Hedge or Not to Hedge?

Suppose that the U.S. Boeing Corporation has just exported a Boeing 747 to British Airways and billed 10 million, payable in one year. At the same time, the corporation has also imported several key components for manufacturing the airplanes from Germany and has been billed 10 million, payable in one year. The Assistant Treasurer at the Corporation oversees finding ways to hedge its foreign currency risk of British pounds and euros. Lately, the pounds and euros are very volatile against U.S. dollars. He is considering forward, money market, and options hedge. The Assistant Treasurer just finished collecting the spot, forward, and currency options quotes from the Bloomberg terminal, which are as follows:

The treasurer keeps note that he can borrow and lend foreign currencies at the ask and bid rates, respectively. He also reminds himself that he has learned from his finance courses in the university: always buy at the ask and sell at the bid. He needs to prepare a memo analysing currency hedging for the Finance Committee in two days addressing which strategy would be better: forward hedge? Money market hedge? Option hedge? He is considering five possible exchange rate scenarios for dollar-pound and dollar-euro in one year so that he can show his analysis to the Committee. These exchanges rates are: $1.30/, $1.40/, $1.46/, $1.50/, $1.60/ for dollar-pound and $1.00/, $1.10/, $1.18/, $1.20/, $1.30/ for dollareuro. After doing all the calculations, he wants to decide which hedging strategy would be preferable. First, he plans to find the outcomes of the forward and money market hedging, then use the same forward rates as the strike exchange rates for options market hedging. After that, he plans to find the future spot rates that would make him indifferent between option and forward outcomes. He believes that this process would help him in identifying whether an option hedge would be helpful, given that options require up-front costs. He has prepared a few tables for the forward and options outcomes that can be used to understand the overall situation better:

