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EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022 EF3320 Security Analysis and Portfolio Management – Problem Set 1 This problem set is to be turned in by Friday, 28 January 11:00 pm. Please present your work using MS Word or PDF and submit online on Canvas. You may use Excel for calculation but the final solution should be presented in MS Word or PDF. 1. Price-Weighted Index Consider a price-weighted index of the following three stocks: Stock Price per share on day 0 Shares outstanding (millions) A 80 40 B 120 10 C 200 2 a) Suppose that we construct the price-weighted index on day 0. What is the current index level? Solution: At the beginning, the index level is the simple average of prices: 80 + 120 + 200 = 133.333 3 b) On day 0, stock B splits three for one so that its share price becomes $40 and the number of shares outstanding becomes 30 millions. What should be the new divisor for the index? Solution: The divisor d satisfies the following equation: 133.333 = 80 + 40 + 200 . d Solving for the unknown, we find d = 2.4. c) Following are stock prices on day 1. 1 Instructor: Yongjin Kim EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022 Stock Price per share on day 1 Shares outstanding (millions) A 88 40 B 36 30 C 190 2 What is the index level on day 1? What is the return on the stock index from day 0 to 1? X 88+36+190 88+36+290 X X Using the divisor that was updated on day 0, the index on day 1 is = X 2.4 X 2.4 130.833. The rate of return on the index from day 0 to 1 is Solution: 130.833 − 133.333 = −1.88%. 133.333 2. Limit and Market Orders Suppose that the current limit order book of Tencent shares are as follows: Bid/Ask Price Size Ask 456.00 200 Ask 455.90 700 Ask 455.80 400 Bid 454.20 300 Bid 454.10 100 Bid 454.00 100 a) A new market order arrives to buy 500 shares of Tencent. What will be the average price that this market order is executed? How will the limit order book change? Solution: The new market orders will be matched to multiple existing orders – order to sell 400 shares at $455.80 and order to sell 100 shares at $455.90. The average price of the market order is 400 100 (455.80) + (455.90) = $455.82. 500 500 2 Instructor: Yongjin Kim EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022 After this market order, the limit order book will change to Bid/Ask Price Size Ask 456.00 200 Ask 455.90 600 Bid 454.20 300 Bid 454.10 100 Bid 454.00 100 b) Afterwards, a new limit order arrives to buy 300 shares at $454.30. Will this order be executed immediately? How will the limit order book change? Solution: The new limit order cannot be executed immediately, as there are no existing orders to sell at a price of $454.30 or lower. Then, the new limit order is added, so the limit order book will change to Bid/Ask Price Size Ask 456.00 200 Ask 455.90 600 Bid 454.30 300 Bid 454.20 300 Bid 454.10 100 Bid 454.00 100 c) Finally, a new limit order arrives to sell 200 shares at $454.25. Will this order be executed immediately? Solution: The new limit order is executed immediately as it is matched to the existing orders to buy at $454.30. 3 Instructor: Yongjin Kim EF3320 Security Analysis and Portfolio Management - Semester B 2021/2022 3. Buying on Margins A trader purchases 300 shares of stock at $40 per share. She borrows $4,000 from her broker to help pay for the purchase. The maintenance margin requirement is 30%. a) If the share price next day falls to $30, will she receive a margin call? Solution: With the new share price, the percentage margin is 300 × 30 − 4000 = 55.56%. 300 × 30 As the percentage margin is still higher than the maintenance margin, there will be no margin call. b) In what range of stock price of S will she receive a margin call? Solution: The margin call takes place when 300 × S − 4000 < 0.3. 300 × S Thus, when S < $19.048, the investor receives a margin call. 4 Instructor: Yongjin Kim