The stock of APPL sells $190 per share (Latest Close Price) on June 13th, 2023. The rate on Treasury bills is 1.4%. Suppose an analyst at Morgan Stanley just announced the following forecast on the APPL stock price range on July 13th, 2023: Economy Status Boom Normal economy Recession Probability 20% 65% 15% APPL Stock Price x $195 x $220 $185 x $195 $170 x $185 A. Suppose you totally trust this forecast from the analyst, calculate the expected holding-period return and standard deviation of the holding-period return over one month for APPL stock as well as the corresponding Sharpe ratios if you are (i) extremely pessimistic; (ii) extremely optimistic. (Do not round intermediate calculations. Round your answers to 4 decimal places.) (Hint: think about what your prediction of the exact stock price will be within each possible stock price range under each economy status if you are extremely pessimistic or extremely optimistic, and then use the corresponding exact price under each economy status to calculate expected return and standard deviation.) B1. Suppose you have enough funds (which allows you to buy/long the stock totally by using your own funds or sell/short the stock by borrowing the stock from the broker) and decide to trade 1,500 shares of APPL stocks. If you want to maximize your possible return after one month based on current information, what direction of trading will you choose if you are (i) extremely pessimistic; (ii) extremely optimistic and explain why simply. (Hint: you can use your results from A) B2.Base on your decision and the conditions in B1, you start to submit your market +order. You find the current order book structure is the follows: Limit Buy Orders(Bid) Limit Sell Orders(Ask) Price Price $189.5 $189.2 $ 188.8 $ 188.3 $ 188.2 Shares 200 500 700 400 600 $ 191.5 $ 191.6 $ 192.2 $ 192.5 $ 192.8 Shares 100 100 300 1000 200 On July 13th, 2023, you closed your position by submitting a limit order of $195 per share. The order was successfully executed. What is your profit or loss (not return) of the trading strategy after you closed your position according to the trading direction when you are (i) extremely pessimistic; (ii) extremely optimistic. B3. Now suppose you initially have $200,000 (can be used as collateral in the case of short sales on margins or used to buy the stock in the case of buying on margins) and all the other conditions are as the same as those in B1. You are allowed to trade by using a margin account. The maximum allowable margin is 50% according to FRB Reg T. The broker charges you the collateral in the case of short selling or provides you with the loan (with zero interest rate) in the case of buying according to the latest close price of APPL stock ($190 per share). Are you possible to trade on margin for the 1500 shares according to the trading direction when you are (i) extremely pessimistic; (ii) extremely optimistic. (Hint: calculate the maximum allowable share number to be traded by using the maximum allowable margin) B4 Suppose the maintenance margin is 30%. You used up the maximum allowable margin (maximize your financial leverage) to trade the 1500 shares of APPL stocks and invest your remaining funds on the Treasury-bill with annual interest rate 1% (1%/365 per day). The broker charges you the collateral in the case of short selling or provides you with the loan (with zero interest rate) in the case of buying according to the latest close price of APPL stock ($190 per share). The following table is some observations of daily + price records of APPL stock during the period from June 13th, 2023 to July 13th, 2023. (Assume in any other dates between June 13th, 2023 and July 13th, 2023, you did not receive any margin calls or execute any orders) OPEN June 14th, 2023 $190.3 June 19th, 2023 $198.3 June 23rd, 2023 $198.3 June 27th, 2023 $214.87 June 30th, 2023 $195.3 $186.9 $175.3 Date July 4th, 2023 July 12nd, 2023 HIGH $198.5 $205.5 $219.24 $215.5 $195.3 $187.5 $195.5 LOW $189.2 $197.2 $197.2 $210.2 $186.2 $170.87 $174.9 CLOSE $195.29 $203.03 $217.87 $212.57 $187.42 $171.84 $194.33 Would you receive a margin call before your plan to close your position on July 13th, 2023 if all the conditions are the same as those in B2 and explain why? Please discuss both the trading cases if you are (i) extremely pessimistic; (ii) extremely optimistic? B5. Continue with the case in B4. If you received the margin and don't have any additional funds, you had to close your position immediately at the time when you received the margin call (suppose the market is liquid so you can trade at price when you receive the margin call). Alternatively, if you did not receive a margin call, you would close your position on July 13th, 2023 by a executed limit order of $195 per share as the description in B2. The initial order book structure and the market order you submitted to construct your position is also the same as the description in B2. Calculate the final return of your trading in both cases if you are (i) extremely pessimistic; (ii) extremely optimistic.