The Risks of Short Selling: In the text, we mentioned that short-selling can entail a lot more risk if the investor’s guesses are wildly incorrect than taking the more conventional long position of buying and holding and asset.
A. Suppose oil currently sells for $50 a barrel. Consider two different investors: Larry thinks that oil prices will rise, and Darryl thinks they will fall. As a result, Larry will take a long position in the oil market while Darryl will take a short position. Both of them have enough credit to borrow $10,000 in cash or an equivalent amount (at current prices) in oil. (For purposes of this exercise, do not worry about any opportunity costs associated with the interest rate—i.e. simply assume an interest rate of 0—and suppose oil can be stored without cost.)
(a) Consider Larry first. How much will he have one year from now if he carries through with his strategy of investing all his money in oil and oil one year from now stands at $75 a barrel.
(b) Now consider the worst case scenario: A new energy source is found and oil is no longer worth anything 1 year from now. Larry’s guess about the future was wildly incorrect. How much has he lost?
(c) Next, consider Darryl. How much will he have 1 year from now (if he carries through with his strategy to sell oil short) if the price of oil one year from now stands at $25 a barrel.
(d) Suppose instead that Darryl’s prediction about the future was wildly incorrect and the price of oil stands at $100 a barrel next year. How much will he have lost if he leaves the oil market at that point?
(e) Was the scenario in (d) the worst-case scenario for Darryl? Is there a limit to how much Darryl might lose by “going short”? Is there a limit to the losses that Larry might incur?
(f) Can you explain intuitively — without referring to this example— why short-selling entails Inherently more risk for investors who are very wrong in their predictions than going long in The market does?
B. Suppose more generally that a barrel of oil sells at price p0 on the current “spot market”—which is defined as the market for oil that is currently being sold. Suppose further that you expect the price of a barrel of oil on the spot market n years from now to be pn. Suppose the annual interest rate is r .
(a) Can you write down an equation πLn (p0,pn,r,q) that gives the profit (expressed in current dollars) from going long in the oil market for n years by buying q barrels of oil today?
(b) How high does the ratio pn/p0 have to be in order to justify going long in the oil market in this way? Can you make intuitive sense of this?
(c) Next, can you write down the equation for πSn (p0,pn,r,q) —the profit from selling q barrels of oil short by borrowing them now and repaying them in n years? (Assume that the person you are borrowing the oil from expects you to return (1+r )n times as much oil — i.e. he is charging the interest to be paid in terms of barrels of oil.)
(d) How high can pn/p0 be to still warrant a short selling strategy of this type? Can you make intuitive sense of this?