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10-                                  Chapter 10:                            Capital Market History:                       ...
10-       Chapter Outline        10.1        Returns        10.2        Holding-Period Returns        10.3        Return S...
10-       10.1 Returns        • Dollar Returns              – the sum of the cash received and                the change i...
10-       10.1 Returns        • Dollar Returns              – the sum of the cash received and                the change i...
10-       10.1 Returns      McGraw-Hill Ryerson   © 2005 McGraw–Hill Ryerson Limited
10-       10.1 Returns        Dollar Return = Dividend + Change in Market Value      McGraw-Hill Ryerson                  ...
10-       10.1 Returns        Dollar Return = Dividend + Change in Market Value      McGraw-Hill Ryerson                  ...
10-       10.1 Returns: Example      McGraw-Hill Ryerson      © 2005 McGraw–Hill Ryerson Limited
10-       10.1 Returns: Example        • Suppose you bought 100 shares of BCE one year          ago today at $25. Over the...
10-       10.1 Returns: Example        • Suppose you bought 100 shares of BCE one year          ago today at $25. Over the...
10-       10.1 Returns: Example        • Suppose you bought 100 shares of BCE one year          ago today at $25. Over the...
10-       10.1 Returns: Example        • Dollar Returns              – $520 gain                            •Percentage Re...
10-       10.1 Returns: Example        • Dollar Returns              – $520 gain                                          ...
10-        • Exactly one year ago you purchased 100 shares of          Texaco Inc. for $57.4375 per share. Todays stock pr...
10-        • Suppose that, one year ago, you bought 100 shares of          Ply-Mor Corporation common stock for $32 per sh...
10-       Technical Issue: Timing of Dividends        • We have assumed that the dividend is paid at the end of the       ...
10-       10.2 Holding Period Returns        • The holding period return is the return that an          investor would get...
10-       Holding Period Return: Example        • Suppose your investment provides the following          returns over a f...
10-       Holding Period Return: Example        • An investor who held this investment would have          actually realiz...
10-       Holding Period Return: Example        • Note that the geometric average is not the same          thing as the ar...
10-        • Two years ago you purchased a share of stock for          $40.00. The first year that you owned the stock you...
10-       Holding Period Returns        • A famous set of studies dealing with the rates of returns on          common sto...
10-       The Definitions Change over Time        • The current approximate definitions are as follows:             Big Ca...
10-       Growth under Various Investments          The Future Value of an Investment of $1 in 1948         10000.0000    ...
10-         Fear of eurozone crisis             contagion triggers           global sell-off           Stock and bond mark...
10-        • Containment of debt crisis              should be Europes          top priority:           – Europe probably ...
10-        • Greek debt fears boost U.S. dollar        • Euro continues slide        • Last Updated: Wednesday, May 5, 201...
10-       10.3 Return Statistics        • The history of capital market returns can be summarized by          describing t...
10-        Historical Returns, 1957-2003                                     Average       Standard                 Invest...
10-      10.4 Average Stock Returns and Risk-Free Returns        • The Risk Premium           is the additional return (ov...
10-       Risk Premia        • Suppose that The National Post announced that the current          rate for one-year Treasu...
10-                   Risk Increases Incrementally              Gov’t T-Bills     rf              Gov’t Bonds       Horizo...
10-       The Risk-Return Tradeoff (1957-2003)      McGraw-Hill Ryerson           © 2005 McGraw–Hill Ryerson Limited
10-       The Risk-Return Tradeoff (1957-2003)                                 11.00                                  8.75...
10-       The Risk-Return Tradeoff (1957-2003)                                 11.00                                  8.75...
10-       The Risk-Return Tradeoff (1957-2003)                                 11.00                                  8.75...
10-       The Risk-Return Tradeoff (1957-2003)                                 11.00                                      ...
10-       Rates of Return 1957-2003                                        Common Stocks                                  ...
10-       Rates of Return 1957-2003                                                 Common Stocks                         ...
10-       Rates of Return 1957-2003                                                 Common Stocks                         ...
10-       Rates of Return 1957-2003                                                 Common Stocks                         ...
10-       Rates of Return 1957-2003                                                 Common Stocks                         ...
10-       Risk Premiums        • Rate of return on T-bills is essentially           risk-free.        • Investing in stock...
10-       The Long Run        • Over the entire 20th century the Canadian performance in          financial markets has be...
