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Fin 525 Week 8

Fin 525 Week 8. Asset Pricing Models and the Stock Project. The Stock Prediction and Hedging Project in Three Parts. Predict the closing price of Green Mountain Coffee Roasters: (Nasdaq ticker: GMCR ) on December 1, 2006 (5 pts.)

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Fin 525 Week 8

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  1. Fin 525 Week 8 Asset Pricing Models and the Stock Project

  2. The Stock Prediction and Hedging Project in Three Parts • Predict the closing price of Green Mountain Coffee Roasters: (Nasdaq ticker: GMCR) on December 1, 2006 (5 pts.) • Create a portfolio that hedges as completely as possible the risk from 10,000 shares of GMCR for the period from 4 p.m. November 10 through 4 p.m. December 1. Portfolios are graded based on the standard deviations they achieve (20 pts.) • Write up an explanation of what you did in 1. and 2. in 1,000 words or less (75 pts.) Professor Ross Miller • Fall 2006

  3. Key Dates and Times for the Stock Project • Both your prediction and your hedging portfolio are due Sunday, November 12, 2006 at 6 p.m. via e-mail in a standard format to rmmiller@uamail.albany.edu. You can use millerrm@nycap.rr.com as a fallback if the first address does not work for you. • Clicking on the above links for many e-mail programs will create an e-mail message this is properly formatting for submission • The write-up is due at the beginning of class on November 13 (Monday section) and November 15 (Wednesday section) Professor Ross Miller • Fall 2006

  4. Part 1: Stock Price Prediction • Prediction is for the price of a single share of GMCR in $US at the closing of normal Nasdaq trading (usually 4 p.m. or slightly after) on December 1, 2006 as reported on http://finance.yahoo.com. • The objective is to come as close as possible • Guaranteed grades for price prediction accuracy • Within 2% - 5 pts. • Within 4% - 4 pts. • Within 6% - 3 pts. • Grade intervals may be widened at the professor’s discretion Professor Ross Miller • Fall 2006

  5. Part 2: Hedge Construction • You must hold 10,000 shares of GMCR • You can supplement these shares with either short or long holdings (in multiples of 100 shares) chosen from any or all of the following six securities: • Nasdaq 100 Trust (QQQQ) • S&P Depository Receipts (SPY) • Starbucks (SBUX) • Wal-Mart (WMT) • Google (GOOG) Professor Ross Miller • Fall 2006

  6. Part 2: Hedge Construction (Cash Considerations) • All long positions must be paid for in cash • No purchases on margin • Note that the GMCR shares alone will cost about $400,000 at current stock prices • All short positions will generate 90% of their sale price in cash • This is the typically the best deal any institutional client can get from a broker • Your initial cash (capital) investment must be between $100,000 and $1,000,000 Professor Ross Miller • Fall 2006

  7. Short Selling • Selling a stock short involves borrowing shares, selling them, and buying them back at a future date • The short seller must pay dividends • Only institutional short sellers get to use to the some of the proceeds of the short sale • Short selling is one of those things that works easy in theory, but may be fraught with difficulties (and margin calls) in practice • Fortunately, selling ETFs (SPY, QQQQ, etc.) short is not difficult, which is one reason that they are so actively traded Professor Ross Miller • Fall 2006

  8. An Example of How Short Selling Works • Suppose SPY is at $130/share and you sell 1,000 shares short • Your brokerage account is credited with the proceeds of $130,000 • An individual customer would not get to use the proceeds and would have to post margin instead • In the GMCR exercise, you get access to 90% of the proceeds, which is 0.9 x $130,000 = $117,000 • If SPY goes down to $120/share, you can buy the shares back at $120,000 and make $10,000 (ignoring commissions, taxes, etc.) Professor Ross Miller • Fall 2006

  9. Part 2: Hedge Construction (Leverage Considerations) • The total “notional amount” of your portfolio cannot exceed $3,000,000 • The notional amount is the sum of the absolute values of each position (see the next slide for an example) Professor Ross Miller • Fall 2006

