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Chapter 5 Calculating Rates Of Return

Chapter 5 Calculating Rates Of Return. Using Rates Of Return . Uses Comparing investments in different assets Measuring historical performance Determining future investment Estimating the cost of capital Percentage Figures Standard Practice Dollar Amount Meaningless.

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Chapter 5 Calculating Rates Of Return

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  1. Chapter 5Calculating Rates Of Return

  2. Using Rates Of Return • Uses • Comparing investments in different assets • Measuring historical performance • Determining future investment • Estimating the cost of capital • Percentage Figures Standard Practice • Dollar Amount Meaningless

  3. Measuring Historical Performance • Ex-Post Rates of Return • Realized rates of return • Ex-Ante Rates of Return • Expected rates of return • Requires Knowledge of Risk • Risk-return relationship

  4. Determining Future Investment • Estimate • Future return • Future fluctuations of returns • Historical Averages • Give best estimate of future returns • Estimate future fluctuations of returns • Next Year’s Returns • May be dramatically different

  5. Estimating Cost Of Capital • Rates of Return • Used to estimate the firm’s cost of capital • NPV calculations • Utilizing historical rates of return • Calculated in more than one way

  6. Rate-Of-Return Calculations • Different Methods • Yield different results • Could Use Method Giving Best Result • Lack of standard would affect comparability • AIMR • Association of Investment Management and Research • Established strict guidelines

  7. Simple Rates Of Return • HPR • Holding period return EMV - BMV + I R = BMV • Limitations (does not account for) • Timing of cash dividends • Accrued interest

  8. Capital gain or loss Rate of return components Cash flow yield

  9. Approaches To Computing The Rate Of Return • Linking Method • Calculate to each subperiod • Cash dividends date determines subperiod • Simple to calculate • Index Method superior calculation • Cash flows used to purchase additional units • Useful to understanding time weighted computations

  10. Bond Returns • Cash Basis • Ignores accrued interest • Accrual Basis • Bond interest accrues daily • Price paid for bonds • Includes accrued interest • AIMR accepted

  11. After-Tax Rates Of Return • Includes the Impact of Taxes • Ordinary income • Capital gains EMVn - BMVn - N0(Pn - P0)Tg+ In(I - T) Rn = BMVn

  12. Inflation-Adjusted Rates Of Return • Reduction of Purchasing Power • Inflation Measured By CPI • Consumer Price Index • Real Rate of Return CPI1 - CPI0 h = CPI0

  13. Exchange Rates • Falling Dollar • Good for U. S. investors in foreign countries • Bad for foreign investors in U. S. • U. S. industry more competitive • Foreign securities become more valuable • Foreigners shy away from U. S. markets

  14. Rate Of Return Adjusted For Foreign Exchange Risk fxn (DC / FC) RD = (1 + RL) - 1 fx0 (DC / FC) Alternative Method RD = (1 + Rfx) (1 + RL) - 1

  15. Average Rate Of Return • Measuring Returns Across Years • Arithmetic Average • Adds the realized rate of return over different periods • Correct for one period of time • Unbiased estimate of future expected rates of return • Geometric Method • Compounds rates of return • Measures actual growth of assets

  16. Adjusted Rate Of Return • Accounts for the Timing of Cash Dividends • Called Time-Weighted Rate of Return • Called Rate of Return in Rest of Textbook • AIMR Approved

  17. Importance Of Indexes • Stock Indexes • Measure the general performance of an economy • Benchmark For Gauging Performance • Money manager • Bond fund manager • Serves as a Guide for Mutual Fund Performance • Assess Overall Direction of the Market • Estimates Statistical Parameters Beta • Used as Underlying Securities in Derivatives

  18. Indexes Differ • By Which and How Many Securities • By How the Index is Adjusted for Change • By Method Used to Adjust Index

  19. Types Of Indexes • Price-Weighted Index • Value-Weighted Index • Equally Weighted Index

  20. Price-Weighted Index • Value • Found by adding the prices of each security and dividing by a divisor • Divisor • Adjusted for stock dividends and splits and other changes • Easy to Mimic

  21. Value-Weighted Indexes • Value • Based on the total market value of a security • Market Capitalization • The greater the market capitalization the greater the securities influence • Not affected by stock dividends or splits

  22. Equally Weighted Index • Value • Give each security the same weight • Arithmetic Method • Results in higher values than geometric • Multiplicative Method • Geometric

  23. Stock Indexes • Most are Value-Weighted • Automatically adjusting for stock splits • Weight based on market capitalization • Easy to Develop and Maintain

  24. Bond Indexes • Track Different Segments of Bond Market • Incorporate Total Returns (1970’s) • Prior Indexes Ignored Coupon Payments • Bonds Change Because • Of finite maturity change risk • Call features • Pricing Problems Due to Lack of Trading

  25. Differences In Bond Indexes • Weighting Methods • Reinvest of Intramonth Cash Flows • Maturity Structure of Index

  26. Tracking Rates Of Return Over Time • Common Stock is More Volatile than Bonds • Common Stock Offers Higher Return than Bonds • Positive Relationship Between Risk and Return

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