10-       Equity Premium        • Equity premium is historically high        • One issue is defining the proper risk free ...
10-       Equity Premium        • Equity premium is historically high        • This is not the case in the ‘new reality’  ...
10-       U.S. Stock Market Volatility       The volatility                      of stocks is not constant from year to ye...
10-       U.S. Stock Market Volatility       The volatility                      of stocks is not constant from year to ye...
10-       U.S. Stock Market Volatility       The volatility                      of stocks is not constant from year to ye...
10-       10.5 Risk Statistics        • There is no universally agreed-upon definition of risk.        • The measures of r...
10-       Other Risk Measures        •    Value at Risk     (percentile of the loss distribution):        •    Conditional...
10-          Normal Distribution      It is assumed that stock      returns follow this type      of distribution.       M...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Normal Distribution        • A large enough sample drawn from a normal distribution          looks like a bell-s...
10-       Value at Risk        • This is the most amount of money we can lose x% of the          time – one tailed calcula...
10-       Value at Risk        • This is the most amount of money we can lose x% of the          time – one tailed calcula...
10-       Normal Distribution                              Normal                              approximation              ...
10-       Normal Distribution                                                           S&P 500 Return Frequencies        ...
10-       Return Distributions        • The skewness of a distribution is a measure of the          asymmetry of the distr...
10-                Normal Distribution      McGraw-Hill Ryerson                                        54                 ...
10-       10.6 Summary and Conclusions        • This chapter presents returns for five asset classes:           – Canadian...
10-       Questions        (Text 10.3) You purchased a stock one year ago at $42 per        share. The stock just paid a d...
10-       Question                                   #sd      McGraw-Hill Ryerson   © 2005 McGraw–Hill Ryerson Limited
10-       Question        What is the 99% VaR on a $100 pension plan that has an        expected return of 8.5% and volati...
10-       Question        What is the 99% VaR on a $100 pension plan that has an        expected return of 8.5% and volati...
10-       Question        What is the 99% VaR on a $100 pension plan that has an        expected return of 8.5% and volati...
10-       Question        What is the 99% VaR on a $100 pension plan that has an        expected return of 8.5% and volati...
10-       Question        What is the 99% VaR on a $100 pension plan that has an        expected return of 8.5% and volati...
10-       Question        What is the 99% VaR on a $100 pension plan that has an        expected return of 8.5% and volati...
10-       Question        What is the 99% VaR on a $100 pension plan that has an        expected return of 8.5% and volati...
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Chapter 10

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  • Why do capital markets exist?\nWhat is the motivation for people to invest?\nWhat types of investments are available?\nHow do we know that we are getting a return that is appropriate and how do we measure that return? Is return relative to something or is it absolute?\nWhat have the markets done over the last number of years? What will they do over the next number of years?\n\nWe are at a place where many assumptions are being challenged, many practices are being challenged, many thoughts and market ‘common sense’ are being challenged.\n
  • We will begin with a discussion about returns and how to measure them.\nIn case you feel that returns are not important, or that the appropriate measurement of them is not important, look at this next slide.\n
  • Obviously, our discussion on returns will just touch the surface of how to measure performance. It is a hot topic in the industry.\n
  • Two components to return: Capital appreciation/depreciation and dividends (can be $0)\nOur initial investment is a cash outflow and when (or if) we were to sell the stock at a time in the future, we would or could realize a gain or loss.\n\nUnrealized gains/losses are possible and are valuable. If there is a capital appreciation/depreciation we could hold the stock past the valuation date or we could sell it.\n
  • Two components to return: Capital appreciation/depreciation and dividends (can be $0)\nOur initial investment is a cash outflow and when (or if) we were to sell the stock at a time in the future, we would or could realize a gain or loss.\n\nUnrealized gains/losses are possible and are valuable. If there is a capital appreciation/depreciation we could hold the stock past the valuation date or we could sell it.\n
