Hi, I need help with # 4 part b,c, and d. Could you please type out the solutions to these problems so that I will know how to do it writing it and you can send it via Word Document.

Assignment 1 Prof. Hanh Le Due at the start of class on Wednesday, February 10 Fill in the following information on the rst page of your submission: Name: Class section and time: Students you work with on this assignment: 1. (1 pt) For this question, circle or state the correct answers. You do not need to provide explanations or show workings. Consider the following limit order book. The time at which each order came in is inside the bracket Limit buy order Price Shares $39.75 100 (7:00 am) $39.50 100 (7:05 am) Limit sell order Price Shares $40.25 100 (7:02 am) $40.50 100 (7:09 am) (a) If a market buy order for 50 shares comes in, at what quantity and price will it be lled? A) 100 shares at $39.75 per share B) 100 shares at $40.25 per share C) 50 shares at $40.50 per share D) 50 shares at $39.50 E) 50 shares at $40.25 per share (b) Ignore part (a) of the question and assume that a limit sell order comes in with an ask price of $39 and quantity of 160, at what price and quantity will it be lled? A) 100 shares at $39.75 and 60 shares at $39.50 B) 160 shares at $39.75 1 C) 160 shares at $39.50 D) 100 shares at $39.50 and 60 shares at $39.75 2. (0.5 pt) Assume you purchased 500 shares of XYZ common stock on margin at $40 per share from your broker. If the initial margin is 60%, the amount you borrowed from the broker is A) $20,000 B) $12,000 C) $8,000 D) $15,000 Show your workings. 3. (1.5 pt) You are among the OTC market makers in the stock of Bio-Engineering, Inc. and quote a bid of 102 1/4 and an ask of 102 1/2. Suppose that you have a zero inventory. (a) On Day 1 you receive market buy orders for 10,000 shares and market sell orders for 4,000 shares. How much do you earn on the 4,000 shares that you bought and sold? What is the dollar value of your inventory at the end of the day? (Hints: It is possible to have negative inventory. Further, the value per share of inventory can be computed as the average of the bid and the ask.) (b) Before trading begins on Day 2 the company announces trial testing of a cure for acne in mice. The quoted bid and ask jump to 110 1/4-1/2. During Day 2 you receive market sell orders for 8,000 shares and buy orders for 2,000 shares. What is your total prot or loss over the two-day period? What is the value of your inventory at the end of Day 2? (c) What is a market maker's objective? Is there anything you could have done during Day 1, consistent with a market maker's objective, that would have improved your performance over the two-day period? 4. (1 pt) The probability distribution of returns for the two stocks X and Y are as follows RY Probability RX 0.1 -0.05 0.01 0.3 0.03 -0.1 0.4 -0.04 0.02 0.2 0 -0.03 (a) Calculate the expected returns of stocks X and Y (b) Calculate the standard deviations of returns on stocks X and Y (c) Calculate the covariance between the returns of stocks X and Y 2 (d) Calculate the correlation between X's and Y's stock returns. Interpret this correlation. 5. (1 pt) Suppose that the S&P 500 index has mean E(Rm ) = 16% and standard deviation M = 10%, and suppose that the T-bill rate (the risk-free asset) Rf = 8%. Answer the following questions: (a) What is the expected return and standard deviation of a portfolio that is totally invested in the risk-free asset? (b) What is the expected return and standard deviation of a portfolio that has 50% of its wealth in the risk-free asset and 50% in the S&P 500 index? (c) What is the expected return and standard deviation of a portfolio that has 125% of its wealth in the S&P 500 index, nanced by borrowing 25% of its wealth at the risk-free rate? (d) What are the weights for investing in the risk-free asset and the S&P 500 index that produce a standard deviation for the entire portfolio that is twice the standard deviation of the S&P 500 index? What is the expected return on that portfolio? 6. (bonus point) Palm makes handheld computers and was owned by 3Com, a company selling computer network systems and services. On March 2nd, 2000, 3Com sold a fraction of its stake in Palm to the general public via an initial public oering (IPO). In this transaction, called an equity carve-out, 3Com retained ownership of 95 percent of the shares. 3Com announced that it would eventually spin o its remaining shares of Palm to 3Coms shareholders before the end of the year. 3Com shareholders would receive about 1.5 shares of Palm for every share of 3Com that they owned. After the rst day of trading, Palm closed at $95.06 a share and 3Com was trading at $81.81. (a) Can you generate a trading strategy using Palm and 3Com stock that will always generate positive prots? (Hint: You need to go buy a xed number of stocks in one company and short sell a xed number of stocks in the other company so that your payos are never negative.) (b) What happens if you cannot short-sell companies like Palm? (c) How can you explain these prices? 3