  10. Notional Amount Limit of $3,000,000:An Example • Suppose that GMCR is worth $40/share at the close on Friday, November 10, 2006 • Your mandatory 10,000 shares will generate a notional amount of $400,000, leaving you with $2,600,000 • If you were to sell 100,000 shares of SBUX short at $38/share, that would generate a notional amount of $3,800,000—more than the $2,600,000 available to you Professor Ross Miller • Fall 2006

  11. How Your Hedges are Evaluated • Lower volatilities earn higher grades • The portfolio volatility is the daily standard deviation of its return over the three-week period (fourteen trading days) • The spreadsheet with last semester’s results will give you a good idea of how this all works • Google was the required holding back then • More capital was necessary because Google was expensive • The exercise lasted only two weeks, not three Professor Ross Miller • Fall 2006

  12. How Hedges are Evaluated (continued) • The 7 lowest volatilities are guaranteed 20 out of 20 points • The next 14 lowest volatilities are guaranteed at least 19 out of 20 points Professor Ross Miller • Fall 2006

  13. E-mail Submission • If you can, use the automated mail entry form in Slide 2 • Those unable to use the automated form can simply e-mail their submission to rmmiller@uamail.albany.edu • The next slide shows what a submission looks like: • The predicted price is next to GMCR • The portfolio selections are given below it Professor Ross Miller • Fall 2006

  14. Sample E-Mail Submission Last Name: Miller GMCR 35.51 QQQQ 700 SPY SBUX WMT 1200 GOOG -700 Professor Ross Miller • Fall 2006

  15. Stock Submission Validation Spreadsheet • As soon after the market closes on Friday, November 10, 2006, an Excel spreadsheet will be made available on WebCT that you can use to validate your submission before e-mailing it • The validation spreadsheets checks: • The capital requirement • The notion capital limit • That only multiples of 100 shares are used Professor Ross Miller • Fall 2006

  16. Stock Prediction and Hedging Project Write-Up • 1,000-word limit is strictly enforced • Up to 3 optional tables or figures of reasonable size are allowed in addition to the 1,000 words • Formatting guidelines • Single-spaced within paragraphs and double-spaced between paragraphs • 12-point standard proportional typeface • Left-hand justified • Margins of at least 1 inch on all sides Professor Ross Miller • Fall 2006

  17. Stock Prediction and Hedging Project Write-Up (continued) • Should be readable with Microsoft Word or Adobe Acrobat • Restrained use of hyperlinks is fine • Do not include macros in your spreadsheets or files in formats other than DOC, PDF, and XLS • The write-up may be either e-mailed or submitted as hard copy in class or both Professor Ross Miller • Fall 2006

  18. Stock Project: Some Last Comments • Grades for write-ups are available in class the week after they are submitted • Predictions/portfolios will be graded by 11PM on December 1 and all grades will be made available through WebCT • You should send a practice e-mail submission to me between Monday, November 6 and Thursday, November 9 and I will reply to it Professor Ross Miller • Fall 2006

  19. The Major Resource for Doing the Project:Fin525Fall2006StockProject.xls • 104 weeks of historical stock data for each stock in the exercise and for 3-month Eurodollars (the “risk-free” rate that the professor often uses • A summary of the data and how the stocks are correlated with one another • A full computation of beta for GMCR using this data • A spreadsheet that shows how different hedges would have worked over the past 104 weeks Professor Ross Miller • Fall 2006

  20. Financial Analysis Is More Art Than Science • There are no “Generally Accepted Financial Principles” • Important (and often arbitrary) choices • Frequency of data (daily, weekly, monthly, quarterly, annual) • When to start and end time periods • How far back in time to go • How many data points to use • You are stuck using the data this is available to you Professor Ross Miller • Fall 2006