  • Two components to return: Capital appreciation/depreciation and dividends (can be $0)\nOur initial investment is a cash outflow and when (or if) we were to sell the stock at a time in the future, we would or could realize a gain or loss.\n\nUnrealized gains/losses are possible and are valuable. If there is a capital appreciation/depreciation we could hold the stock past the valuation date or we could sell it.\n
  • Two components to return: Capital appreciation/depreciation and dividends (can be $0)\nOur initial investment is a cash outflow and when (or if) we were to sell the stock at a time in the future, we would or could realize a gain or loss.\n\nUnrealized gains/losses are possible and are valuable. If there is a capital appreciation/depreciation we could hold the stock past the valuation date or we could sell it.\n
  • Two components to return: Capital appreciation/depreciation and dividends (can be $0)\nOur initial investment is a cash outflow and when (or if) we were to sell the stock at a time in the future, we would or could realize a gain or loss.\n\nUnrealized gains/losses are possible and are valuable. If there is a capital appreciation/depreciation we could hold the stock past the valuation date or we could sell it.\n
  • Mathematically:\n\nWe can decompose the return several ways to help clarify where the return comes from\n
  • Mathematically:\n\nWe can decompose the return several ways to help clarify where the return comes from\n
  • Timeline:\nP0=25\nV0=25*100=2500\nDiv = 0.2/share\nDiv=0.2*100 = 20\n\nP1=30\nTherefore, 30-25+.0=5.20/share\nTotal dollar return = 5.20*100=(30-25+.2)*100=520\n\nPercentage gain = 520/2500 = 20.8%\n
  • Timeline:\nP0=25\nV0=25*100=2500\nDiv = 0.2/share\nDiv=0.2*100 = 20\n\nP1=30\nTherefore, 30-25+.0=5.20/share\nTotal dollar return = 5.20*100=(30-25+.2)*100=520\n\nPercentage gain = 520/2500 = 20.8%\n
  • Timeline:\nP0=25\nV0=25*100=2500\nDiv = 0.2/share\nDiv=0.2*100 = 20\n\nP1=30\nTherefore, 30-25+.0=5.20/share\nTotal dollar return = 5.20*100=(30-25+.2)*100=520\n\nPercentage gain = 520/2500 = 20.8%\n
  • Timeline:\nP0=25\nV0=25*100=2500\nDiv = 0.2/share\nDiv=0.2*100 = 20\n\nP1=30\nTherefore, 30-25+.0=5.20/share\nTotal dollar return = 5.20*100=(30-25+.2)*100=520\n\nPercentage gain = 520/2500 = 20.8%\n
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  • Geometric versus arithmetic. Generally, if there is variation (which there will be in stock returns) then go is the way t o go.\n
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  • We will discuss these in context in a moment.\n
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  • This graph: \ngeneral observations: the market goes up if we stand back far enough to look at it.\nStocks outperform增持 over the long run.\n\nWhy do stocks outperform?\nRisk is rewarded报偿 in the long run.\nWe will see this more in a moment when we look at the distributions of the classes of investments.\n\nALWAYS THINK ABOUT THE RISK PERSPECTIVE. IF YOU THINK YOU ARE GETTING FREE RETURN, YOU ARE FOOLING YOURSELF.\n
  • Contagion, bubbles, valuations tank, returns increase, how much extra return is needed for the added risk\n
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  • Safe haven, flight to safety\n
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  • In the text page 276, you see that small cap stocks are included and have a risk premium of 7.77% and std 22.29%\nON BOARD RISK PREMIUM BUILD UP\n\nMORE RETURN, MORE RP MORE RISK\n\nWhy care about inflation? May be an issue going forward\n
  • the additional return by taking more risk than the risk free rate\n\nReturn = Rrf + Rrp\n
  • The rp has been too large and there is forecat to be a moderation 3-4% real return over a long term real government bond for an all equity fund\n
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  • The greatest lower bound of x, given the probability of loss greater than or equal to a threshold\nVAR has three components. Greatest loss for a given probability over a given period of time.\n
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  • This has the hallmarks of a VAR statement\nIt deals with the maximal loss for a given probability, the time element is due to the loss distribution being over time\n
  • One issue with VAR is that the assumption of equity returns being normally distributed. We know that this is not true. \n\nFat tails, greater chance of greater loss.\nGives a theoretical and practical issue with VAR.\nAlso, because we need to have the correlations between each pair of assets, this is an issue with large portfolios.\n
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  • percentage return = dollar return/capital \n\ndollar return = 2.4 + 31 - 42\n\n
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  • Transcript of "Chapter 10"