\begin{tabular}{|l|l|} \hline \multicolumn{2}{|l|}{ Exchange Rates: } \\ \hline Spot exchange rate ($/f) & 1.50 \\ \hline Spot exchange rate ($/) & 1.20 \\ \hline Forward exchange rate ($/)1 year & 1.46 \\ \hline Forward exchange rate ($/)1 year & 1.18 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|l|}{ Money Market Rates: } \\ \hline & Bid (\%) & Ask (\%) \\ \hline U.S. interest rate (per annum) & 6.10 & 6.12 \\ \hline U.K. interest rate (per annum) & 8.87 & 9.00 \\ \hline German interest rate (per annum) & 8.00 & 8.05 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline OptionsMarkets: & \multicolumn{4}{|l|}{ Call options (\$/) } & \multicolumn{3}{l|}{ Call options (\$/) } \\ \hline & Strike & Bid & Ask & Strike & Bid & Ask \\ \hline & 1.30 & 0.040 & 0.041 & 1.00 & 0.035 & 0.040 \\ \hline & 1.40 & 0.031 & 0.034 & 1.10 & 0.031 & 0.035 \\ \hline & 1.46 & 0.028 & 0.030 & 1.18 & 0.026 & 0.030 \\ \hline & 1.50 & 0.021 & 0.026 & 1.20 & 0.020 & 0.025 \\ \hline & 1.60 & 0.196 & 0.020 & 1.30 & 0.018 & 0.020 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|} \hline OptionsMarkets: & \multicolumn{4}{l|}{ Put options (\$/f) } & \multicolumn{3}{l|}{ Put options (\$/) } \\ \hline & Strike & Bid & Ask & Strike & Bid) & Ask \\ \hline & 1.30 & 0.003 & 0.005 & 1.00 & 0.020 & 0.021 \\ \hline & 1.40 & 0.005 & 0.010 & 1.10 & 0.022 & 0.024 \\ \hline & 1.46 & 0.010 & 0.020 & 1.18 & 0.024 & 0.029 \\ \hline & 1.50 & 0.020 & 0.030 & 1.20 & 0.029 & 0.031 \\ \hline & 1.60 & 0.030 & 0.040 & 1.30 & 0.035 & 0.038 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{3}{|l|}{ Forward position outcome } \\ \hline FutureSpotExchangeRate(ST) & Unhedged Position & Hedged Position & Gains/LossesfromHedge \\ \hline$1.30 & & & \\ \hline$1.40 & & & \\ \hline$1.46 & & & \\ \hline$1.50 & & & \\ \hline$1.60 & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{3}{|l|}{ Forward position outcome } \\ \hline FutureSpotExchangeRate(ST) & Unhedged Position & Hedged Position & Gains/LossesfromHedge \\ \hline$1.00 & & & \\ \hline$1.10 & & & \\ \hline$1.18 & & & \\ \hline$1.20 & & & \\ \hline$1.30 & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline Option market outcome \\ \hline FutureSpotExchangeRate(ST) & ExerciseDecision & GrossDollarProceeds & Option Cost & NetDollarProceed \\ \hline$1.30 & & & & \\ \hline$1.40 & & & & \\ \hline$1.46 & & & & \\ \hline$1.50 & & & & \\ \hline$1.60 & & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline \multicolumn{5}{|l|}{ Option market outcome } \\ \hline FutureSpotExchangeRate(S) & ExerciseDecision & GrossDollarProceeds & Option Cost & NetDollarProceed \\ \hline$1.00 & & & & \\ \hline$1.10 & & & & \\ \hline$1.18 & & & & \\ \hline$1.20 & & & & \\ \hline$1.30 & & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|} \hline \multicolumn{2}{|l|}{ Exchange Rates: } \\ \hline Spot exchange rate ($/f) & 1.50 \\ \hline Spot exchange rate ($/) & 1.20 \\ \hline Forward exchange rate ($/)1 year & 1.46 \\ \hline Forward exchange rate ($/)1 year & 1.18 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|} \hline \multicolumn{3}{|l|}{ Money Market Rates: } \\ \hline & Bid (\%) & Ask (\%) \\ \hline U.S. interest rate (per annum) & 6.10 & 6.12 \\ \hline U.K. interest rate (per annum) & 8.87 & 9.00 \\ \hline German interest rate (per annum) & 8.00 & 8.05 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline OptionsMarkets: & \multicolumn{4}{|l|}{ Call options (\$/) } & \multicolumn{3}{l|}{ Call options (\$/) } \\ \hline & Strike & Bid & Ask & Strike & Bid & Ask \\ \hline & 1.30 & 0.040 & 0.041 & 1.00 & 0.035 & 0.040 \\ \hline & 1.40 & 0.031 & 0.034 & 1.10 & 0.031 & 0.035 \\ \hline & 1.46 & 0.028 & 0.030 & 1.18 & 0.026 & 0.030 \\ \hline & 1.50 & 0.021 & 0.026 & 1.20 & 0.020 & 0.025 \\ \hline & 1.60 & 0.196 & 0.020 & 1.30 & 0.018 & 0.020 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|} \hline OptionsMarkets: & \multicolumn{4}{l|}{ Put options (\$/f) } & \multicolumn{3}{l|}{ Put options (\$/) } \\ \hline & Strike & Bid & Ask & Strike & Bid) & Ask \\ \hline & 1.30 & 0.003 & 0.005 & 1.00 & 0.020 & 0.021 \\ \hline & 1.40 & 0.005 & 0.010 & 1.10 & 0.022 & 0.024 \\ \hline & 1.46 & 0.010 & 0.020 & 1.18 & 0.024 & 0.029 \\ \hline & 1.50 & 0.020 & 0.030 & 1.20 & 0.029 & 0.031 \\ \hline & 1.60 & 0.030 & 0.040 & 1.30 & 0.035 & 0.038 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{3}{|l|}{ Forward position outcome } \\ \hline FutureSpotExchangeRate(ST) & Unhedged Position & Hedged Position & Gains/LossesfromHedge \\ \hline$1.30 & & & \\ \hline$1.40 & & & \\ \hline$1.46 & & & \\ \hline$1.50 & & & \\ \hline$1.60 & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|} \hline \multicolumn{3}{|l|}{ Forward position outcome } \\ \hline FutureSpotExchangeRate(ST) & Unhedged Position & Hedged Position & Gains/LossesfromHedge \\ \hline$1.00 & & & \\ \hline$1.10 & & & \\ \hline$1.18 & & & \\ \hline$1.20 & & & \\ \hline$1.30 & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline Option market outcome \\ \hline FutureSpotExchangeRate(ST) & ExerciseDecision & GrossDollarProceeds & Option Cost & NetDollarProceed \\ \hline$1.30 & & & & \\ \hline$1.40 & & & & \\ \hline$1.46 & & & & \\ \hline$1.50 & & & & \\ \hline$1.60 & & & & \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|} \hline \multicolumn{5}{|l|}{ Option market outcome } \\ \hline FutureSpotExchangeRate(S) & ExerciseDecision & GrossDollarProceeds & Option Cost & NetDollarProceed \\ \hline$1.00 & & & & \\ \hline$1.10 & & & & \\ \hline$1.18 & & & & \\ \hline$1.20 & & & & \\ \hline$1.30 & & & & \\ \hline \end{tabular}