  21. The Usefulness of Historical Data • Not very useful for computing the absolute level of returns unless the data goes back through several business cycles • Do not expect GMCR to go up by over 30% in price every year • Doexpect the S&P 500 to generate a total return of about 10% (or about 5% above the risk-free rate) every year • Historical data is more useful for determining volatilities, correlations, and betas (which are a kind of correlation) Professor Ross Miller • Fall 2006

  22. The Standard Deviation of Returns • This is also known as the stock’s volatility; however, there are other methods of measuring volatility • Volatility is a standard measure of the stock’s risk—higher volatility means more risk • Annualizing volatility is somewhat tricky: For weekly returns, we multiply by 52 to annualize Professor Ross Miller • Fall 2006

  23. Some Numbers from the 2 Years from Mid-October 2004 to Mid-October 2006 Professor Ross Miller • Fall 2006

  24. Correlation • A function that connects two parallel series of numbers, such as stock returns (Excel uses CORREL) • Varies from -1 to 1 • 1 is perfectly correlated • 0 is uncorrelated (as if the two series were chosen independently of one another • -1 is perfectly uncorrelated (when one series zigs, the other series zags) Professor Ross Miller • Fall 2006

  25. Correlation Among the Stocks in the Project(From the “Correlations” Worksheet) Professor Ross Miller • Fall 2006

  26. Two Ways to Reduce Portfolio Volatility • Add more assets • Even though most assets are to some degree correlated with one another though common factors, as long as that correlation is less than 1, added assets tends to reduce portfolio volatility • Sell the appropriate assets short as a hedge • Related stocks—for example, those in the same industry Professor Ross Miller • Fall 2006

  27. A Simple Experiment • Go to the Portfolio Volatility What-If worksheet in Fin525Fall2006StockProject.xls spreadsheet • Add 1,000 shares of any single stock to the 10,000 shares of GMCR • Notice that the portfolio volatility (standard deviation) goes down in every case Professor Ross Miller • Fall 2006

  28. Why Does This Work? • While the additional stocks may amplify risk factors they have in common with GMCR, their “specific risks” promote diversity, which lowers portfolio volatility • Because this risk is easy to diversify away, the market does not reward anyone for bearing it • The observation that only holding undiversifiable risk can increase one’s expected returns is at the heart of the Capital Asset Pricing Model (CAPM) Professor Ross Miller • Fall 2006

  29. The Financial World Consists of “Risk Factors” • The standard form of CAPM assumes that there is a single risk factor that is commonly represented by the S&P 500 Index (SPY works just fine as a substitute) • More complex factor models include factors for things like growth vs. value and size (large cap vs. small cap) • GMCR contains substantial risk not captured by any factor Professor Ross Miller • Fall 2006

  30. How Do We Find Common Risk Factors? • Regression analysis and related statistical tools (discriminant analysis, factor analysis, neural networks, etc.) • These tools perform what is known as variance decomposition • The variance of the stock or portfolio that we are interested in is decomposed into two parts • Specific (or idiosyncratic) variance/risk/volatility • Market (or systematic) variance/risk/volatility Professor Ross Miller • Fall 2006

  31. The CAPM Equation (again) Expected return = Risk-free return + Premium for risk Where E(ri) is the expected return for stock irfis the risk-free rate of returniis the beta for stock iE(rM) is the expected market rate of return Professor Ross Miller • Fall 2006

  32. CAPM as a Regression Equation • The independent variable (x in most textbooks) is the excess return on the market index • The dependent variable (y in most textbooks) is the excess return on the asset/portfolio • Beta (the slope of the regression line) is the amount of market risk in the asset/portfolio • Alpha (the intercept of the regression line) is the risk-adjusted performance of the asset/portfolio Professor Ross Miller • Fall 2006

  33. Beta, Beta, Oh Which Beta to Use • Betas are available in abundance on the Internet • For many stocks, different sources have very different value of beta depending on how they compute it • Frequency of data used • Amount of history • “Adjustments” to beta’s value, some valid, some not • How you use beta can effect which one to use • In general, if you know what you are doing, you are better off computing your own betas Professor Ross Miller • Fall 2006

