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ChapterMcGraw-Hill/IrwinCopyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.1A Brief History ofRisk and Return1-2Example I: Who Wants To Be A Millionaire?• You can retire with One Million Dollars (or more).• How? Suppose:– You invest $300 per month.– Your investments earn 9% per year.– You decide to take advantage of deferring taxes on your investments.• It will take you about 36.25 years. Hmm. Too long.1-3Example II: Who Wants To Be A Millionaire?• Instead, suppose:– You invest $500 per month.– Your investments earn 12% per year– you decide to take advantage of deferring taxes on your investments• It will take you 25.5 years.• Realistic?• $250 is about the size of a new car payment, and perhaps your employer willkick in $250 per month• Over the last 80 years, the S&P 500 Index return was about 12%Try this calculator: cgi.money.cnn.com/tools/millionaire/millionaire.html1-4A Brief History of Risk and Return• Our goal in this chapter is to see what financial market history cantell us about risk and return.• There are two key observations:– First, there is a substantial reward, on average, for bearing risk.– Second, greater risks accompany greater returns.1-5Dollar Returns• Total dollar return is the return on an investment measured indollars, accounting for all interim cash flows and capital gains orlosses.•Example:Loss) (or Gain Capital Income Dividend Stock a on Return Dollar Total+=1-6Percent Returns• Total percent return is the return on an investment measured as apercentage of the original investment.• The total percent return is the return for each dollar invested.• Example, you buy a share of stock:)Investment Beginning (i.e., Price Stock BeginningStock a on Return Dollar Total Return Percentor Price Stock BeginningLoss) (or Gain Capital Income Dividend Stock a on Return Percent=+=1-7Example: Calculating Total Dollarand Total Percent Returns• Suppose you invested $1,000 in a stock with a share price of $25.• After one year, the stock price per share is $35.• Also, for each share, you received a $2 dividend.• What was your total dollar return?– $1,000 / $25 = 40 shares– Capital gain: 40 shares times $10 = $400– Dividends: 40 shares times $2 = $80– Total Dollar Return is $400 + $80 = $480• What was your total percent return?– Dividend yield = $2 / $25 = 8%– Capital gain yield = ($35 – $25) / $25 = 40%– Total percentage return = 8% + 40% = 48%Note that $480divided by$1000 is 48%.1-8A $1 Investment in Different Typesof Portfolios, 1926—2005.1-9Financial Market History1-10The Historical Record:Total Returns on Large-Company Stocks.1-11The Historical Record:Total Returns on Small-Company Stocks.1-12The Historical Record: Total Returns on U.S. Bonds.1-13The Historical Record:Total Returns on T-bills.1-14The Historical Record:Inflation.1-15Historical Average Returns• A useful number to help us summarize historical financial data is thesimple, or arithmetic average.• Using the data in Table 1.1, if you add up the returns for large-companystocks from 1926 through 2005, you get about 984 percent.• Because there are 80 returns, the average return is about 12.3%. Howdo you use this number?• If you are making a guess about the size of the return for a year selectedat random, your best guess is 12.3%.• The formula for the historical average return is:nreturnyearly Return AverageHistoricaln1i==1-16Average Annual Returns for Five Portfolios1-17Average Returns: The First Lesson• Risk-free rate: The rate of return on a riskless, i.e., certaininvestment.• Risk premium: The extra return on a risky asset over the risk-freerate; i.e., the reward for bearing risk.• The First Lesson: There is a reward, on average, for bearing risk.• By looking at Table 1.3, we can see the risk premium earned bylarge-company stocks was 8.5%!1-18Average Annual RiskPremiums for Five Portfolios1-19Why Does a Risk Premium Exist?• Modern investment theory centers on this question.• Therefore, we will examine this question many times in the chaptersahead.• However, we can examine part of this question by looking at thedispersion, or spread, of historical returns.• We use two statistical concepts to study this dispersion, or variability:variance and standard deviation.• The Second Lesson: The greater the potential reward, the greater therisk.1-20Return Variability: The Statistical Tools• The formula for return variance is ("n" is the number of returns):• Sometimes, it is useful to use the standard deviation, which isrelated to variance like this:()1NRR ó VAR(R)N1i2i2===VAR(R) ó SD(R) ==1-21Return Variability Review and Concepts• Variance is a common measure of return dispersion. Sometimes,return dispersion is also call variability.• Standard deviation is the square root of the variance.– Sometimes the square root is called volatility.– Standard Deviation is handy because it is in the same "units" as the average.• Normal distribution: A symmetric, bell-shaped frequencydistribution that can be described with only an average and astandard deviation.• Does a normal distribution describe asset returns?1-22Frequency Distribution of Returns onCommon Stocks, 1926—20051-23Example: Calculating Historical Varianceand Standard Deviation• Let’s use data from Table 1.1 for large-company stocks.• The spreadsheet below shows us how to calculate the average, thevariance, and the standard deviation (the long way…).(1) (2) (3) (4) (5)Average Difference: Squared:Year Return Return: (2) - (3) (4) x (4)1926 13.75 12.12 1.63 2.661927 35.70 12.12 23.58 556.021928 45.08 12.12 32.96 1086.361929 -8.80 12.12 -20.92 437.651930 -25.13 12.12 -37.25 1387.56Sum: 60.60 Sum: 3470.24Average: 12.12 Variance: 867.5629.45Standard Deviation:1-24Historical Returns, Standard Deviations, andFrequency Distributions: 1926—20051-25The Normal Distribution andLarge Company Stock Returns1-26Key facts on Normal Distribution• The normal distribution is completely described by itsmean and standard deviation• The normal distribution is symmetric• The standard normal distribution has mean 0 andstandard deviation 1.• The probability of being within 1 standard deviation of themean is about 2/3• The probability of being within 2 standard deviations ofthe mean is about .95• The probability of being within 3 standard deviations ofthe mean is about .99• Real world returns are asymmetric


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UCSC ECON 80H - A Brief History of Risk and Return

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