Finance 3000

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Finance 3000

  1. 1. Syllabus for Course Finance 3000 Hawaii Pacific University <ul><ul><li>Professor : Dr. Gunter Meissner, Business: 544 0807, Office: FHT 5 th floor #1 </li></ul></ul><ul><ul><li>E-mail: gmeissne@aol.com, Web: www.dersoft.com </li></ul></ul><ul><li>Contents: The course focuses on three main issues: </li></ul><ul><ul><ul><li>a) Basics of Finance </li></ul></ul></ul><ul><ul><ul><li>b) Asset management </li></ul></ul></ul><ul><ul><ul><li>c) Debt Management </li></ul></ul></ul>Goals: a) The student will be familiar with basic financial concepts such as the Time value of money concept,Capital Budgeting (Investment decision process) and Working capital management. b) Asset management: In the field of asset management every student will be a competent fund manager and financial adviser at the end of the semester. The student will learn about the two major investments: Bonds and stocks. The student will know how to apply the latest concepts and strategies of trading.
  2. 2. Syllabus for Course Finance 3000 cont. <ul><ul><li>c)Debt management: </li></ul></ul><ul><ul><li>In the field of debt management the student will be familiar with the classical types of liabilities of a company (stocks, bonds, loans). Also, the student will learn how to use financial innovations such as interest rate and currency swaps, caps, floors, dual-currency bonds and convertibles in order to reduce cost and the various types of risk. </li></ul></ul><ul><li>Literature: 1) Slides on www.dersoft.com/hpu </li></ul><ul><li> 2) Essentials of Corporate Finance, Ross, Westerfield, Jordan </li></ul><ul><li> 3) Trading Financial Derivatives, Gunter Meissner </li></ul><ul><li> 4) Outperform the Dow: Using Options, Futures and Portfolio Strategies to Beat the Market, Gunter Meissner </li></ul><ul><li> 5) Credit Derivatives : Application, Pricing, and Risk Management, </li></ul><ul><li> Gunter Meissner (will be used for Risk Management) </li></ul><ul><li> 6) Dictionary of Finance and Investment Terms, Downes, Goodman </li></ul><ul><ul><ul><li>7) RISK Magazine (available at Library desk) </li></ul></ul></ul>
  3. 3. <ul><li>Grading: Participation/Homework 10% </li></ul><ul><li> Trading game 10% </li></ul><ul><ul><ul><li>Financial paper 20% </li></ul></ul></ul><ul><ul><ul><li>Presentation of Financial Paper 10% </li></ul></ul></ul><ul><ul><ul><li>Mid-Term 25% </li></ul></ul></ul><ul><li> Final 25% </li></ul>F < 60.00 95.00 =< A =< 100 90.00 =< A- < 95.00 Grading Point System 86.66 =< B+ < 90.00 83.33 =< B < 86.66 80.00 =< B- < 83.33 76.66 =< C+ < 80.00 73.33 =< C < 76.66 70.00 =< C- < 73.33 65.00 =< D+ < 70.00 60.00 =< D < 65.00
  4. 4. Syllabus for Course Finance 3000 cont. Financial paper : Each student will write a 10 page paper and present it leading a 30 minute discussion on his/her findings. The paper has to be handed in one week before presentation. APA style, have a Table of Contents, have a Conclusion! The paper has to show your own thought process ! Don’t cite too much, but analyze ! Permanent homework: Read, listen to financial news!! Bring questions to class! The quality of the argument is important, not the argument itself !
  5. 5. Finance as a Science Hard Sciences • Math/Statistics • CS/IT • Nature Sciences (Physics, Chemistry, Astrophysics Gene Technology) These sciences use Math, Logic and Computers to solve problems; there is usually a “right “ or “wrong” Soft Sciences • Marketing • Management • Communication These sciences use Psychology, Sociology and common sense to solve problems; there is usually a “probably better” or “probably worse” Finance • Time Value of Money Concept • Corporate Finance • Stock/Bond Analysis • Portfolio Theory (CAPM) • Derivatives (Futures, Swaps, Options) • Risk Management • Accounting • Behavioral Finance • Investments
  6. 6. Should we learn Finance? Of course!!!! Why should we learn Finance??
  7. 7. Topics for financial paper 1)Analysis of the financial system of a certain country, especially the exchange 2) The American Bond Market: History (Junk Bonds in the 80’s to today), Types of Bonds (Plain vanilla, floater…), Correlation of major Bond markets 3) Bond theory: Rate of return, Duration, Convexity, Bond stripping 4) The American stock market, History (1929 to today), Correlation to other major markets Perspective, where does it go? 5)Stock analyses, P/E ratio, dividend yield, certificate, dividends, buybacks, stock splits, 6) World stock indices, Dow, Nasdaq, S&P, NYSE, Russel 2000, Dax , Nikkei, FTSE, Hang-Seng, Indices of Emerging Markets, (B-share, Bolsa…), Correlation! Perspective 7) World commodity markets, Overview, indices (CRB), recent developments, Outlook - which one’s to buy 8) CAPM, Theory, Implication, Practical relevance today? 9) Monetary policy in the US, Instruments, Usage, Success 10) European Monetary Union, Too early?, too unprepared?
  8. 8. 11) Balance sheet of a company, Structure and Contents, Valuable for a potential investor? How to improve it 12) Hong-Kong July 1, 1997, One country - Two systems, Status quo analyses - Outlook 13)Economic indicators: NAPM, CPI, PPI, initial jobless claims, employment cost index (ECI), non-farm payrolls, unemployment, GDP, consumer confidence, beige book 14) Mergermania – A threat to the capitalistic system? 15) Swaps – Theory and Practice 16)Convertibles – Types and Pricing 17) Dividend Policy – Effects on the stock price 18) The World bank and the IMF – Structure and Goals 19) Insider Trading 20) Technical Analysis – Trick or Treat 21) Capital gains tax in the USA 22) Mortgage backed securities in the USA Topics for financial paper cont.
