Questions -

Q1. XYZ stock is currently trading at $100. The one-year effective interest rate is 5% ($1 lent today yields $1.05 one year from now). A one year put with strike price $105 is priced at $5.

Suppose you buy one put for $5, buy one share for $100, and borrow $100. Graph the PAYOFF function for this position (i.e., 1 put + 1 share - $100 loan). Be sure to label the points, if any, where the graph intercepts the x-axis or y-axis.

What common derivative is the combination of investments (put+share+ borrowing) equivalent to? In the absence of arbitrage, what should be the price of this derivative if it were available?

Q2. Suppose you are advising a widget manufacturing firm on risk management strategy. It has a factory capable of producing ten widgets per year. This year, the firm has a contract to produce 10 widgets for $1000 each. The payment is delivered now, so that the firm has $10,000. The firm's labor cost is $500 per widget, which it must pay now. At the end of the year, each widget must be finished with a coating of one unit of zerbil, an input that cannot be stored and currently costs $400 per unit. The firm has no other resources and no access to other sources of external financing. If it fails to meet its production target, it loses its factory and future rights to produce. The lending rate is zero percent.

a) What objective would you target for this firm when formulating a risk management strategy? In other words, what outcome are you trying to achieve or avoid?

b) Consider the derivatives: 1) forwards, 2) calls, and 3) puts. For each derivative, identify the direction of the position (e.g., long or short) that you would take to manage risk in this situation. Assume that the underlying asset for the derivative in each case is zerbil.

c) Suppose the only derivative available is a one year put on zerbil with strike price 500. It is priced at $50. Could you use this derivative to help you accomplish your goal in a)? What would you do? Also, describe the circumstances, if any, under which your strategy would accomplish your goal, and those, if any, under which it would fail.

d) Suppose now that, in addition to the put described in c), there is also a one year call option on zerbil with strike price 500 that is priced at $25. Is there a risk management strategy for the firm that will fully protect against bankruptcy? Describe it.

Q3. Suppose you are advising a gold mining firm on risk management strategy. It has a mine capable of producing ten ounces of gold per year. This year, the firm plans to produce 10 ounces. The firm's cost of production in $1000 per ounce, which it is committed to paying at the end of the year. The firm has no cash and no access to other sources of external financing. If it fails to meet its production target, it loses its factory and future rights to produce. The lending rate is zero percent.

a) What objective would you target for this firm when formulating a risk management strategy? In other words, what outcome are you trying to achieve or avoid?

b) Consider the derivatives discussed in class: 1) forwards, 2) calls, and 3) puts. Assume the underlying in each case is gold. For each derivative, identify the direction of the position (e.g., long or short) that you would take to manage risk in this situation (assuming that the firm is in fact able to buy the derivative, if a premium is necessary).

c) Suppose the only derivative available is a forward with forward price $1000. Could you use this derivative to help you accomplish your goal in a)? How? Also, describe the circumstances, if any, under which your strategy would accomplish your goal, and those, if any, under which it would fail.

d) Suppose now that, instead of the forward contract, there is a one year call option on gold with strike price 1100 that is priced at $100. Could you use this derivative to help you accomplish your goal in a)? How? Also, describe the circumstances, if any, under which your strategy would accomplish your goal, and those, if any, under which it would fail.