  34. What About the Risk-Free Rate and the Market Premium? • The yield of 3-month T-bills makes a fine risk-free rate • You can find it here • At the close of trading on 11/3/2006 it was 5.07% • A reasonable number for the risk premium, E(rM)-rf is 5.5%, as was used last week in the GE example Professor Ross Miller • Fall 2006

  35. The CAPM Regression in Graphic Form AssetExcessReturns . . . . . . . . . . . . . . . . . . . MarketExcess Returns . . . . . . . . . . . . . . . . . . . . . . . Professor Ross Miller • Fall 2006

  36. My Favorite Equation in BKM (page 320) i can be anything (stock or portfolio) and this equation separates the variance of that stock (or portfolio) into a systematic piece and a specific piece Linear regression or handy functions within Excel can be used to find beta Professor Ross Miller • Fall 2006

  37. Why is This Equation Useful? • The amount of variance captured by the market is known as R2 (often written R-squared) • You can (in a statistical sense) get rid of all systematic risk by selling short the market index in an amount indicated by beta • You are left with the specific risk, which you can then do what you want with (leverage, diversify, etc.) Professor Ross Miller • Fall 2006

  38. How Things Tie Together • When you have a single market factor (BKM refer to it as an “index”), then the R in R2 is the same as the correlation between the portfolio/asset and the “market” (usually written as r, just to confuse you) • You do not have to use any form of regression analysis to get beta in Excel, you can use the CORREL function on excess returns to get r, and then use the formula on the previous slide to solve for beta: Professor Ross Miller • Fall 2006

  39. Regression Analysis in Excel • In Fin525Fall2006StockProject.xls look at the worksheet called “GMCR Regression for CAPM beta” • Excel has built-in function for single variable regression • Excel has an Analysis ToolPak for doing all kinds of regression (single and multiple variable) • One can also “hard-wire” regressions into Excel using the matrix math and summation functions Professor Ross Miller • Fall 2006

  40. The Results of Regressing GMCR Weekly Returns Against SPY Weekly Returns Professor Ross Miller • Fall 2006

  41. The Regression Equation • Here is the regression equation for GMCR relative to SPY: So, alpha = 0.003 (per week) and beta = 0.727 Professor Ross Miller • Fall 2006

  42. Things to Make You Happy • Beta and R2 do not depend on the frequency (daily, weekly, monthly, or whatever) of the data you use • All that matters is that the same time period is used consistently Professor Ross Miller • Fall 2006

  43. Things to Make You Unhappy • Alpha, sigma, and anything involving returns does depend on the frequency of the data used in the regression • To convert a weekly alpha into an annual alpha (approximately), use the same compounding conversion that we used to returns earlier Professor Ross Miller • Fall 2006

  44. One Way to Minimize Portfolio Volatility • Excel’s Analysis ToolPak comes with a Solver tool. • Fin525Fall2006StockProject.xls comes with the Solver already set up to minimize the portfolio volatility over the historical 104-week time period • Your problem is how to adapt this spreadsheet to come up with a forward-looking portfolio • Note that the prices of the stocks are usually quite different now than they were two years ago Professor Ross Miller • Fall 2006

  45. A Final Word to Preserve Your Professor’sSanity • There is no “good” or “bad” level of volatility—just because a certain number could have been achieved looking backward does not mean that it can be achieved going forwards • Certain of my students in the past have developed an unhealthy obsession with certain levels of volatility, please do not repeat their mistake Professor Ross Miller • Fall 2006

  46. For Week 9 • Work on the stock project, giving special attention on the material in Fin525Fall2006StockProject.xls • You can also look at Fin525Spring2006GoogleTrack.xls to see how the second part of the project is graded Professor Ross Miller • Fall 2006

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