  9. 9. Topics for financial paper cont. 23) Mutual funds – Buy the one that has performed best? 25) Futures - Practical application and pricing 26) Options - Practical application and pricing 27) Programming the Black-Scholes model or binomial option pricing model 28) US Retirement Tools: IRA’s and 401K’s 29) The Asian financial crises part 2 – Impact on the US and world economy with a time lag? 30) Business cycles – Obsolete? 31) The Japanese economy: solutions to a 10-year recession 32) The Hawaiian economy: solutions to a 10-year ailing economy 33) Forecasting methodologies for stocks; an overview 34) Chapter 11 bankruptcy protection 35) Working capital management 36) Mergers and Aquisitions
  10. 10. Topics for financial paper cont. 38) Finance and Neural Networks 39) Finance and Fuzzy Logic 40) Finance and Chaos Theory 41) Derivatives: Curse or Blessing for Society ? 42) Internet IPO’s: A sure bet for professionals ? 43) Has the Fed done a good job lately? 44) Technical Analysis: An empirical test 37) Foreclosures, A sure bet? 45) US Retirement Plans (IRA’s and 401 K’s) 46) Do Stocks outperform Bonds in the long run? 47) Is the US sliding into a recession? 48) Day-trading – Only for Professionals? 49) E-Banking and E-Trading – Pros and Cons 50) Can international market correlations be exploited by traders? 51) Do Intra-day trends exist, that can be exploited by traders? 52) Collateralized Debt Obligations (CDO’s) – Pros and Cons
  11. 11. 53) How to write a Business Plan – Write a detailed plan for your own company 54) Buy outs – Types, Pros Cons, Success rates Topics for financial paper cont. 55) Are Bond Prices and Stock Prices positively or negatively correlated? 61) Malaysia’s Lesson from the Asian Financial Crisis: Should we ignore help from the IMF? 56) Are Stock Prices and Volatility negatively correlated? 57) Does an Increase in Volatility indicate an Market Reversal? 58) Does the Internet reduce company's cost of capital? 60) Venture Capital: A Good Investment? 59) Will the Internet make Brokers obsolete? 67) Choose your own topic 62) Bush’s Anti Missile Shield: Technologically and financially ridiculous? 63) Credit Derivatives: What are they, what are they good for? 64) Where is the value in Behavioral Finance? 65) Investing in Hedge Funds – Too risky? 66) The Tobin tax – Can it decrease currency speculation and volatility?
  12. 12. Topics for financial paper cont. 68) The recent accounting scandals – What happened, what has to be done? 71) The Value at Risk concept 72) Basel II – The BIS proposal to banking supervision 73) Corporate Risk Management: Market Risk, Credit Risk, Operational Risk 75) Credit Risk Management 76) A survey of credit risk vendors 78) Pricing Credit Derivatives (Chapter 5 in Meissner’s book) 79) Investing in ETFs – A good idea? What are the costs? 80) The Daimler-Chrysler Merger - A success story? The $275 million lawsuit 77) Operational Risk – The next generation 81) Dell’s direct sales strategy – The model of the future? 69) The Enron – Arthur Anderson saga – What went wrong? Lessons to learn 70) The WorldCom accounting scandal 74) Credit Derivatives – An Overview
  13. 13. Topics for financial paper cont. 82) CEO and executive management compensation - Just a disgrace or harmful for shareholder value? Should there be a cap? 83) Is the stock market crash over? Prediction for the future! 84) The US credit score - How is it derived, Is there to much emphasis on it? 85) The target Fed Funds rate – How does it exactly work? 86) The US bankruptcy law – Too lenient? 87) The Sarbanes-Oxley Compliance Solution – Pros and Cons 88) The US Double Deficit – A Danger for International Financial Markets? 89) Should China float its Yuan? 90) Hedge Funds – What are their main strategies? Should they be regulated? 91) Market Timing – How does it exactly work? Should it be restricted? 92) Reits – Invest now? 93) The US corporate tax law – Favoring the big? 94) Martha Stuart – Wrongfully Convicted?
  14. 14. Topics for financial paper cont. 95) Bondstripping – How does it work? 96) The weak dollar – Curse or Blessing for the US economy? 97) Nanotechnology stocks – A good investment? 98) The EU expansion to 25 states – Chaos in the making? 99) Robert Engle’s 2003 Nobel-Prize rewarded GARCH theory – Justified? 100) Volatility on Volatility – A good trading indicator? 101) “Mexifornia” - Should illegal immigrants receive the green card? 102) Microsoft – A falling giant? 103) A Model for a Fair Exchange Rate 104) A Fundamental Analysis Model to forecast stock prices 105) Fannie Mae and Freddy Mac – Too much profit, too little benefit for mortgagors? Should they be privatized? 106) Should stock options be expensed? 107) Kmart – Sears, Another Failed Merger? 108) Hedgestreet – Derivatives for the small investor. A useful tool?
  15. 15. Topics for financial paper cont. 109) Stock market forecast for the next year 110) Fundamental and Technical Analysis of the Hawaii’s “Big Four” 111) High-Tech in Hawaii – An Analysis of Kamakura Corporation www.kamakuraco.com 112) An Analysis and Improvement of Kamakura’s ‘Technical Report’ 113) IBM selling its PC division to Lenovo – A good idea? 114) The Shareholder Value Concept – Outdated, Too shortsighted? 115) Is Management Compensation in the US too high? – Should there be a Cap? 116) Hyundai –Currently number 7, soon number 1? 117) Walmart, 2% of US GDP – Success by employee discrimination? 118) The Boeing –Airbus Battle, No chance for Boeing? 119) The IPO process – Unfair? Corrupt? 120) How are Stock prices and Bond prices correlated? An empirical Study 121) A Model for a Fair Stock Price – Combining fundamental and technical analysis 122) Are we in the middle of a housing bubble, which will pop soon?
  16. 16. Topics for financial paper cont. Choose your own topic, preferably finance related!! 123) Investible Hedge Fund Indexes – Where do we stand? 124) GM and Ford – What to do to fight Asia and Europe? 125) Do markets bottom and top on high volatility? 126) Private Equity Firms – Course or Blessing for the Economy? 127) Islamic Law (Shari’ah) – Opportunities and Challenges 128) Can we exploit the downturn during the earnings warning season? 129) Should GM merge with Nissan-Renault? 130) Ethics in Finance – Is there any?
  17. 17. Jobs Jobs Jobs Generally: Don’t study on easy street!!! MBA FINANCE CFP Treasury Department of any Company (CFO, CRO, FRM) Banking (Trader, Marketer, Manager, Sales, CFA) Commercial Bank Investment Bank / Brokerage House
  18. 18. To be Successful on the Job : Intelligence/ Knowledge Experience Emotional Intelligence • Self-awareness (realize how you come across) • Self-regulation (suspend a decision, analyze first) • Sensitivity (cultural; sense emotional problems) • Motivation / Ambition (work smart and work hard) • Social Skills (Communication, Team-skill, Persuasiveness) Stay single !!!
