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### Understanding Rates of Return: Calculating, Comparing, and Estimating Future Investments ###

This chapter delves into the concept of rates of return and their vital role in investment analysis. It covers how to compute returns using various methods, the importance of historical performance in forecasting future returns, and the relationship between risk and return. It discusses metrics such as simple, average, and inflation-adjusted rates, as well as after-tax considerations and the impact of foreign exchange. Gain insights into determining the cost of capital and utilize established guidelines to optimize investment decision-making. ###

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### Understanding Rates of Return: Calculating, Comparing, and Estimating Future Investments ###

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Presentation Transcript

  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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