L Pch6

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  • Note the log scale.
  • L Pch6

    1. 1. Investments Chapter 6: Rates of Return
    2. 2. Different Methods yield Different Rates of Return <ul><li>Investment managers, who are rated on their performance, have an incentive to use those methods that make them look best. </li></ul>
    3. 3. Standardisation of Methods <ul><li>In response to this incentive the Association of Investment Management and Research (AIMR) has established guidelines to calculate rates of return. </li></ul><ul><li>A global standard is also evolving (the Global Investment Performance Standards). </li></ul>
    4. 4. Ex-post and Ex-ante Rates of Return <ul><li>Ex-post rates of return </li></ul><ul><li>Rates of return that has already been earned. </li></ul><ul><li>Ex-ante rates of return </li></ul><ul><li>Rates of return expected to occur in the future. </li></ul>
    5. 5. Simple Rate of Return <ul><li>Two components included: </li></ul><ul><li>1. Capital gains or losses. </li></ul><ul><li>2. Cash flow yield. </li></ul><ul><li>Calculated over the investment period and depicted as a percentage of the dollar amount invested. </li></ul>
    6. 6. Simple Returns <ul><li>Dollar Returns </li></ul><ul><ul><li>the sum of the cash received and the change in value of the asset, in dollars. </li></ul></ul><ul><li>Percentage Returns </li></ul><ul><ul><li>the sum of the cash received and the change in value of the asset divided by the original investment. </li></ul></ul>Time 0 1 Initial investment Ending market value Dividends
    7. 7. <ul><li>Dollar Return = Dividend + Change in Market Value </li></ul>Simple Returns
    8. 8. Adjusted Rate of Return: I <ul><li>The simple rate of return does not account for the timing of the cash flows received . </li></ul><ul><li>Two approaches to compute the adjusted rate of return: </li></ul><ul><li>1. Linking method. </li></ul><ul><li>2. Index method. </li></ul>
    9. 9. Sample Mean <ul><li>Two methods: </li></ul><ul><li>1. Arithmetic average. 2. Geometric average. </li></ul><ul><li>The arithmetic average doesn’t compound the rates of return. Hence, if the returns are not constant, the arithmetic average is upwardly biased . </li></ul>
    10. 10. Holding-Period Returns (Linking Method) <ul><li>The holding period return (linking method) 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 r i : </li></ul>
    11. 11. Holding Period Return: Example <ul><li>Suppose your investment provides the following returns over a four-year period: </li></ul>
    12. 12. Holding Period Return: Example <ul><li>An investor who held this investment would have actually realized an annual return of 9.58%: </li></ul><ul><li>So, our investor made 9.58% on his money for four years, realizing a holding period return of 44.21% </li></ul>
    13. 13. Holding Period Return: Example <ul><li>Note that the geometric average is not the same thing as the arithmetic average: </li></ul>
    14. 14. Arithmetic or Geometric? <ul><li>Start with 100, remain 100 first year, decrease to 50 next year and increase to 100 the third year. </li></ul>
    15. 15. Adjusted Rate of Return: II <ul><li>Besides timing of the cash flows, rates of return also need to be adjusted for other developments: </li></ul><ul><li>1. Stock splits. </li></ul><ul><li>2. Stock dividends. </li></ul><ul><li>3. Rights acquired. </li></ul><ul><li>4. Accrued interest on bonds (accrues daily). </li></ul><ul><li>5. Changes in the composition of the portfolio. </li></ul>
    16. 16. Other Complications <ul><li>Taxes, inflation and (for foreign investors) exchange rates generally change the return of an investor. </li></ul><ul><li>Solutions: </li></ul><ul><li>1. After-tax rates of return. </li></ul><ul><li>2. Inflation-adjusted rates of return. </li></ul><ul><li>3. Exchange rate-adjusted rates of return. </li></ul>
    17. 17. INDICES <ul><li>An index measures the performance of a certain segment of the financial markets. </li></ul>
    18. 18. Stock Indexes <ul><li>Can be categorized as: </li></ul><ul><li>1. Price-weighted </li></ul><ul><li>(Example: Dow Jones Industrial Average.) </li></ul><ul><li>2. Value-weighted </li></ul><ul><li>( Example: S & P 500.) </li></ul><ul><li>3. Equally-weighted </li></ul>
    19. 19. Bond Indices: I <ul><li>The set of bonds in a bond index is always changing. </li></ul><ul><li>Reasons: </li></ul><ul><li>1. Bonds have finite maturities. </li></ul><ul><li>2. Call features within bonds. </li></ul>
