Chapter 6 The Returns and Risks from Investing

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

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

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

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

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

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

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

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, =

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

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

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

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

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

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

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

Equity Risk Premium, ERP, = Risk Premiums

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

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 ( )

On an inflation-adjusted basis Cumulative Wealth Indexes