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Tutorial 1 Week 2 – Background of Equity Investments Q.1. BDBKM, Ch. 3, Q.5 What are the differences between a stop loss order, a limit sell order and a market order? Answer: A stop loss order is a trade that is not to be executed unless the stock hits a specified price limit. The stop loss is used to limit losses when prices are falling. A limit sell order is an order specifying a price at which an investor is willing to sell a security at. A market order directs the broker to buy or sell at whatever price is available in the market. Q.2. BDBKM, Ch. 3, Q. 6 How do margin trades magnify both the upside potential and downside risk of an investment portfolio? Answer: Margin is a type of leverage that allows investors to post only a portion of the value of the security they purchase. As such, when the price of the security rises or falls, the gain or loss represents a much higher percentage, relative to the actual money invested. Q.3. Describe the three components of transaction costs. Explain which of these three components will be the most relevant for the following investors: a. A retail investor who buys $3000 worth of Commonwealth Bank shares. b. An institutional investor that invests $100,000 in a microcap firm that has a market capitalization of $3 million. Answer: The three components of transaction costs are: Brokerage Commission – The fee paid to a broker for facilitating the transaction. Bid-Ask Spread – The difference between the best price an investor is currently willing to buy and sell the stock at. When an investor places a market order they ‘cross the spread’ and pay this implicit fee. Market (or price) Impact – Where a large transaction moves the price such that the average price that shares are bought or sold for are less favourable than the best available quote. a. Brokerage Commission would be the biggest component for this investor. At

CBA is a large cap firm, it would have a low spread and there would be no market impact for a trade of this size. b. Both bid-ask spread and market impact would be most relevant. As the firm is a microcap, it is likely that it will have a substantial spread. Given the investor is placing a trade for more than 3% of the outstanding shares on issue, there is likely to be a very substantial market impact when the trade is placed.

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Q.4. BDBKM, Ch. 3, Q. 11 You are optimist about Telecom shares. The current market price is $50 per share, and you have $5,000 of your own to invest. You borrow an additional $5,000 from your broker and invest $10,000 in the shares. How far does the price of Telecom shares have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately. Lecturer’s Hint: Margin call happens when the equity in your account to the value of your stocks falls below the maintenance margin level of 30%. Answer: As the share price is $50 and total investment in the shares is $10,000, you are holding 200 shares. Assume P is the share price at which the maintenance margin call is triggered. The value of the 200 shares is 200P. As you borrowed $5000 from the broker, your equity = Total Assets – Total Liabilities = (200P – $5000). You will receive a margin call when:

200P  $5000 200P

= 0.30, i.e. when P = $35.71 or lower.

Q.5. BDBKM, Ch. 3, Q. 14 You’ve borrowed $20,000 on margin to buy shares in Worley Parsons, which are now selling at $40 per share. Your account starts at the initial margin requirement of 50%. The maintenance margin is 35%. Two days later, the share price falls to $35 per share. a. Will you receive a margin call? b. How low can the price of Worley Parsons shares fall before you receive a margin call? Answer: a. You borrowed $20 000 and given the initial margin requirement of 50%, you would have put in an initial margin of another $20 000 (i.e. your own equity). The total amount of $40 000 is sufficient for you to buy 1000 shares of Worley Parsons at $40 per share. When the share price falls to $35 per share, the market value of 1000 shares is $35 000. Your equity is: Total Assets – Total Liabilities = $35 000 - $20 000 = $15 000. The percentage margin is: Equity / Total Assets = $15 000/$35 000 = 42.9%. Your percentage margin exceeds the required maintenance margin. Hence, you will not receive a margin call!

b. Assume P is the share price at which the maintenance margin call is triggered. 1000 shares are now worth 1000P. Given your liabilities of $20 000, your equity is (1000P - $20 000). You will receive a margin call when the ratio of equity to the value of 1000 shares falls below 35%: 3