    1. 1. 10- Chapter 10: Capital Market History: An Overview McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    2. 2. 10- Chapter Outline 10.1 Returns 10.2 Holding-Period Returns 10.3 Return Statistics 10.4 Average Stock Returns and Risk-Free Returns 10.5 Risk Statistics 10.6 Summary and Conclusions McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    3. 3. 10- 10.1 Returns • Dollar Returns – the sum of the cash received and the change in value of the asset, in dollars. •Percentage Returns – the sum of the cash received and the change in value of the asset divided by the original investment. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    4. 4. 10- 10.1 Returns • Dollar Returns – the sum of the cash received and the change in value of the asset, in Dividends dollars. Ending market value Time 0 1 •Percentage Returns – the sum of the cash received and the Initial change in value of the asset divided by investment the original investment. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    5. 5. 10- 10.1 Returns McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    6. 6. 10- 10.1 Returns Dollar Return = Dividend + Change in Market Value McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    7. 7. 10- 10.1 Returns Dollar Return = Dividend + Change in Market Value McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    8. 8. 10- 10.1 Returns: Example McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    9. 9. 10- 10.1 Returns: Example • Suppose you bought 100 shares of BCE one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share × 100 shares). At the end of the year, the stock sells for $30. How did you do? McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    10. 10. 10- 10.1 Returns: Example • Suppose you bought 100 shares of BCE one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share × 100 shares). At the end of the year, the stock sells for $30. How did you do? • Quite well. You invested $25 × 100 = $2,500. At the end of the year, you have stock worth $3,000 and cash dividends of $20. Your dollar gain was $520 = $20 + ($3,000 – $2,500). McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    11. 11. 10- 10.1 Returns: Example • Suppose you bought 100 shares of BCE one year ago today at $25. Over the last year, you received $20 in dividends (= 20 cents per share × 100 shares). At the end of the year, the stock sells for $30. How did you do? • Quite well. You invested $25 × 100 = $2,500. At the end of the year, you have stock worth $3,000 and cash dividends of $20. Your dollar gain was $520 = $20 + ($3,000 – $2,500). • Your percentage gain for the year is McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    12. 12. 10- 10.1 Returns: Example • Dollar Returns – $520 gain •Percentage Returns McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    13. 13. 10- 10.1 Returns: Example • Dollar Returns – $520 gain $20 $3,000 Time 0 1 •Percentage Returns -$2,500 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    14. 14. 10- • Exactly one year ago you purchased 100 shares of Texaco Inc. for $57.4375 per share. Todays stock price is $71.40, and over the past year you received cash dividends of $1.80 per share. What is the percentage increase in price? What is the percentage return from dividends? What is your total return for the year? V0 = 5743.75 V2 = 7140 div = 180 dollar return = 180 + (7140-5743.75) = 1406.25 percentage return = 1406.25/5743 = 24.49% from div = 180/5743.75 = 3.13% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    15. 15. 10- • Suppose that, one year ago, you bought 100 shares of Ply-Mor Corporation common stock for $32 per share. During the year, you received cash dividends of $250. Ply-Mor common stock is currently selling for $33.50 per share. How much did you earn in capital gains over the year? What was your total dollar return? Calculate your capital gains yield, dividend yield, and total percentage return. V0 = 3200 div = 250 V1 = 3350 dollar return = 250 + 3350 - 3200 = 400 capital gain yield = 150/3200 = 4.69% dividend yield = 250/3200 = 7.81% total percentage yield = 12.5% © 2005 McGraw–Hill Ryerson Limited McGraw-Hill Ryerson
    16. 16. 10- Technical Issue: Timing of Dividends • We have assumed that the dividend is paid at the end of the year. • What to do if the dividend is paid before the end of the year? There are different alternatives: – Assume the proceeds are lent out and receive the risk- free interest rate. – Assume the proceeds are reinvested in the stock. • Best is to determine exactly when the dividend is received and to include the return that comes from reinvesting the McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    17. 17. 10- 10.2 Holding Period Returns • The holding period return is the return that an investor would get when holding an investment over a period of n years, when the return during year i is given as ri: McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    18. 18. 10- Holding Period Return: Example • Suppose your investment provides the following returns over a four-year period: McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    19. 19. 10- Holding Period Return: Example • An investor who held this investment would have actually realized an annual return of 9.58%: • So, our investor made 9.58% on his money for four years, realizing a holding period return of 44.21% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    20. 20. 10- Holding Period Return: Example • Note that the geometric average is not the same thing as the arithmetic average: McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    21. 