Part $3$: Exploiting Mispricing$$ For this part, use hw$1$data.xls$.$ The sheet labeled $3$Com Palm$$ contains data on $3$Com and$$ Palm stock prices.$$ Suppose that it is March $6,2000.$ You decide to exploit the negative stub of $3$Com. For$$ each share of $3$Com stock, a shareholder will eventually receive $1\mathrm{.}5$ shares of Palm. Thus, you believe that P$3$Com $1\mathrm{.}5$PP alm$\mathrm{.}11.$ Suppose that you believe that $3$Com is fairly priced and that its stub value is $$0($i$.$e$.$ its only value comes from Palm$).$ What should Palm$$s price be in a market that is$$ both frictionless and free from arbitrage?$2.$ Suppose that you now decide to exploit the negative stub value of $3$Com. You short$$ sell $150$ shares of Palm and buy $100$ shares of $3$Com. You use the $3$Com shares as$$ collateral in the Palm short sale. What does your balance sheet look like? $($i$.$e$.$ What$$ are your assets, liabilities, and equity?$)$ What is your margin?$3.$ Jump ahead to March $9,2000.$ What does your balance sheet look like? $4.$ If you are forced to unwind your position on March $9,2000,$ what is your return?$25.$ Why is your return in the previous part negative even though this appears to be a clear arbitrage trading strategy? What would your return have been if you were able to hold the position until July $28,2000$ after $1\mathrm{.}5$ Palm shares were distributed for each$3$Com share?$$