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# L Pch6

## by Nguyen Thuy, Working at Hanoikids on Dec 26, 2009

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## L Pch6Presentation Transcript

• Investments Chapter 6: Rates of Return
• Different Methods yield Different Rates of Return
• Investment managers, who are rated on their performance, have an incentive to use those methods that make them look best.
• Standardisation of Methods
• In response to this incentive the Association of Investment Management and Research (AIMR) has established guidelines to calculate rates of return.
• A global standard is also evolving (the Global Investment Performance Standards).
• Ex-post and Ex-ante Rates of Return
• Ex-post rates of return
• Rates of return that has already been earned.
• Ex-ante rates of return
• Rates of return expected to occur in the future.
• Simple Rate of Return
• Two components included:
• 1. Capital gains or losses.
• 2. Cash flow yield.
• Calculated over the investment period and depicted as a percentage of the dollar amount invested.
• Simple 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.
Time 0 1 Initial investment Ending market value Dividends
• Dollar Return = Dividend + Change in Market Value
Simple Returns
• Adjusted Rate of Return: I
• The simple rate of return does not account for the timing of the cash flows received .
• Two approaches to compute the adjusted rate of return:
• 2. Index method.
• Sample Mean
• Two methods:
• 1. Arithmetic average. 2. Geometric average.
• The arithmetic average doesn’t compound the rates of return. Hence, if the returns are not constant, the arithmetic average is upwardly biased .
• 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 :
• Holding Period Return: Example
• Suppose your investment provides the following returns over a four-year period:
• 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%
• Holding Period Return: Example
• Note that the geometric average is not the same thing as the arithmetic average:
• Arithmetic or Geometric?
• Start with 100, remain 100 first year, decrease to 50 next year and increase to 100 the third year.
• Adjusted Rate of Return: II
• Besides timing of the cash flows, rates of return also need to be adjusted for other developments:
• 1. Stock splits.
• 2. Stock dividends.
• 3. Rights acquired.
• 4. Accrued interest on bonds (accrues daily).
• 5. Changes in the composition of the portfolio.
• Other Complications
• Taxes, inflation and (for foreign investors) exchange rates generally change the return of an investor.
• Solutions:
• 1. After-tax rates of return.
• 2. Inflation-adjusted rates of return.
• 3. Exchange rate-adjusted rates of return.
• INDICES
• An index measures the performance of a certain segment of the financial markets.
• Stock Indexes
• Can be categorized as:
• 1. Price-weighted
• (Example: Dow Jones Industrial Average.)
• 2. Value-weighted
• ( Example: S & P 500.)
• 3. Equally-weighted
• Bond Indices: I
• The set of bonds in a bond index is always changing.
• Reasons:
• 1. Bonds have finite maturities.
• 2. Call features within bonds.
• Sample Return Statistics
• Describe or summarize a sample of past rates of return
• Note: (statistics describing a sample of ex-ante rates of return are discussed in chapter 7).
• 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.
• 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.
• Sample Covariance and Sample Correlation
• Give information on the dependency between various assets and how they move together:
• Covariance (measure of dependence in units such as dollars or percentages).
• Correlation (measure of dependence on a scale of – 1 to +1, thus more comparable).
• Holding Period Returns
• 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.
• 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:
• Large-Company Common Stocks
• Small-company Common Stocks
• Long-Term Corporate Bonds
• Long-Term U.S. Government Bonds
• U.S. Treasury Bills
• 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.
• 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
• 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 market data is this long-run excess of stock return over the risk-free return.
• The average excess return from large company common stocks for the period 1926 through 1999 was 9.2% = 13.0% – 3.8%
• The average excess return from small company common stocks for the period 1926 through 1999 was 13.9% = 17.7% – 3.8%
• The average excess return from long-term corporate bonds for the period 1926 through 1999 was 2.3% = 6.1% – 3.8%