  19. 19. Who manages Money??? Individuals Companies Countries Economic Unions EU, Nafta, Asean Debt Assets Reasons: Reasons: Recorded on a
  20. 20. Conclusion: Bear Market Bull Market Bear Market Bull Market Bear Great Depression Post War Growth 1973 and 1978 OPEC Crises Black Monday 1987 Start of new Bear Market, March 2000
  21. 21. Conclusion: The Dow from 1928 to today
  22. 22. Comparing the Major Indices Conclusion:
  23. 23. Trading in the New Millenium Criteria of good trader What we trade What we do When we trade How trades are executed How we trade <ul><li>Fundamental analysis </li></ul><ul><li>Technical analyses </li></ul><ul><li>Intuition </li></ul>(Book chapter 2) Where we trade <ul><li>Seasons </li></ul>Broker versus Trader
  24. 24. Broker versus Trader What is a broker? A broker is a person who invests your money until is gone (Woody Allan) A broker is an Trader at Bank A (Buyer) Trader at Bank B (Seller) Broker There are interbank brokers: Private Investor A Exchange Broker There are “private investor” brokers Who takes price risk??
  25. 27. Investment Products Mutual Funds are About of all mutual fund managers underperform their benchmark!!! Why????
  26. 28. General Reason: Specific Reasons:
  27. 29. Investment Products What about Hedge Fund or Fund of Funds performance?? Difficult to know.. Performance results suffer from ‘survivorship bias’ and ‘reporting bias’ (also called backfill bias)
  28. 30. Investment Products Considering the mutual fund performance disaster, what shall we do ? Invest passively in as QQQQ, SPY, DIA, etc or (Holding company depositary receipts) as BBH (Biotech), Internet (HHH) or UTH (Utilities) etc
  29. 31. Where we trade <ul><li>on an exchange </li></ul><ul><li>OTC (over the counter) </li></ul>(Book p.10,11)
  30. 32. How trades are executed <ul><li>Electronically </li></ul><ul><li>Open outcry </li></ul>(Book p.13,14)
  31. 33. On-line Trading First step: To trade: Execution of the trade: The broker checks the order (in terms of size and price) and puts it into the pit or computerized trading system The execution of the trade is displayed on your computer screen
  32. 34. On-line Trading, cont. Advantages of On-line trading: Disadvantages of On-line trading:
  33. 35. Open Outcry Seat Exchange Hawaii Pit Book p.13 Pit Pit
  34. 36. Computerized Trading (as the NASDAQ) Bid Size Offer Size $ 88 3000 $ 90 200 $ 91 100 $ 99 300 $ 96 250 $ 94 50 AMZN Book p.13
  35. 37. Computerized Trading (as the NASDAQ) Bid Size Offer Size $ 88 3000 $ 90 200 $ 91 100 $ 99 300 $ 96 250 $ 94 50 Book p.13 AMZN
  36. 38. Computerized Trading (as the NASDAQ) “ Level 2” trading allows an investor to see an ECN (Electronic Communication Network) screen
  37. 39. What we do <ul><li>Speculate </li></ul><ul><li>Arbitrage </li></ul><ul><li>Hedge </li></ul>(Book p.5,6,9)
  38. 40. More on Speculation Difference Gambling - Speculation - Investing The chances of winning when gambling are The chances of winning when speculating are Example: Exception: In contrary to speculation, investing is
  39. 41. More on Speculation These days, speculation is done ON MARGIN This means Example: An investor wants to buy Yahoo, which trades at $100. He buys it on margin, which is 40%, and only pays The same logic applies to short selling. Short selling is Warning: Only speculate with money you can afford to lose
  40. 42. More on Arbitrage Example: Two traders quote the following prices for 1oz of Gold London Bid Offer Tokyo Bid Offer Is arbitrage possible? The term Arbitrage is often deliberately misused as in “Risk-Arbitrage = Take-over Arbitrage” or “ Interest rate Arbitrage = Yield curve Arbitrage”
  41. 43. Criteria of a good trader (Book p.15,16)
  42. 44. The Philosophy of Stock Price Forecasting No Forecast Possible : The markets are “efficient”= All information about a stock is incorporated in the current stock price. This is equivalent to the “ Random Walk Hypothesis”= Forecast Possible: • Fundamental Analysis • Technical Analysis • Seasonalities • Times Series Analysis • Neural Networks • Chaos Theory • Econometric Models (“Outperform the Dow” Book chapter 2)
  43. 45. How we trade trading are decisions based on <ul><li>Fundamental analysis </li></ul><ul><li>Technical analyses </li></ul><ul><li>Intuition </li></ul>(Book p.16,17) <ul><li>Seasons </li></ul>
  44. 46. Fundamental analysis Fundamental analysis is trying to forecast the movement of a stock price based on political, economical, sector-specific and company-specific data. <ul><li>Political stability is essential </li></ul><ul><li>Macro-economic data are to be analyzed </li></ul><ul><li>Sector is of importance </li></ul><ul><li>Company specific data are crucial </li></ul>(Book p.16,17)
  45. 47. Financial Ratios An Overview of Popular Financial Ratios 2) Liquidity Ratios Current Ratio = Total Current Assets / Total Current Liabilities Net Working Capital = Total Current Assets - Total Current Liabilities Cash Flow = (Cash +Marketable Securities) / Total Current Liabilities 1) Earnings Ratios PE Ratio = Market Price / Earnings per Share (will be discussed) Earnings per Share = Earnings / Number of Outstanding Stock (will be discussed) Dividend Yield = (Annual) Paid Dividend / Current Market Price (will be discussed) PEG Ratio = Market Price / Earnings per Share / Growth Rate (will be discussed)
  46. 48. Financial Ratios An Overview of Popular Financial Ratios 3) Profitability Ratios Return On Equity = Earnings / Net Worth of Company 1) (will be discussed) Operating Profit Margin = Operating Income / Net Sales Net Profit Margin = Net Income / Net Sales Book Value = Net worth of company 1) / Number of outstanding stock 4) Capitalization Ratios Debt-to-Equity Ratio (also called leverage) = (Bonds + Preferred Stock) / Net Worth of Company 1) 1) The Net Worth of a company = Shareholders Equity = Total Current Assets – Total Current Liabilities
  47. 49. Earnings ratios One of the most important ratios is the price-earnings ratio, PE The PE is the price of the stock divided by the earnings per share of the company. The earnings in the PE ratio can be trailing, current or expected. If the company is healthy and earnings are growing, the trailing PE ratio is higher than the current PE ratio, which is again higher than the expected (also called forward) PE ratio. The PE, which is published in newspapers and on screens, is usually the expected PE. As an example, if the stock of a company trades at $100 and next years expected earnings per share is $5, then the expected PE ratio is Result:
  48. 50. A fairly new ratio is the Price Earnings Growth ratio, PEG It is the PE ratio divided by next years expected growth rate: Example: The price of IBM is $100, the earnings per share is $2, And the next years expected growth rate is 50 (%). What is the PEG ratio? PEG ratios below 1 are considered fairly cheap, PEG’s of over 1 are considered fairly expensive Earnings ratios
  49. 51. Of importance is also the earnings per share ratio. It shows the allocation of the earnings to each share. For example, if the earnings last year was $10 million and the number of outstanding stock is 10 million shares, the earnings per share is This number is calculated after deducting taxes and dividends from the earnings. Earnings ratios
