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NYU COR1-GB 2311 - Equities - Positions and Portfolio Returns

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Foundations of Finance: Equities: Positions and Portfolio Returns Prof. Alex Shapiro 1 Lecture Notes 4b Equities: Positions and Portfolio Returns I. Readings and Suggested Practice Problems II. Stock Transactions Involving Credit III. Portfolio Returns IV. Appendix V. Additional Readings Buzz Words: Going Long, Buying on Margin, Selling Short, Percentage Margin, Maintenance Margin, Portfolio WeightsFoundations of Finance: Equities: Positions and Portfolio Returns 2 I. Readings and Suggested Practice Problems BKM, Chapter 3: Sections 3.6-3.7. Suggested Problems, Chapter 3: 2-4, 13, 14. II. Stock Transactions involving Credit Use the stock of XYZ corporation as an example. The following are the dividends and closing prices for XYZ: Date Dividend: XYZ Closing Price:XYZ end Jan 0 8 end Feb 0 10 end Mar 0 7 Suppose you have $8000 cash at the end of January. Your balance sheet at the end of January looks like: Assets Liabilities Cash 8000 Net Worth 8000 Total Assets 8000 Total Liab & Net W. 8000 Assume your broker requires interest of 1% per month on any funds borrowed from her. Any funds placed with your broker also earn 1%. We consider this rate (EAR=12.68%) as the riskless rate (known in advance with certainty). Note that XYZ’s stock is a risky asset because its price over time is not known in advance.Foundations of Finance: Equities: Positions and Portfolio Returns 3 A. Long the Stock Long the Stock: Means buying the stock with your own funds. Example At the end of January, you want to invest your $8000 in XYZ shares at the closing price; so buy 1000 shares: Assets Liabilities 1000 XYZ sh @ $8 8000 Net Worth 8000 Total Assets 8000 Total Liab & Net W. 8000 By the end of February, XYZ s price has gone up: Assets Liabilities 1000 XYZ sh @ $10 10000 Net Worth 10000 Total Assets 10000 Total Liab & Net W. 10000 By the end of March, XYZ s price has plunged: Assets Liabilities 1000 XYZ sh @ $7 7000 Net Worth 7000 Total Assets 7000 Total Liab & Net W. 7000Foundations of Finance: Equities: Positions and Portfolio Returns 4 B. Buying Stock on Margin (Leveraging) Buying Stock on Margin: Means buying stock using funds borrowed from a broker. The client is charged an interest on the borrowed funds (plus a fee). Percentage margin: refers to net worth (value of the stock less amount borrowed) as a percentage of the value of the stock: Percentage Stockof ValueWorth Net = Margin × 100% 1. The Board of Governors of the Federal Reserve System (that has the authority to set the margin-credit limit by the Securities Exchange Act of 1934) has set the minimum initial margin at 50%. (Regulation T, part 220 – Credit by Brokers and Dealers.) So the borrowed amount must be less than 50% of the value of the stock purchased. Usually, the investor is not allowed to let the portion of debt rise higher than 75% of the value of the stocks in the account (Percentage Margin must remain above 25%). 2. If the percentage margin falls below the maintenance margin set by the broker (which may be above 25%), the customer has to put up enough collateral to satisfy the maintenance margin.Foundations of Finance: Equities: Positions and Portfolio Returns 5 At the end of January, you want to buy 1400 shares in XYZ. You thus need to borrow 1400 × $8 - $8000 = $3200 from your broker. Percent Margin = 8000/11200 = 71.43%>50%: Assets Liabilities 1400 XYZ sh @ $8 11200 Loan 3200 Net Worth 8000 Total Assets 11200 Total Liab & Net W. 11200 By the end of February, XYZ s price is up: Percent Margin = 10768/14000 = 76.91%. Assets Liabilities 1400 XYZ sh @ $10 14000 Loan ($3200@1%) 3232 Net Worth 10768 Total Assets 14000 Total Liab & Net W. 14000 By the end of March, XYZ s price has plunged: Percent Margin = 6536/9800 = 66.69%. Assets Liabilities 1400 XYZ sh @ $7 9800 Loan ($3232@1%) 3264 Net Worth 6536 Total Assets 9800 Total Liab & Net W. 9800Foundations of Finance: Equities: Positions and Portfolio Returns 6 C. Short Selling Stock Short Selling Stock: Means borrowing the stock and selling it. Proceeds from the sale must remain with the broker. The short-seller will return the stock back when asked to do so by the broker, or when he/she chooses to do so, whichever occurs first. If the stock pays dividends, the short-seller must pay them to the original owner. Percentage margin: refers to net worth as a percentage of the value of the stock borrowed: Percentage Borrowed Stockof ValueWorth Net = Margin × 100% If the percentage margin falls below the maintenance margin set by the broker, the customer has to put up enough collateral to satisfy the maintenance margin.Foundations of Finance: Equities: Positions and Portfolio Returns 7 Example 1. At the end of January, you have $8000 in cash with your broker, and you want to short-sell 1400 shares of XYZ. a. You borrow 1400 shares of XYZ. The loan is denominated in shares of XYZ not in dollars. Assets Liabilities 1400 XYZ sh @ $8 11200 Loan (1400 sh @ $8) 11200 Cash 8000 Net Worth 8000 Total Assets 19200 Total Liab & Net W. 19200 b. You sell the borrowed shares at the closing price at the end of January: Percent Margin = 8000/11200 = 71.43% Assets Liabilities Cash 19200 Loan (1400 sh @ $8) 11200 Net Worth 8000 Total Assets 19200 Total Liab & Net W. 19200 2. By the end of February, XYZ s price has gone up: Percent Margin = 5392/14000 =38.51% Assets Liabilities Cash ($19200@1%) 19392 Loan (1400 sh@$10) 14000 Net Worth 5392 Total Assets 19392 Total Liab & Net W. 19392Foundations of Finance: Equities: Positions and Portfolio Returns 8 2. By the end of March, XYZ s price has plummeted: Percent Margin = 9786/9800 = 99.86% Assets Liabilities Cash ($19392@1%) 19586 Loan (1400 sh@$7) 9800 Net


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