from the difference in option payoffs divided by the difference in stock prices. The risk-free position is selected so that both the up-state and down-state portfolio payoffs match the call payoffs. Finally, Shah reviews Figure 1, which plots the total expiration profit from purchasing one share of stock and writing one call option. The position has a constant maximum gain when the stock finishes above USD 104, decreases below that price, and breaks even at USD 95. Candidates should identify the combined position from the shape of the plotted profit line rather than treating the graph as an option-only payoff. Premiums received and the initial stock purchase price are included in the plotted profit.

Meridian Wealth Advisors manages concentrated equity positions for taxable private clients. Investment strategist Daniel Ross is evaluating European options for hedging and return enhancement. Unless otherwise stated, the options can be exercised only at expiration, there are no transaction costs or taxes, and market participants can borrow and lend at the stated risk-free rate. Ross first reviews one-year options on Stock X. The stock pays no dividends, and European calls and puts have identical exercise prices and expiration dates. He observes the market call premium but does not have a put quote. He therefore plans to use put–call parity, discounting the exercise price at the annual effective risk-free rate. Ross notes that parity concerns option values today, not expiration profits, and that the present value of the exercise price must be used. Ross next evaluates a European call on Stock Y using a one-period binomial model. The stock will have one of two possible prices at the option's expiration. Because both stock-state prices and the risk-free return are supplied, the call can be valued either by constructing a replicating portfolio or by applying risk-neutral probabilities. The actual subjective probability of an up move is not required. The call has no value in a state in which the stock finishes below the exercise price. A Meridian client already owns Stock X and wants to remain exposed to appreciation because selling the position would disrupt the client's strategic allocation. The client will accept the payment of an option premium but requires a minimum value at which the shares can effectively be sold during the one-year horizon. The client does not want to cap the position's potential gain. Ross compares buying a put with writing a call and replacing the stock with a call. For a separate income-oriented account, Meridian purchased shares at the price reported in Exhibit 1 and simultaneously wrote calls against all shares. The premium was received at initiation and is included when measuring profit. If the stock finishes above the exercise price, the shares will be called away. Ross must therefore calculate the strategy's maximum profit using the stock gain up to the exercise price plus the premium received. Exhibit 1 contains the parity and strategy information, and Exhibit 2 contains the binomial-model inputs.

A nine-month long forward on a zero-coupon bond has delivery price USD 940. With three months remaining, the bond is worth USD 936.30 and the three-month continuously compounded rate is 4%. The forward value is closest to:

A commodity's spot price is USD 80.00. With continuous compounding, the one-year risk-free rate is 5%, storage cost is 3%, and convenience yield is 2%. The calculated value of the one-year forward price is closest to:

A manager needs linear market exposure and prioritizes reducing bilateral counterparty risk through central clearing and daily settlement. Which instrument is most appropriate?

A stock is USD 75 and will pay a USD 1 dividend in three months. At a 4% continuously compounded rate, the six-month forward price is closest to: