Solve the following problems and write or type your answers on this form. Notice that your results for Problem 1 should be used for Problems 2, 3, and 4.\ \ * * * * *\ Suppose that you have a short position in physical gold, which has been profitable over the past several months. You would like to wait until June to take your profits, but you are concerned that the gold price could increase at some point during the next 4 months and wipe out your gains.\ \ Assume the spot price for gold is $1860, the forward price for gold in 4 months is $1856, the premium for a June $1860 call option is $41.80, and the premium for a June $1860 put option is $40.40. Assume an interest rate for 4 months (February to June) of 2% (i.e., 6% annual simple interest for 1/3 of a year). Ignore commissions, margins, and other transaction costs.\ \ PROBLEM 1. Show the profit table for your short gold investment (the unhedged position in gold only, without any forwards or options) over a range of market prices for gold from $1760 to $1960 in $20 increments. [Hint: If you are short gold, do you pay interest or receive interest?] Use as many columns as you need. Then answer the following questions.\ \ Market Price Premium\ Value of Shorting Profit \ 1760 \ 1780 \ 1800 \ 1820 \ 1840 \ 1860 \ 1880 \ 1900 \ 1920 \ 1940 \ 1960 \ \ a) If your position in physical gold is short, are you at risk from higher prices or lower prices?\ \ \ \ b) What is the maximum net profit over the $1760 to $1960 price range? \ \ \ \ c) What is the maximum net loss (or minimum net profit) over the $1760 to $1960 price range?\ \ \ \ d) At what gold price does the breakeven price occur? Give an exact value.