  50. 52. Closely related to the earnings per share is the return on equity The return of equity shows how profitable each share is. Return on equity is calculated as the return (= earnings) divided by the common stock at par (the original issue price of the stock) + capital surplus (difference between the current stock price and the par stock price) + retained earnings. For example, if the yearly return of a company is $1,000,000, and the sum of common stock at par + capital surplus + retained earnings is $10,000,000, the return on equity is Earnings/Profitability ratios
  51. 53. Another important ratio is the dividend yield It is the dividend divided by the current price of the stock. For example, if the dividend per year is $2 and the price of the stock is $100, then the dividend yield is High tech stocks e.g. Yahoo often do not pay a dividend. Earnings ratios
  52. 54. Technical analysis Technical analysis is trying to forecast the movement of a stock price from the pattern it has moved in the past. The philosophy of technical analysis <ul><li>Chart patterns reflect the fundamental data in an economy or a company </li></ul><ul><li>The markets move in trends </li></ul><ul><li>History repeats itself </li></ul>(Book p.17,18)
  53. 55. Theories of Technical Analysis a) Simple chart patterns Trend, support resistance, double tops and bottoms, triple tops bottoms, head and shoulders, flag b) Moving average convergence-divergence (MACD) c) Fibonacci Ratios and Elliot Wave principle d) Relative strength index (RSI) (Book p.17-33)
  54. 56. a) Simple chart patterns The trend is your friend An upward trend is a movement with consecutive higher lows and consecutive higher highs: A downward trend is a movement with consecutive lower lows and consecutive lower highs. A sideward trend is a movement which does not exceed a certain high and which does not fall below a certain low. (Book p.18)
  55. 57. a) Simple chart patterns cont. Support - Resistance A support level is a level, where the market is expected to from dropping, and possibly reverse to the upside. If however the support level is broken to the downside, a further significant is to be expected. A resistance level is a level, where the market is expected to from rising, and possibly reverse to the downside. If however the resistance is broken to the upside, a further significant is to be expected. (Book p.22-25)
  56. 58. Support - Resistance cont. Breaking of a resistance (dashed line) Resistance and support as the previous low and high (Book p.22-23)
  57. 59. Support - Resistance cont. A support line, created by connecting previous lows False breakout (Book p.23-25)
  58. 60. a) Simple chart patterns cont. An ideal double top formation Triple top formation (Book p.25-26)
  59. 61. a) Simple chart patterns cont. <ul><ul><ul><li>Ideal head and shoulders formation </li></ul></ul></ul>Flag formation with an upward breakout (Book p.27-28)
  60. 62. b) Moving average convergence-divergence (MACD) The MACD uses three exponentially smoothed averages to identify, like the concepts a) through c), a trend reversal or the continuation of a trend. The first, called the MACD1 indicator, is the difference between two exponential averages, usually a 26-day and a 12-day average. The second, called Signal indicator , is the 9-day moving average of the MACD1 indicator. The MACD indicator reduces to two indicators: The term convergence and divergence refers to a narrowing respectively widening of the MACD1 and the Signal indicator. A buy signal is given, when the more volatile average, the MACD1 indicator, crosses the less volatile average, the Signal indicator, from beneath. If the MACD1 line crosses the Signal line from above, a sell signal is given. (Book p.2-29)
  61. 63. Moving average convergence - divergence (MACD) (Book p.28,29)
  62. 64. b) Moving average convergence-divergence (MACD) Example: What is the EMA t for EMA t-1 = 10 and K = 0.2 (9 periods) P t = 12 EMA t = P t = 8 EMA t = P t = 4 EMA t = So? Calculation:
  63. 65. Fibonacci Ratios and Elliot Wave Principle In the 13th century the mathematician Fibonacci discovered a number series with some quite astonishing results. Adding two numbers to derive a result, then taking the last added number and adding it to the result, gives 1+1=2; 1+2=3; 2+3=5; 3+5=8 and so on, which gives the number series Dividing consecutive numbers in this series by one another: Dividing a number by the one following two places behind: Technical analysts consider these numbers crucial. (Book p.30)
  64. 66. Fibonacci Ratios and Elliot Wave Principle cont. In its most basic form, the principle says, that markets move in a repetitive cycle of five waves to the upside, followed by three waves to the downside. (Book p.30,31) Elliot set certain rules for his principle, which are necessary for a certain pattern to qualify as an Elliot wave: In 1946 the retired accountant Ralph Elliot wrote his book &quot;Nature's law - The Secret of the Universe&quot;. In this book he stated the “Elliot Wave Principle”.
  65. 67. Fibonacci Ratios and Elliot Wave Principle cont. 1) correction wave 2 can never retrace more than 100% of wave 1 2) wave 3 can never be the shortest wave of waves 1, 3, or 5 3) the low of wave 4 is higher than the high of wave 1 Mandatory Elliot Wave rules: (Book p.30,31)
  66. 68. Voluntary Elliot Wave rules based on Fibonacci numbers: <ul><li>The minimum length of wave 3 is the length of wave 1 plus 61.8% of wave 1 </li></ul><ul><li>Wave 4 should reverse to the upside, after having retraced 38.2% of wave 3 </li></ul>• Highs and lows of the Elliot wave can be expected on day 13, 21, 34, 55, and 89 Fibonacci Ratios and Elliot Wave Principle cont. The disadvantage of the Elliot Wave principle is the (Book p.30,31)
  67. 69. Relative strength index (RSI) The RSI was developed by Welles Wilder in 1978 It is based on the assumption, that after a strong rally the market is overbought and will enter into a downward correction phase. Similarly, after a strong fall, the market is assumed to be oversold and it will enter into an upward correction phase. The RSI tries to measure the degree of overboughtness respectively oversoldness and tries to identify, when the correction phase is likely to begin. The RSI does not work well in markets that have a very long and strong upward or downward trend. (Book p.30,31)
  68. 70. Relative strength index (RSI) cont. The RSI is calculated as (2.2) RSI = 100 - (100 /( 1 + (Avg Up/Avg Dn))) Avg Up=Sum of all changes for advancing periods divided by total of periods Avg Dn = Sum of all changes for declining periods divided by total of periods Given these data, Avg Up = Avg Dn = According to equation (2.2) RSI = Due to equation (2.2), the RSI can take values between 0 and 100 An example: (Book p.32)
  69. 71. Relative strength index (RSI) cont. 40-day price movement of a stock Resulting 10-day RSI An RSI of over 70 indicates an overbought market; an RSI of below 30 indicates an oversold market. Result:
  70. 72. Critical appraisal of technical analysis Technical analysis is not voodoo, Does technical analysis implicitly include fundamental data? Not much empirical evidence! Main justification of technical analysis: (Book p.33) or is it?