21. 10- • Two years ago you purchased a share of stock for $40.00. The first year that you owned the stock you received a 75% return; over the second year, however, the stock fell by 50%. What is your share of stock worth today? What was your average rate of return over the two years? What was your holding period return during this time? - 40×1.75×0.5 = 35 -0.75 - 0.5 / 2 = 0.125 -1.75×0.5-1 = -0.125 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    22. 22. 10- Holding Period Returns • A famous set of studies dealing with the rates of returns on common stocks, bonds, and Treasury bills in the U.S. was conducted by Roger Ibbotson and Rex Sinquefield. • James Hatch and Robert White examined Canadian returns. • The text presents year-by-year historical rates of return starting in 1948 for the following five important types of financial instruments: – Large-Company Canadian Common Stocks – Large-Company U.S. Common Stocks – Small-Company Canadian Common Stocks – Long-Term Canadian Bonds – Canadian Treasury Bills McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    23. 23. 10- The Definitions Change over Time • The current approximate definitions are as follows: Big Cap - Market cap of $10 billion and greater Mid Cap - $2 billion to $10 billion Small Cap - $300 million to $2 billion Micro Cap - $50 million to $300 million Nano Cap - Under $50 million • From Investopedia McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    24. 24. 10- Growth under Various Investments The Future Value of an Investment of $1 in 1948 10000.0000 1000.0000 100.0000 $41.09 $21.48 10.0000 Common Stocks 1.0000 Long Bonds T-Bills 0.1000 1948 1958 1968 1978 1988 1998 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    25. 25. 10- Fear of eurozone crisis contagion triggers global sell-off Stock and bond markets across the world posted a sharp decline as traders worried that a Greek rescue would not stop the eurozones sovereign-debt problems from spreading into other weak European economies. "This is a big sell-off, and it is not just in Europe," said Nick Chamie, a strategist at RBC Capital Markets. "It is across the globe and in almost all asset classes." McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    26. 26. 10- • Containment of debt crisis should be Europes top priority: – Europe probably didnt get its strategy right in trying to cope with Greeces sovereign-debt crisis, according to The Economists Free Exchange blog. "To properly ring- fence the crisis, ministers should probably have acknowledged the need to restructure Greeces debt and worked to do so in an orderly fashion, all while extending unlimited liquidity and significant lines of credit to European economies threatened by contagion," the blog notes. "... The first, second, and third priority have to be containing the crisis. European leaders seem depressingly slow to grasp this." McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    27. 27. 10- • Greek debt fears boost U.S. dollar • Euro continues slide • Last Updated: Wednesday, May 5, 2010 | 1:00 PM ET A higher U.S. dollar pulled oil prices and the Toronto Stock Exchange lower for a second day Wednesday, while gold rebounded. • Investors worried about the possibility of the Greek debt crisis spreading to other European countries and took profits after a run-up in stocks after better-than-expected corporate earnings. Traders bought the U.S. dollar, and that dragged commodities — which are priced in U.S. dollars — lower. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    28. 28. 10- 10.3 Return Statistics • The history of capital market returns can be summarized by describing the – average return – the standard deviation of those returns – the frequency distribution of the returns. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    29. 29. 10- Historical Returns, 1957-2003 Average Standard Investment Annual Return Deviation Distribution Canadian common stocks 10.64% 16.41% Long Bonds 8.96 10.36 Treasury Bills 6.80 4.11 Inflation 4.29 3.63 – 60% 0% + 60% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    30. 30. 10- 10.4 Average Stock Returns and Risk-Free Returns • The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk. • One of the most significant observations of stock and bond market data is this long-run excess of security return over the risk-free return. – The average excess return from Canadian large- company common stocks for the period 1957 through 2003 was 3.84% = 10.64% – 6.80% – The average excess return from Canadian long-term bonds for the period 1957 through 2003 was 2.16% = 8.96% – 6.80% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    31. 31. 10- Risk Premia • Suppose that The National Post announced that the current rate for one-year Treasury bills is 5%. • What is the expected return on the market of Canadian large- company stocks? • Recall that the average excess return from Canadian large- company common stocks for the period 1957 through 2003 was 3.84% • Given a risk-free rate of 5%, we have an expected return on the market of Canadian large-company common stocks of 8.84% = 3.84% + 5% McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    32. 