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Learning about Return and Risk from The Historical Record

Learning about Return and Risk from The Historical Record. Chapter 5. Determinants of the level of Interests. Real and Nominal rates of Interest The equilibrium Real Rate of Interest The equilibrium Nominal Rate of Interest Taxes and Real Rate of Interest more….

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Learning about Return and Risk from The Historical Record

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  1. Learning about Return and Risk from The Historical Record Chapter 5 Bodi Kane Marcus Ch 5

  2. Bodi Kane Marcus Ch 5 Determinants of the level of Interests • Real and Nominal rates of Interest • The equilibrium Real Rate of Interest • The equilibrium Nominal Rate of Interest • Taxes and Real Rate of Interest more…

  3. Fisher effect: Approximation nominal rate = real rate + inflation premium R = r + i or r = R - i Example r = 3%, i = 6% R = 9% = 3% + 6% or 3% = 9% - 6% Fisher effect: Exact r = (R - i) / (1 + i) 2.83% = (9%-6%) / (1.06) Empirical Relationship: Inflation and interest rates move closely together Bodi Kane Marcus Ch 5 Real vs. Nominal Rates

  4. Supply • Households • Demand • Businesses • Government’s Net Supply and/or Demand • Federal Reserve Actions Bodi Kane Marcus Ch 5 Factors Influencing Rates

  5. The equilibrium Real Rate of Interest Interest Rates Supply r1 r0 Demand Q0 Q1 Funds Bodi Kane Marcus Ch 5 Pergeserankurva Demand kekanandapatterjadikarenapemerintahmenerapkan budget deficit  permintaanakanuangmeningkat  interest rate naik

  6. Bodi Kane Marcus Ch 5 Risk and Risks Premium • Holding Period Returns • Expected Return and Standard Deviation • Excess Returns and Risk Premiums more……

  7. Bodi Kane Marcus Ch 5 Holding Period Returns Rates of Return: Single Period HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one

  8. Ending Price ($) = 48 Beginning Price ($) = 40 Dividend ($) = 2 HPR = (48 - 40 + 2 )/ (40) = 25% Bodi Kane Marcus Ch 5 Rates of Return: Single Period Example

  9. 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2 Bodi Kane Marcus Ch 5 Characteristics of Probability Distributions

  10. Bodi Kane Marcus Ch 5 Characteristics of Probability Distributions • Mean: The simple mathematical average of a set of two or more numbers 2) Variance : A measure of the dispersion of a set of data points around their mean value.  • Variance is a mathematical expectation of the average squared deviations from the mean. 3) Skewness : an asymmetry in the distribution of the data values

  11. Bodi Kane Marcus Ch 5 The Coefficient of Variation (CV) • A statistical measure of the dispersion of data points in a data series around the mean. It is calculated as follows: The coefficient of variation represents the ratio of the standard deviation to the mean. In the investing world, CV determine how much volatility (risk) in comparison to the amount of return you can expect from your investment. Source: Investopedia

  12. Bodi Kane Marcus Ch 5 Normal Distribution s.d. s.d. r Symmetric distribution

  13. E ( r ) = p ( s ) r ( s ) s Bodi Kane Marcus Ch 5 Measuring Mean: Scenario or Subjective Returns Subjective returns p(s) = probability of a state r(s) = return if a state occurs 1 to s states

  14. Numerical Example: Subjective or Scenario Distributions Bodi Kane Marcus Ch 5 StateProb. of State r in State 1 .1 -.05 2 .2 .05 3 .4 .15 4 .2 .25 5 .1 .35 E(r) = (.1)(-.05) + (.2)(.05)...+ (.1)(.35) E(r) = .15

  15. 2 Variance = p ( s ) [ r - E ( r )] s s Bodi Kane Marcus Ch 5 Subjective or Scenario Measuring Variance or Dispersion of Returns Standard deviation = [variance]1/2 Using Our Example: Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2...+ .1(.35-.15)2] Var= .01199 S.D.= [ .01199] 1/2 = .1095

  16. Geom. Arith. Stan. Series Mean% Mean%Dev.% Large Stock 10.5 12.5 20.4 Small Stock 12.6 19.0 40.4 LongT Gov 5.0 5.3 8.0 T-Bills 3.7 3.8 3.3 Inflation 3.1 3.2 4.5 Bodi Kane Marcus Ch 5 Annual Holding Period Returns