  71. 73. Trading according to Seasons Since 1950, 86.97% of the Dow gain occurred in the month from November to April !!!  Sell in May and go away (Data since 1968)
  72. 74. Trading according to Seasons cont. Table of monthly graph
  73. 75. Trading according to Seasons cont.
  74. 76. Trading according to Seasons cont. From the former table we can see that in 8 out of 12 month, the increase in the first two weeks of the month was higher than in the second half of the month. The increase in week 3 and 4 was only higher than the increase in week 1 and 2 in If we look at the absolute changes and sum up all the increases in the first two weeks of each month, we get 73.68%. Also, 12.53% + 13.94% = 26.47% of the Dow increase occurred in the
  75. 77. Trading according to Seasons cont. What’s the “best” trading day of the week?? Results do depend on the time frame of data selection
  76. 78. Trading according to Seasons cont. Result:
  77. 79. Summary of Investing <ul><li>Diversify! Diversify! Diversify! CAPM shows that </li></ul><ul><li>Diversification increases the ratio! </li></ul><ul><li>Mutual Funds are outdated! underperform </li></ul><ul><li>their benchmark! </li></ul><ul><li>Hence, invest ‘passively’ in </li></ul><ul><li>Use seasonal patterns if you invest shorter term </li></ul><ul><li>Use the business cycles! </li></ul><ul><li>What about Hedge Funds? </li></ul>
  78. 80. Summary of Investing cont. <ul><li>Growth stocks or value stocks ? Buy growth stocks, </li></ul><ul><li>small caps and junk bonds in an </li></ul> Trend is your friend ! Enjoy the ride; don’t try to predict a trend-reversal  Realize once a while!  Is patience is a virtue ?;  Invest, don’t speculate ; If you do speculate, watch the market and only speculate with the money you can afford to  Buy beaten up-high tech stocks lose admit your are wrong!
  79. 81. What should we base our trading decision on ?? Fundamental analysis ? Technical analysis ? Seasons ? Intuition ?
  80. 82. 2) Bonds versus Stocks Bonds Definition: A bond is a promissory note. The bond issuer promises to pay a specific sum of cash flows to the bond holder .
  81. 83. Types of bonds: <ul><li>Debentures (unsecured debt obligation, i.e. savings account) </li></ul><ul><li>Short term bonds: Commercial paper (2 to 270 days, issued </li></ul><ul><li>by top banks and companies), Certificates of deposit (CD’s) </li></ul><ul><li>(several days to years, issued by banks) </li></ul><ul><li>Mortgage bonds (secured by real estate) </li></ul><ul><li>Zero bonds (pay no coupon) </li></ul>Bonds cont. <ul><li>Treasuries: </li></ul>Treasury bills: Maturity up to 1 year, auctions of 91 and 270 day treasury bills take place weekly, minimum $5,000 Treasury notes: Maturity 1 year to 10 years, minimum $1,000 Treasury bonds: Maturity 10 years to 30 years, minimum $1,000 Treasury Bonds are local and state but not federal tax exempt • Savings Bonds: Issued by US Government for small investors, Denomination from $50, usually local, state, and federal tax exempt but lower yield than Treasuries
  82. 84. Bonds cont. Types of bonds cont. <ul><ul><ul><li>Eurobonds (An American company issues a bond outside the US and pays dollar interest and dollar principal) </li></ul></ul></ul>(Australian company, which invests in Japan and believes the Yen will devalue, issues a bond in yen, pays yen coupon and returns Australian Dollar at maturity (at maturity the issuer exchanges yen into Austral. $ at a fixed exchange rate, which is guaranteed by the underwriter)) <ul><li>Dual currency bonds </li></ul><ul><li>Floating rate bonds </li></ul>• Inflation linked bonds • Credit linked bonds <ul><li>Junk bonds (credit rating of issuer is bad) </li></ul>
  83. 85. Main differences between bonds and stocks 1) Bond prices return to their issue price (Fish-effect) Stock prices are assumed normally or log-normally distributed t T P (Book p.203)
  84. 86. Main differences between bonds and stocks cont. t T P “ Distribution function” of a bond and a stock (Book p.203)
  85. 87. Main differences between bonds and stocks cont. Normal versus log-normal distribution of a stock Result: (Book p.197)
  86. 88. Main differences between bonds and stocks cont. <ul><ul><ul><li>2) </li></ul></ul></ul>3) 4)
  87. 89. Main differences between bonds and stocks cont. Main criteria of stocks <ul><li>Preferred stock </li></ul><ul><li>Convertible </li></ul><ul><li>IPO’s (going public) </li></ul><ul><li>Buy backs </li></ul><ul><li>Stock splits </li></ul><ul><li>Mergers / Spin-offs </li></ul><ul><li>Ratios: P/E ratio, earnings per share, return on equity, dividend yield </li></ul><ul><li>Beta </li></ul>
  88. 90. Bond pricing The price of a bond B is the sum of all discounted future cash flows. The cash flows of a 5 year coupon bond with a principal amount of $100 and a 3% annual coupon looks as follows: 1y 2y 3y 4y 5y B?
  89. 91. Bond pricing cont. Mathematically, the discounted sum of all future cash flows is where B : Bond price n : number of coupon payments c t : coupon at time t (known interest rate payments, paid every 6 months in the US) y : yield to maturity PA : principal amount Treating the last coupon and tbe PA as one coupon c n , we get (Book p.105,106) (4.24)
  90. 92. Bond pricing cont. Example 1: What is the price of 4 year 5% annual coupon bond with a 3% yield and a principal amount of 100? Example 2: What is the price of 4 year 5%-coupon bond with a 5% yield and a principal amount of 100? (Book p.105,106)
  91. 93. Bond pricing cont. What is the Yield??? <ul><li>The yield (also called yield to maturity) is the of the bond </li></ul><ul><li>expressed as an annual percentage, if the bond is bought at the current </li></ul><ul><li>market price and held to maturity, assuming no default risk </li></ul>c) The yield curve (yield with respect to time) expresses in an economy for AAA rated bonds The higher the yield, the better to buy the bond???? b) The yield is the used in the discount factor df = 1 / (1+y) t to derive the present value (the price of the bond). [FV x df = PV]
  92. 94. Bond pricing cont. Dirty versus Clean Price The price found on screens and in newspapers usually the Clean Price If an investor buys a bond, he has to pay the clean price Plus the ACCRUED INTEREST The accrued interest is the interest that is calculated daily and has accumulated since the last coupon date The price that is actually paid when buying the bond is therefore the Dirty Price = Clean Price + Accrued Interest (Book p.291)
  93. 95. Bond pricing cont. Example: A bond trades at 103.00, has a coupon of 6% and the last coupon date was 50 days ago. What does an investor have to pay when he buys the bond? He has to pay the dirty price, which is the clean price + accrued interest: Naturally, when you sell a bond, you sell it at the Dirty price (Book p.291)
  94. 96. Stocks Pricing Bonds are priced by discounting all the (known) future cash flows back to today. The same logic can be applied for stocks. However, the dividend of a stock is unknown, so we have to make an assumption about future dividends. Usually companies let their dividends grow with a constant rate g, for example 3%. Also, since stocks do not have a maturity date, we have to use infinite time periods. This leads us to the following equation for the price of a stock:
  95. 97. Stocks Pricing with the Constant-Growth Dividend Model S = Stock price, D 0 = last paid Dividend, g = dividend growth rate, i = discount rate (also called required return of the stock) Example: A company's last paid dividend was $2. The growth rate of the dividend is expected to be 3%. The discount rate is 6%. What is the stock price using 5 future periods?