32. 10- Risk Increases Incrementally Gov’t T-Bills rf Gov’t Bonds Horizon risk, reinvestment risk, interest rate Corporate Bonds Default risk ST Bonds Default risk LT Bonds Horizon, reinvestment, interest rate Stocks Other McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    33. 33. 10- The Risk-Return Tradeoff (1957-2003) McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    34. 34. 10- The Risk-Return Tradeoff (1957-2003) 11.00 8.75 Annual Return Average 6.50 4.25 2.00 0 6.25 12.50 18.75 25.00 Annual Return Standard Deviation McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    35. 35. 10- The Risk-Return Tradeoff (1957-2003) 11.00 8.75 Annual Return Average 6.50 T-Bills 4.25 2.00 0 6.25 12.50 18.75 25.00 Annual Return Standard Deviation McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    36. 36. 10- The Risk-Return Tradeoff (1957-2003) 11.00 8.75 Annual Return Average Long Bonds 6.50 T-Bills 4.25 2.00 0 6.25 12.50 18.75 25.00 Annual Return Standard Deviation McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    37. 37. 10- The Risk-Return Tradeoff (1957-2003) 11.00 Large-Company Stocks (mean = 10.64%, σ=16.4%) 8.75 Annual Return Average Long Bonds 6.50 T-Bills 4.25 2.00 0 6.25 12.50 18.75 25.00 Annual Return Standard Deviation McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    38. 38. 10- Rates of Return 1957-2003 Common Stocks Long Bonds T-bills McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    39. 39. 10- Rates of Return 1957-2003 Common Stocks Long Bonds T-bills 50.00 37.50 25.00 12.50 0 -12.50 -25.00 -37.50 1955 1968 1980 1993 2005 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    40. 40. 10- Rates of Return 1957-2003 Common Stocks Long Bonds T-bills 50.00 37.50 25.00 12.50 0 -12.50 -25.00 -37.50 1955 1968 1980 1993 2005 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    41. 41. 10- Rates of Return 1957-2003 Common Stocks Long Bonds T-bills 50.00 37.50 25.00 12.50 0 -12.50 -25.00 -37.50 1955 1968 1980 1993 2005 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    42. 42. 10- Rates of Return 1957-2003 Common Stocks Long Bonds T-bills 50.00 37.50 25.00 12.50 0 -12.50 -25.00 -37.50 1955 1968 1980 1993 2005 McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    43. 43. 10- Risk Premiums • Rate of return on T-bills is essentially risk-free. • Investing in stocks is risky, but there are compensations . • The difference between the return on T-bills and stocks is the risk premium for investing in stocks. – Rstock = Rt-bill + rp McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    44. 44. 10- The Long Run • Over the entire 20th century the Canadian performance in financial markets has been very close to that of the US, in both risk and return • Other industrialized countries have also done almost as well • There is some concern that the large observed average risk premium for stocks cannot persist in the long run McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    45. 45. 10- Equity Premium • Equity premium is historically high • One issue is defining the proper risk free asset to use. • A long-term real return bond seems to be best McGraw-Hill Ryerson 42 © 2005 McGraw–Hill Ryerson Limited
    46. 46. 10- Equity Premium • Equity premium is historically high • This is not the case in the ‘new reality’ • A premium of 2-3% over long, real bonds is to be expected McGraw-Hill Ryerson 43 © 2005 McGraw–Hill Ryerson Limited
    47. 47. 10- U.S. Stock Market Volatility The volatility of stocks is not constant from year to year. Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    48. 48. 10- U.S. Stock Market Volatility The volatility of stocks is not constant from year to year. 60.00 45.00 30.00 15.00 0 31 36 41 46 51 56 61 66 71 76 81 86 91 96 19 19 19 19 19 19 19 19 19 19 19 19 19 19 Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    49. 49. 10- U.S. Stock Market Volatility The volatility of stocks is not constant from year to year. 60.00 45.00 30.00 15.00 0 31 36 41 46 51 56 61 66 71 76 81 86 91 96 19 19 19 19 19 19 19 19 19 19 19 19 19 19 Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    50. 50. 10- 10.5 Risk Statistics • There is no universally agreed-upon definition of risk. • The measures of risk that we discuss are variance and standard deviation. – The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of this time. – Its interpretation is facilitated by a discussion of the normal distribution. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    51. 51. 10- Other Risk Measures • Value at Risk (percentile of the loss distribution): • Conditional Value at Risk (Conditional Tail Expectation): • Downside Semivariance: McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    52. 52. 10- Normal Distribution It is assumed that stock returns follow this type of distribution. McGraw-Hill Ryerson 47 © 2005 McGraw–Hill Ryerson Limited