    20. 20. Sample Return Statistics <ul><li>Describe or summarize a sample of past rates of return </li></ul><ul><li>Note: (statistics describing a sample of ex-ante rates of return are discussed in chapter 7). </li></ul>
    21. 21. Risk Statistics <ul><li>There is no universally agreed-upon definition of risk. </li></ul><ul><li>The measures of risk that we discuss are variance and standard deviation. </li></ul><ul><ul><li>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. </li></ul></ul><ul><ul><li>Its interpretation is facilitated by a discussion of the normal distribution. </li></ul></ul>
    22. 22. Return Statistics <ul><li>The history of capital market returns can be summarized by describing the </li></ul><ul><ul><li>average return </li></ul></ul><ul><ul><li>the standard deviation of those returns </li></ul></ul><ul><ul><li>the frequency distribution of the returns. </li></ul></ul>
    23. 23. Sample Covariance and Sample Correlation <ul><li>Give information on the dependency between various assets and how they move together: </li></ul><ul><li>Covariance (measure of dependence in units such as dollars or percentages). </li></ul><ul><li>Correlation (measure of dependence on a scale of – 1 to +1, thus more comparable). </li></ul>
    24. 24. Holding Period Returns <ul><li>A famous set of studies dealing with the rates of returns on common stocks, bonds, and Treasury bills was conducted by Roger Ibbotson and Rex Sinquefield. </li></ul><ul><li>They present year-by-year historical rates of return starting in 1926 for the following five important types of financial instruments in the United States: </li></ul><ul><ul><li>Large-Company Common Stocks </li></ul></ul><ul><ul><li>Small-company Common Stocks </li></ul></ul><ul><ul><li>Long-Term Corporate Bonds </li></ul></ul><ul><ul><li>Long-Term U.S. Government Bonds </li></ul></ul><ul><ul><li>U.S. Treasury Bills </li></ul></ul>
    25. 25. The Future Value of an Investment of $1 in 1926 $40.22 $15.64 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.
    26. 26. Historical Returns, 1926-1999 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. – 90% + 90% 0% Average Standard Series Annual Return Deviation Distribution Large Company Stocks 13.0% 20.3% Small Company Stocks 17.7 33.9 Long-Term Corporate Bonds 6.1 8.7 Long-Term Government Bonds 5.6 9.2 U.S. Treasury Bills 3.8 3.2 Inflation 3.2 4.5
    27. 27. Average Stock Returns and Risk-Free Returns <ul><li>The Risk Premium is the additional return (over and above the risk-free rate) resulting from bearing risk. </li></ul><ul><li>One of the most significant observations of stock market data is this long-run excess of stock return over the risk-free return. </li></ul><ul><ul><li>The average excess return from large company common stocks for the period 1926 through 1999 was 9.2% = 13.0% – 3.8% </li></ul></ul><ul><ul><li>The average excess return from small company common stocks for the period 1926 through 1999 was 13.9% = 17.7% – 3.8% </li></ul></ul><ul><ul><li>The average excess return from long-term corporate bonds for the period 1926 through 1999 was 2.3% = 6.1% – 3.8% </li></ul></ul>
    28. 28. Risk Premiums <ul><li>Rate of return on T-bills is essentially risk-free. </li></ul><ul><li>Investing in stocks is risky, but there are compensations. </li></ul><ul><li>The difference between the return on T-bills and stocks is the risk premium for investing in stocks. </li></ul><ul><li>An old saying on Wall Street is “You can either sleep well or eat well.” </li></ul>
    29. 29. Risk Premia <ul><li>Suppose that The Wall Street Journal announced that the current rate for on-year Treasury bills is 5%. </li></ul><ul><li>What is the expected return on the market of small-company stocks? </li></ul><ul><li>Recall that the average excess return from small company common stocks for the period 1926 through 1999 was 13.9% </li></ul><ul><li>Given a risk-free rate of 5%, we have an expected return on the market of small-company stocks of 18.9% = 13.9% + 5% </li></ul>
    30. 30. The Risk-Return Tradeoff
    31. 31. Rates of Return 1926-1999 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.
    32. 32. Stock Market Volatility 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. The volatility of stocks is not constant from year to year.

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