1000P  $20 000 = 0.35, i.e. when P = $30.77 or lower. 1000P Q.6. An investor bought a share for $50. Three years later and the investor sold the share for $60. The investor received $12 in dividends over this period. a. Calculate the holding period return on this investment. b. Calculate the average annual return assuming compounding. c. Calculate the average annual return if there is no compounding. Answer a. HPR =

쳌䁣ꀀ香䁞쳌 䁞쳌

= 44%

b. HPRann = [(1+HPR)1/n] – 1 = [(1+0.44)1/3] – 1 = 0.129243 c. HPRann = 0.44/3 = 0.146667 Q.7. BDBKM, Ch. 5, Q. 1 Suppose you’ve estimated that the fifth-percentile value at risk of a portfolio is -30%. Now you wish to estimate the portfolio’s first-percentile VaR (i.e. the value below which 1% of the returns lie). Will the 1% VaR be greater or less than -30%? Answer: Value-at-Risk (VaR) tells you how much you can expect to lose on your portfolio in a given time period at a given level of probability. The 1% VaR will be less than the 5% VaR of −30%. As percentile or probability of a return declines, so does the magnitude of that return. Thus, a 1 percentile probability will produce a smaller VaR than a 5 percentile probability.

Q.8. Draw a complete binomial tree in which the asset price can double (probability of up is .5) or decrease by half for the next three 3 periods. The initial price is 16 and the initial wealth of 100 in the risky asset. There is a risk-free asset that yields zero returns a) b) c)

What is the expected wealth if the investor always put 50 percent of her wealth on the risky asset? Implement a stop-loss order when asset price drops to 8. What’s the expected wealth of implementing a stop-loss order?

a). We normalize initial price so it is easier to compute returns. So P=16 is now 1. The top state then yields a return of 2^3 = 8 while the low-priced state yields (1/2)^3. Please see spreadsheet Final prices 8

Final wealth 128

338

4

4

64

169

2

32

169

0.5

8

84

2

32

169

0.5

8

84

0.5

8

84

0.125

2

42

Expected wealth

142

If the investor allocates 50 percent, then this means that final risky allocation is 50% and 50% of risk-free. We work with terminal values since the allocation of 50% is constant across all periods and states. Each terminal node has a probability of 1/16 of occurring. So the final wealth is 142.

b. The stop-loss leads to terminal wealth as follows. The investor sells the asset and put all her wealth in the risk-free when asset price is equal to 8. This price is the current price. That is, in the first period the investor sells the asset in the down state that leads to the last four terminal states a wealth of 75. Why? The return is 0.5 in the last four states. Thus, 100*.5*.5+ 100*.5*1 = 75.

c. Following the computation of expected wealth, then we have 338*1/8 + 169*2/8 + 84*1/8+ 75*4/8 =132

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Q.9. BDBKM, Ch. 5, Q. 6 The shares of Business Adventures sell for $40 a share. The likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows:

Boom Normal economy Recession

Dividend $2.00 1.00 0.50

Share price $50 43 34

a. Calculate the expected HPR and standard deviation of the HPR if all three scenarios are equally likely b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury notes. The return on notes is 4%. Answer: a. The holding period returns for the three scenarios are:

Boom: (50 – 40 + 2)/40 = 0.30 = 30.00% Normal: (43 – 40 + 1)/40 = 0.10 = 10.00% Recession: (34 – 40 + 0.50)/40 = –0.1375 = –13.75% E(HPR) = [(1/3) × 30%] + [(1/3) × 10%] + [(1/3) × (–13.75%)] = 8.75% 2(HPR) = [(1/3) × (30 – 8.75) 2] + [(1/3) × (10 – 8.75) 2] + [(1/3) × (–13.75 – 8.75)2] = 319.79  = 319.79 = 17.88% b. E(r) = (0.5 × 8.75%) + (0.5 × 4%) = 6.375%  = 0.5 × 17.88% = 8.94%

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