  96. 98. Stocks Pricing with the Constant-Growth Dividend Model Critical Appraisal of the Constant Growth Dividend Model The model shows the inverse relationship between interest rates and Stock prices! The model shows ONE factor that influences the price of a stock. Other factors are expected revenue and earnings growth rate, quality of management, market product, competitors, economy, sector, psychology, legal battles, etc. Many high-tech companies do not pay a dividend (such as Microsoft or Yahoo). In this case the constant dividend growth model is of no value
  97. 99. Dividend Policy As mentioned earlier, companies often have a long-term moderate growth rate of their dividend. This policy is supposed to give confidence in the long term prospective of the company. The share price of companies that have to reduce their dividends, usually suffer a severe decline in the share price. (Emery p.476f)
  98. 100. Dividend Policy The timeline of dividends Dividend declaration date (Amount and Ex-dividend date are announced) Ex-dividend date (Stock price drops by the dividend amount) Holder of Record date (List of share- holders is established) Dividend payment date An investor has to own the stock BEFORE the ex-dividend date in order to receive the dividend. That is why the stock drops at the dividend date.
  99. 101. Dividend Policy Dividends Irrelevance Theorem There is a school of thought lead by Miller and Modigliani , that the payment of dividends is irrelevant for a company and that shareholders should be indifferent to dividends. The theorem says that the payment of dividends will equal the loss of price appreciation of a stock. Thus, the share holder is indifferent to receiving dividends or the stock price increase. This theorem is correct if the following assumptions hold: • No transaction costs when selling stocks (Otherwise dividends would be preferable) or paying dividends (otherwise stock price increases are preferred. • Same tax treatment of dividends and share price increases • The companies management is uninfluenced by dividends and share price increases Do theses assumptions hold in reality???
  100. 102. Dividend Policy In most countries, like the US, dividends are treated less favorable from a tax perspective than stock price increases. One could argue that there is “double taxation” of dividends due to the fact that they are taxed on a corporate level as income, and as income for the individual investor. That is why some countries, like Germany, have a lower tax rate on dividends than on retained earnings of a company. If dividends are taxed higher than stock price increases, it follows, that it is in the companies and share holders interest that no dividends should be paid!!
  101. 103. Dividend Policy It can be argued that some investors simply like receiving dividends (clientele effect) This would make a company that pays dividends a popular choice resulting in an increasing stock price. However, these days investors behave fairly rational, and the clientele effect should be rater small. Conclusion of dividend policy:
  102. 104. The Time Value of Money One dollar today is worth more than one dollar tomorrow. WHY???
  103. 105. The Time Value of Money cont. How much less is a dollar worth in the future? a) Without interest on interest: $100 now are worth in three years with 10% pa: FV = PV (1 + i n) FV : Future value PV : Present value i : interest rate pa n : time in years Book p. 73
  104. 106. The Time Value of Money cont. b) with discrete interest on interest b1) annual interest on interest FV = PV (1+i) n 100 1y 2y 3y
  105. 107. The Time Value of Money cont. b3) monthly interest on interest FV = PV (1+i/m) nm with m = 12 b2) semiannual interest on interest FV = PV (1+i/m) nm with m = 2 (Book p. 74)
  106. 108. The Time Value of Money cont. c) continuously compounded interest on interest With m  infinity, FV = PV (1+i/m) nm becomes e = Eulers number = 2.7182... (Book p. 74)
  107. 109. The Time Value of Money - Application GROI stand for Guaranteed return on investment How does that work??? The investor invests $10,000 and is guaranteed at least $10,000 at maturity The arranger takes a certain amount, invests it at the risk free rate and takes the rest to invest in a risky trade. Example: A Groi has an original investment of $10,000, 7 year maturity, annual interest rate 6%. How much does the arranger invest in the risk-free asset to guarantee the payback of $10,000? = (The $ grows to in 7 years, since The rest,
  108. 110. $6,651 Invested in risk-free asset t0 T grows to $3,349 invested in risky asset may grow to The Groi graphically
  109. 111. Converting Interest Rates a1) To convert a sub-annual rate into an annual rate, we use (3.7) Eff = ((Nom / m) + 1) m -1 where Eff : annual interest rate (effective rate) Nom : sub-annual interest rate (nominal rate) m : interest rate payment frequency per year Thus, a semiannual rate of 9.84% equals an annual rate of A quarterly rate of 9.84% equals an annual rate of Book p.75
  110. 112. Converting Interest Rates cont. a2) Converting an annual (effective) rate into a sub-annual (nominal) rate, so solving equation (3.7) for Nom, gives So an annual (effective) rate of 10.08% results in an semiannual (nominal) rate of An annual (effective) rate of 0.1021 results in a quarterly (nominal) rate of Book p. 75
  111. 113. Converting Interest Rates cont. b1)The conversion of an annual or sub-annual, also called discrete rate, into a continuously compounded rate, is done by equation (3.9) ln (1 + Dis / m ) * m = cc where ln : natural logarithm Dis : discrete interest rate (annual, sub-annual, etc.) m : interest rate payment frequency per year cc : continuously compounded interest rate So an annual (discrete or effective) rate of 10.08% results in a continuously compounded rate of A semiannual (discrete) rate of 9.84% results in a continuously compounded rate of (Book p. 75,76)
  112. 114. Converting Interest Rates cont. b2) Converting a continuously compounded rate into a discrete rate, so solving (3.9) for Dis, gives (3.10) Dis = (e cc/m - 1) * m where Dis, cc, and m are defined as in equation (3.9) A continuously compounded rate of 10% is equal to an annual rate of A continuously compounded rate of 9.61% is equal to a semiannual rate of (Book p. 75,76)
  113. 115. What is the APR (Annual Percentage Rate)? An APR is a nominal interest rate!, thus it ignores interest on interest. Example 1: The APR is calculated as the sub-annual rate (Nom) times the number payments in a year (m). APR = Nom * m An entrepreneur pays 2% interest every 3 months. What is the APR? Thus, interest on interest is ignored
  114. 116. Example 2: A car dealer tells you the APR, which has to be paid twice a year is 4%. What do you have to pay and when? Thus, interest on interest is ignored. What is the APR (Annual Percentage Rate) cont.
