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Chapter 6 The Returns and Risks from Investing

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Explain the relationship between return and risk. Sources of risk. Methods of measuring returns. Methods of measuring risk. Measuring historical returns and risks of major financial assets. Learning Objectives

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Function of both return and risk – At the centre of security analysis How should realized return and risk be measured? – The realized risk-return tradeoff is based on the past – The expected future risk-return tradeoff is uncertain and may not occur Asset Valuation

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Returns consist of two elements: – Yield: Periodic cash flows such as interest or dividends (income return) “Yield” measures relate income return to a price for the security – Capital Gain or Loss: Price appreciation or depreciation The change in price of the asset Total Return = Yield + Price Change Return Components

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Interest Rate Risk –Affects market value and resale price Market Risk –Overall market effects Inflation Risk – Purchasing power variability Business Risk Financial Risk – Tied to debt financing Liquidity Risk – Time and price concession required to sell security Exchange Rate Risk Country Risk – Potential change in degree of political stability Risk Sources

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Two general types: – Systematic (market) risk economy wide factors that impact returns – Non-systematic (non-market) risk Unique characteristics specific to a security Total Risk measured by volatility Systematic risk measured by beta Risk Types

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Total Return is a percentage relating all cash flows received during a given time period, denoted CF t +(P E - P B ), to the start of period price, P B Measuring Returns

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Total Return can be either positive or negative – When cumulating or compounding, negative returns are a problem A Return Relative solves the problem because it is always positive Measuring Returns

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To measure the level of wealth created by an investment rather than the change in wealth, returns need to be cumulated over time Cumulative Wealth Index, CWI n, over n periods, =

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International returns include any realized exchange rate changes – If foreign currency depreciates, returns are lower in domestic currency terms Total Return in domestic currency = Measuring International Returns

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TR, RR, and CWI are useful for a given, single time period What about summarizing returns over several time periods? –Arithmetic mean and geometric mean Arithmetic mean, or simply mean Measures Describing a Return Series

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Arithmetic mean does not measure the compound growth rate over time – Does not capture the realized change in wealth over multiple periods – Does capture typical return in a single period Geometric mean reflects compound, cumulative returns over more than one period Arithmetic Versus Geometric

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Geometric mean defined as the n-th root of the product of n return relatives minus one, or G = Difference between Geometric mean and Arithmetic mean depends on the variability of returns, s Geometric Mean

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Returns measures are not adjusted for inflation – Purchasing power of investment may change over time – Consumer Price Index (CPI) is a possible measure of inflation Inflation-Adjusted Returns

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Risk is the chance that the actual outcome will be different than the expected outcome Standard Deviation measures the deviation of returns from the mean Measuring Risk

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Premium is additional return earned or expected for additional risk – Calculated for any two asset classes Equity risk premium is the difference between stock and risk-free returns Bond default premium is the difference between the return on long term corporate bonds and long term government bonds Risk Premiums

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Equity Risk Premium, ERP, = Risk Premiums

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Since 1938, cumulative wealth indexes show stock returns dominate bond returns – Stock standard deviations also exceed bond standard deviations Annual geometric mean return for the time period between 1938 and 2003 for Canadian common stocks is 10.32% with standard deviation of 16.36% The Risk-Return Record

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SeriesGeom Mean Arithm Mean Standard Deviation Canadian Common Stocks 10.32%11.53%16.36% US Common Stocks 12.09%13.5%17.67% Long-term Government of Canada Bonds 6.07%6.46%9.39% T-bills 5.20%5.28%4.36% Inflation (CPI) 3.97%4.05%3.63% Annual Total Returns (1938-2003)

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On an inflation-adjusted basis Cumulative Wealth Indexes

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