A real-estate developer is building a 50-unit housing complex, the Designer Village Complex, near Boca Raton, Florida. Mortgage rates are currently around 4% and the developer, Sally Zimmerman, thinks that she will be able to sell the units at an average of $200,000 each. One of her great fears is that mortgage rates will climb above 5-6% during the year it will take for construction. Buyers become fewer, and more reluctant, as mortgage rates climb and there is an abrupt drop off at about 5%. Sally prepared a table showing how her expected profit varies with the mortgage rate in one year's time.

Mortgage Rate           2%      2 1⁄2%       3%      3 1⁄2%       4%        4 1⁄2          5%        5 1⁄2          6%         6 1⁄2%

Profit ($ millions)        3           3              3         2.5           2         1.5            1            -1             -3             -3

For simplicity, assume that there are traded options on mortgage rates. Assume further that upon exercise, the holder of a call option receives max [{mortgage rate − strike rate} × 1 million, 0]. The payoffs from a put option are defined in a similar manner. 

Configure a portfolio of options on mortgage rates that would ensure that Sally's profits do not drop below $2 million, but with hedging costs minimized by limiting the upside at $2 million, when interest rates are high.