    53. 53. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    54. 54. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    55. 55. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    56. 56. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. The probability that a yearly return will fall within 16.41-percent of the mean of 10.64-percent will be approximately 2/3. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    57. 57. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    58. 58. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    59. 59. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. The probability that a yearly return will fall within 32.82-percent (2×16.41) of the mean of 10.64-percent will be 0.9544. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    60. 60. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    61. 61. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    62. 62. 10- Normal Distribution • A large enough sample drawn from a normal distribution looks like a bell-shaped curve. The probability that a yearly return will fall within 49.23-percent (3×16.41) of the mean of 10.64-percent will be 0.9974. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    63. 63. 10- Value at Risk • This is the most amount of money we can lose x% of the time – one tailed calculation. 95% of returns -1.64σ are over here. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    64. 64. 10- Value at Risk • This is the most amount of money we can lose x% of the time – one tailed calculation. 95% of returns -1.64σ are over here. On a $1 million portfolio, the 95% VaR is $1 million x (10.64%-1.64x16.41%) = $162,724. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    65. 65. 10- Normal Distribution Normal approximation Mean = 12.8% Std. Dev. = 20.4% Source: © Stocks, Bonds, Bills, and Inflation 2002 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    66. 66. 10- Normal Distribution S&P 500 Return Frequencies 30 16 Normal 12 9 23 approximation Mean = 12.8% 12 Return frequency 11 Std. Dev. = 20.4% 15 5 8 1 2 2 1 1 0 0 0 -0.58 -0.48 -0.38 -0.28 -0.18 -0.08 0.02 0.12 0.22 0.32 0.42 0.52 0.62 Annual returns Source: © Stocks, Bonds, Bills, and Inflation 2002 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    67. 67. 10- Return Distributions • The skewness of a distribution is a measure of the asymmetry of the distribution • It is equal to the average cubed deviation from the mean • Canadian stock returns are negatively skewed, implying that large losses are more probable than for a normal distribution McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    68. 68. 10- Normal Distribution McGraw-Hill Ryerson 54 © 2005 McGraw–Hill Ryerson Limited
    69. 69. 10- 10.6 Summary and Conclusions • This chapter presents returns for five asset classes: – Canadian Large-Company Common Stocks – U.S. Large-Company Common Stocks – Canadian Small-Company Common Stocks – Canadian Long-Term Bonds – Canadian Treasury Bills • Stocks have outperformed bonds over most of the twentieth century, although stocks have also exhibited more risk. • The statistical measures in this chapter are necessary building blocks for the material of the next three chapters. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    70. 70. 10- Questions (Text 10.3) You purchased a stock one year ago at $42 per share. The stock just paid a dividend of $2.40 per share. Today, you sold the stock at $31 per share. What is the percentage return on the stock? McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    71. 71. 10- Question #sd McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    72. 72. 10- Question What is the 99% VaR on a $100 pension plan that has an expected return of 8.5% and volatility (i.e. standard deviation of returns) of 7% p.a. #sd McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    73. 73. 10- Question What is the 99% VaR on a $100 pension plan that has an expected return of 8.5% and volatility (i.e. standard deviation of returns) of 7% p.a. #sd McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    74. 74. 10- Question What is the 99% VaR on a $100 pension plan that has an expected return of 8.5% and volatility (i.e. standard deviation of returns) of 7% p.a. #sd McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    75. 75. 10- Question What is the 99% VaR on a $100 pension plan that has an expected return of 8.5% and volatility (i.e. standard deviation of returns) of 7% p.a. #sd McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    76. 76. 10- Question What is the 99% VaR on a $100 pension plan that has an expected return of 8.5% and volatility (i.e. standard deviation of returns) of 7% p.a. #sd McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    77. 77. 10- Question What is the 99% VaR on a $100 pension plan that has an expected return of 8.5% and volatility (i.e. standard deviation of returns) of 7% p.a. #sd McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
    78. 78. 10- Question What is the 99% VaR on a $100 pension plan that has an expected return of 8.5% and volatility (i.e. standard deviation of returns) of 7% p.a. #sd Thus, the maximum annual loss we can expect (99% of the time) is $7.81 million. McGraw-Hill Ryerson © 2005 McGraw–Hill Ryerson Limited
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