  115. 117. What is the APR (Annual Percentage Rate) cont. Example 2 cont: The car dealer tells you to pay 2% every 6 months, thus the nominal interest rate is 4%. What is the effective (= annual and “real”, ) interest rate? We use equation: Therefore the effective (=annual) interest rate is Result:
  116. 118. More on Corporate Finance <ul><li>Capital Budgeting </li></ul><ul><li>Dividend policy (already discussed) </li></ul><ul><li>Working Capital Management </li></ul><ul><li>Budgeting and financial forecasting </li></ul>
  117. 119. Capital Budgeting Capital budgeting is another term for the Investment decision process When should a company do a certain investment??? Also, an investment can be done because of strategic reasons: <ul><li>Increase market share </li></ul><ul><li>Improve customer relations </li></ul><ul><li>Hurt a competitor </li></ul>(Emery p.298f)
  118. 120. Criteria for the Investment Decision Net present value criteria: Do the investment if the net present value of all future cash flows is >0. (How can we tell, if a an investment will be good or bad) NPV : net present value CF t :outgoing and incoming cash flow at time t (after tax) k : discount rate (=required rate of return) IO : Initial cash outlay
  119. 121. Net present value criteria cont. Example: Volkswagen is considering investing in a new 3-Liter car. The company expects an initial investment in R&D (research and development) of $10,000,000. It expects negative outflows in year 1 and 2 of $2,000,000 and $1,000,000 resp.. It expects profits in year 3 and 4 of $4,000,000 and $5,000,000 resp. and $8,000,000 for the years 5. The discount factor is 4%. Should Volkswagen build the 3-Liter car? NPV = Result:
  120. 122. Capital Budgeting cont. Closely related to the NPV criteria is the Profitability Index or Benefit/Cost ratio According to the profitability index, should Volkswagen do the investment? PI= Result:
  121. 123. Comparing the NPV criteria and the PI Index If the NPV is positive, it follows that the PI will be Thus, the NPV criteria and the PI index are basically identical. Advantage of NPV and PI: Disadvantage of NPV and PI:
  122. 124. Capital Budgeting cont. Internal rate of return (IRR) The internal rate of return measures the return or profit of the investment. It is equivalent to the yield of a bond!! Mathematically, the IRR is the discount rate, that guarantees the future cash flows of the investment (CF) equal the initial outflow (IO):
  123. 125. Features of the Internal rate of return (IRR) Unfortunately, we can’t solve the equation easily for IRR (we have to use search procedures) like Newton-Raphson) Usually , a company has a target IRR . If the calculated IRR is higher than the target IRR, so investment is done, vice versa. As the yield of the bond, the IRR concept (and the NPV and the PI assume), that all cash flows are reinvested at the discount = IRR rate. This is obviously a disadvantage.
  124. 126. The modified IRR (MIRR) The drawback, that in the IRR model the cash flows are reinvested at the IRR rate, is solved in the MIRR model. In the MIRR model the cash flows are reinvested at the MIRR rate. The MIRR rate can be calculated in 2 steps: 1) Calculate the future value of the cash flows using 2) Calculate the MIRR using (is derived from )
  125. 127. The modified IRR (MIRR) Example: A company has an IO of $1,000, and expects inflows of $300 at the end of year 1, $400 at the end of year 2, $500 at the end of year 3 and $600 at the end of year 4. The cash flows are expected to be reinvested at 15%. What is the MIRR rate? 1) The future value of the cash flows is, following FV =
  126. 128. The modified IRR (MIRR) 2) Using the MIRR is As a comparison, the standard IRR of the above example is 24.89% (see ECXEL file NPV IRR comparison)
  127. 129. Comparing the NPV and IRR Method Question: If the NPV and IRR model return different results, what model should we trust??? Example: (see EXCEL file “ NPV IRR comparison”) Solution: Compare the NPV and IRR of the difference in cash flows
  128. 130. Comparing the NPV and IRR Method Result:
  129. 131. Working Capital Management Firstly, the Yield Curve (= Interest rate curve) in an economy is usually steep Yield curves of the US, Germany and Japan on July 15, 1998 Result: Investing money short term results in a lower return (Emery p.579f)
  130. 132. Working Capital Management cont. Liquidity is the ability to pay off debt Profitability is the ability to make profits Working capital and liquidity are often used as synonyms and consist of cash and short term assets. Net working capital is the difference between short term assets and short term liabilities. Short Term assets consist of treasury bills, commercial paper (issued by banks and corporations) and CD’s (issued by banks) Net working capital has to be positive, otherwise you are
  131. 133. Working Capital Management cont. The higher the liquidity (=cash and short term assets) the the risk of defaulting on debt , but The lower the liquidity (=cash and short term assets) the the profitability (long term assets and investment in the firm’s business), but The working capital trade off is the trade-off between liquidity and profitability
  132. 134. Working Capital Management cont. How can we solve the liquidity - profitability trade-off?? We can reduce the trade-off by the Maturity Matching Principle Match long term investments (real estate, trucks, machinery) with Short term assets (computers, software) can be matched with
  133. 135. Financial Forecasting and Budgeting Forecasting in financial management is necessary to determine a companies financial need . Financial Forecasting is principally done in 3 steps: 1. Forecasting of the companies sales revenues and other income over the planing period. 2. Forecasting of the level of necessary investments and other expenses 3. Use 1. and 2 to determine the financial need ((Emery p.648f))
  134. 136. Financial Forecasting and Budgeting cont. Important for a company is the forecast of Sales . There are many forecasting methods is finance: Linear regression analysis, Non-linear regression analysis, Multi-variate regression analysis, Time series analysis, Econometric models, Stochastic processes, Monte-Carlo simulation and more Lets look at a linear regression-analysis to forecast sales:
  135. 137. Financial Forecasting and Budgeting cont. One form of regression analysis is time series analysis. In time series analysis time t is on the x-axis. Example: Let’s assume the sales of Turbodyne (TRBD) are: In January $30,000, in February $34,000, in March $35,000 and in April 39,000. What are the expected sales in May, calculated on a linear time series analysis?