  17. Bodi Kane Marcus Ch 5 Expected Return and Standard Deviation • Spreadsheet 5.1

  18. Bodi Kane Marcus Ch 5 TeknisPenghitungan • Expected Value • Jumlahkanhasilperkalianprobabilitasdengan HPR • Standard Deviation of HPR • Deviasi= HPR dikurangi mean • KuadratkanDeviasi • Kalikanprobabilitas dg Dev2 • Jumlahkan (p* Dev2 ), kemudianpangkat-kan (0.5) ataudiakar • Excess Return • HPR dikurangi RFR • Squared Deviations (Dev2 ) Excess Return • Excess Return dikurangi risk premium, kemudiandikuadratkan • Standard Deviation of Excess Return • Kalikanprobabilitas dg Dev2 Excess Return • Jumlahkan (p* Dev2 ), kemudianpangkat-kan (0.5) ataudiakar

  19. Bodi Kane Marcus Ch 5 Expected Return and Standard Deviation • Problem 5-7 page 151

  20. Bodi Kane Marcus Ch 5 Excess Returns and Risk Premiums • Excess Returns : Returns in excess of the risk-free rate or in excess of a market measure, such as an index fund. • When you have excess returns you are making more money than if you put your money into an index fund like the Dow Jones Industrial Average (DJIA). • Risk Premiums : The return in excess of the risk-free rate of return that an investment is expected to yield.  • An asset's risk premium is a form of compensation for investors who tolerate the extra risk - compared to that of a risk-free asset - in a given investment. Source: Investopedia

  21. Bodi Kane Marcus Ch 5 Time Series Analysis of Past Rates of Return • Time Series versus Scenario Analysis • Expected Returns and the arithmetic Average • The Geometric (Time Weighted) Average Return • The Reward to Volatility (Sharpe) Ratio

  22. Bodi Kane Marcus Ch 5 Time Series Analysis of Past Rates of Return • Time Series versus Scenario Analysis • Time Series Analysis • useful to see how a given asset, security or economic variable changes over time or how it changes compared to other variables over the same time period • Scenario Analysis: The process of estimating the expected value of a portfolio after a given period of time, assuming specific changes in the values of the portfolio's securities or key factors that would affect security values, such as changes in the interest rate. Source: Investopedia

  23. the arithmetic mean of a stock's closing price = $ 74.00 / 5 = $14.80. Bodi Kane Marcus Ch 5 Time Series Analysis of Past Rates of Return • The arithmetic Average: A mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series. Source: Investopedia The arithmetic mean of a stock's closing price = $ 74.00 / 5 = $14.80.

  24. Bodi Kane Marcus Ch 5 Time Series Analysis of Past Rates of Return • The Geometric (Time Weighted) Average Return: The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio.  • The Geometric = {(1+ r1)*(1+r2)*…*(1+rn)} 1/n -1 Average Return more……

  25. Illustration Geometric Mean • Geometric Mean • [(1.15) x(1.20) x (0.80)]1/3 – 1 • = (1.104) 1/3 -1 =0.03353 = 3.353%

  26. Bodi Kane Marcus Ch 5 Time Series Analysis of Past Rates of Return • The Reward to Volatility (Sharpe) Ratio: A ratio developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance.  • The Sharpe ratio is calculated by subtracting the risk-free rate  from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns Source: Investopedia

  27. Bodi Kane Marcus Ch 5 The Normal Distribution Problem 5.6/ CFA Problem/p.153

  28. Bodi Kane Marcus Ch 5 Deviations from Normality Positively skewed Negatively skewed

  29. Bodi Kane Marcus Ch 5 The Historical Record of Returns on Equities and Long Term Bonds • Average Returns and Standard Deviations • Other statistics of Risky Portfolios • Sharpe Ratios • Serial Correlation • Skewness and Kurtosis • Estimates of Historical Risk Premiums • A Global View of the Historical Record more……

  30. Bodi Kane Marcus Ch 5 Average Returns and Standard Deviation

  31. Bodi Kane Marcus Ch 5 Measurement of Risk with non Normal Distributions • Value at Risk (VaR) : A technique used to estimate the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities. • Conditional Tail Expectation (CTE) : an important actuarial risk measure and a useful tool in financial risk assessment. • Lower Partial Standard Deviation (LPSD) : Compute expected lower partial moments for normal asset returns

  32. Bodi Kane Marcus Ch 5 Lower Partial Standard Deviation (LPSD) • Measure of risk non normal distributions • The LPSD for the large and small stock portfolios are not very different from value from the normal distributions because the skews are similar to those from the normal (see Table 5.5)

  33. Risk Real Series Premiums% Returns% LgStk 8.7 9.3 SmStk 15.2 15.8 LT Gov 1.5 2.1 T-Bills 0 0.6 Inflation 0.6 Bodi Kane Marcus Ch 5 Annual Holding Period Risk Premiums and Real Returns

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