  136. 138. Financial Forecasting and Budgeting cont. 1 2 3 4 5 Jan Feb Mar Apr May $30,000 $40,000 The goal is to find a linear regression function r , which minimizes the differences between the observed points and r . We then extrapolate r to find the sales for May. Sales time t r
  137. 139. Financial Forecasting and Budgeting cont. 1 2 3 4 5 Jan Feb Mar Apr May $30,000 $40,000 Sales time t r t a b = S In order to find the regression function r , we have to find a and b .
  138. 140. Financial Forecasting and Budgeting cont. b = a = where n: average of times t; average of times S; number of observations
  139. 141. Financial Forecasting and Budgeting cont. With t = 1,2,3,4 and S= 30,000; 34,000; 35,000; 39,000 b = a =
  140. 142. Financial Forecasting and Budgeting cont. It follows that the estimated Sales at time t =5, so in May, are S = a +b t = This forecast is based on the assumption, that the sales will increase linearly on the basis of historical data.
  141. 143. Financial Forecasting and Budgeting cont. The Sales forecast is often used as a basis to plan other financial items, such as inventories. The Percent of sales method for Financial Forecasting uses a linear forecasting: Forecasted Sales Inventories 30,000 70,000 20,000 30,000
  142. 144. Financial Forecasting and Budgeting cont. Creating a budget A budget is an estimate of revenues and expenditures. A Cash-budget estimates a company’s necessary financial needs based on expected revenues and expenditures. A budget tells you what you can’t afford, but it doesn’t keep you from buying it (William Feather) Revenue = Number of sales * price per sales unit Example: Dell sells 1 million PC’s in the year 2000 for $500 each. What is Dell’s revenue for 2000? ((Emery p.648f))
  143. 145. A Cash budget consists of <ul><li>Estimated Cash receipts </li></ul><ul><li>Estimated Cash payments </li></ul><ul><li>Expected monthly cash balance </li></ul><ul><li>Financial need </li></ul>Financial Forecasting and Budgeting cont.
  144. 146. Financial Forecasting and Budgeting cont. Creating a cash budget
  145. 147. Creating a cash- budget Financial Forecasting and Budgeting cont.
  146. 148. <ul><li>Practice Exam </li></ul><ul><li>Task 1 (25 points) </li></ul><ul><li>1)If the market rises and breaks an important resistance line, </li></ul><ul><li>technical analysis recommends buying </li></ul><ul><li> True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul><ul><li>2) If the market falls and breaks an important support line, </li></ul><ul><li>technical analysis recommends selling. </li></ul><ul><li>True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul><ul><li>3) Speculation means trying to exploit the movement of an asset. </li></ul><ul><li>True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul><ul><li>4) Traders take risks, brokers don’t </li></ul><ul><li>True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul>
  147. 149. <ul><li>5) In the long run, stocks tend to outperform bonds </li></ul><ul><li> True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul><ul><li>6) Arbitrage is another word for risk-less profit </li></ul><ul><li> True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul><ul><li>7) The yield curve of an economy is usually down-ward sloping </li></ul><ul><li>True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul><ul><li>8) When buying on margin, you trade with borrowed money </li></ul><ul><li>True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul><ul><li> 9) The Nasdaq has outperformed the Dow in the last half year </li></ul><ul><ul><ul><li>True False </li></ul></ul></ul><ul><ul><ul><li> </li></ul></ul></ul><ul><li>10) The unemployment rate in the USA is close to 7.2% </li></ul><ul><li>True False </li></ul><ul><ul><ul><ul><li>  </li></ul></ul></ul></ul>
  148. 150. Task 2 (25 points) a) The annual market interest rate is 10%. An investor wants to invest $1000 for 5 years. The banker offers the client to pay back $1000 + $1000 * 0.1 * 5 = $1,500. Is the banker trying to rip off the client? b) If you were the banker, what would you pay back to the client after 5 years? <ul><ul><ul><li>c)A client wants to invest $1000 for 5 years. The banker offers </li></ul></ul></ul><ul><ul><ul><li>to pay 5% quarterly or 5.2% annually. The client decides </li></ul></ul></ul><ul><ul><ul><li>to take 5% quarterly. Did he do the right thing? </li></ul></ul></ul><ul><li>Use (Eff = ((Nom / m) + 1) m –1) Eff and Nom in %! </li></ul>
  149. 151. Task 3 (25 points) a)The annual coupon of a bond is 5%. The annual yield is also 5%. What is the price of the bond with a principal of $1000? b) What is the 20 day accrued interest of the bond? c) What is the difference between the coupon of a bond and the dividend of a stock?
  150. 152. Task 4 (25 points) a) After attending the Fin300 class at HPU, you have become a successful financial advisor. One of your clients wants to invest $100,000 dollars. What are the two questions you ask him first? b) Your client wants to open up a savings account. What is your reply c)What do you suggest to the client as investment alternatives?
  151. 153. Learning e and ln The number e -Eulers number- is an irrational number (a number that cannot be divided by tow integers (an integer is a number without decimals, so -3 and 4 are integers, -3.1 or 4.55 are not) The value of e = 2.71828182…. The decimals of e are indefinite Mathematically e = 1+ 1/1! + 1/2! + 1/3! =… = (1 + 1/m) m with m to infinity e has nice features such as if y = e x then y’ = e x y = e f(x) then y’ = f’(x) e f(x)
  152. 154. The logarithm of the number N to the base a is the exponent to which x has to raised to yield N. Thus Log a N = x if and only if a x = N Examples: Log 10 1 = 0 since 10 0 = 1 Log 10 10 = 1 Log 10 100 = 2 Log 10 1000 = 3 Log 4 16 = Log 10 (0.001) = Logarithm
  153. 155. If the base of the logarithm is e , the logarithm is called natural logarithm . Log e = ln Examples: ln 1 = 0 since 2.7183 0 = 1 ln 10 = 2.326 since 2.7183 2.3026 = 10 ln 100 = 4.6052 since 2.7183 4.6052 = 100 ln -3
  154. 156. Three important rules apply to logarithms: a) ln (a * b) = ln a + ln b b) ln (a / b) = ln a - ln b c) ln a b = b * ln a Rule c) comes in handy for solving equations: Solve for x, when 10 x = 7, using rule c) Mathematically logarithms have nice features such as If y = ln x then y’ = 1/x If y = a x then y’ = a x ln a
  155. 157. Graphically ln x and e are reflected across the y = x line y = x y = e x y = ln x y x 1 1 Logarithmic functions are often used in psychology to explain human behavior.

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