Bob LeClair's Finance and Markets Newsletter For the Week Ending: Change Change 1/1/14 1/4/14 1/11/14 (Week) (Yr-to-Date) Dow Jones Ind. Avg. 16,577 16,470 16,437 (33) (140) (% Change) -0.20% -0.84% S & P 500 Index 1,848 1,831 1,842 11 (6) (% Change) 0.60% -0.32% NASDAQ Composite 4,177 4,132 4,175 43 (2) (% Change) 1.03% -0.05% S & P 500 P/E Ratio S & P 500 Div. Yield T-bill - S&P 500 Yield 19.0 1.94% -1.87% 19.0 1.94% -1.88% 19.0 1.91% -1.86% 0.0 -0.03% 0.02% 0.0 -0.03% 0.02% 30-Year T-Bond Yield 10-Year T-Bond Yield 91-Day T-Bill Yield Yield Spread 3.97% 3.03% 0.07% 3.90% 3.93% 2.99% 0.07% 3.87% 3.80% 2.86% 0.06% 3.75% -0.13% -0.13% -0.01% -0.12% -0.17% -0.17% -0.02% -0.16% 30-Year Mortgage 15-Year Mortgage 1-Year Adjustable Rate 30-Yr. - 1-Yr. ARM Rate 4.48% 3.52% 2.56% 1.92% 4.53% 3.55% 2.56% 1.97% 4.51% 3.56% 2.56% 1.95% -0.02% 0.01% 0.00% -0.02% 0.03% 0.04% 0.00% 0.03% $ Value of Euro (€) Japanese Yen (¥/$) Crude Oil, Spot Price Gasoline, Reg. ($/Gal.) $1.3754 105.33 $98.42 $3.32 $1.3589 104.86 $95.44 $3.33 $1.3665 104.17 $91.66 $3.31 $0.0076 -0.69 -$3.78 -$0.01 -$0.0089 -1.16 -$6.76 -$0.01 2 3 Chapter 1 McGraw-Hill/Irwin A Brief History of Risk and Return Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Learning Objectives To become a wise investor (maybe even one with too much money), you need to know: • How to calculate the return on an investment using different methods. • The historical returns on various important types of investments. • The historical risk on various important types of investments. • The relationship between risk and return. 1-5 A Brief History of Risk and Return • Our goal in this chapter is to see what financial market history can tell 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. • These observations are important investment guidelines. 1-8 Return on Investment • “The level of profit from an investment - the reward for investing.” • Postponement of consumption 9 Components of Return • Current income: – dividends (stocks) – interest (bonds) – rent (real estate) • Capital Gain (Loss): – change in market value 10 “Total Return” • “The sum of the current income and the capital gain (or loss) earned on an investment over a specified period of time.” 11 Total Return Income Capital Gain (Loss) Total Return Income Capital Gain (Loss) TR I (EV - BV) Total Return Income Capital Gain (Loss) TR I (EV - BV) TR(%) I (EV - BV) BV Total Return (%) • • • • • • TR(%) = (I + (EV – BV)) ÷ BV I ÷ BV = ??? I ÷ BV = Dividend Yield (EV – BV) ÷ BV = ??? (EV – BV) ÷ BV = Capital Gain Yield Total Return = Dividend Yield + Capital Gain yield Example: Calculating Total Dollar and Total Percent Returns • • • Suppose you invested $1,400 in a stock with a share price of $35. After one year, the stock price per share is $49. Also, for each share, you received a $1.40 dividend. • What was your total dollar return? – – – – • $1,400 / $35 = 40 shares Capital gain: 40 shares times $14 = $560 Dividends: 40 shares times $1.40 = $56 Total Dollar Return is $560 + $56 = $616 What was your total percent return? – – – Dividend yield = $1.40 / $35 = 4% Capital gain yield = ($49 – $35) / $35 = 40% Total percentage return = 4% + 40% = 44% Note that $616 divided by $1,400 is 44%. 1-19 Annualizing Returns, I • You buy 200 shares of Lowe’s Companies, Inc. at $18 per share. Three months later, you sell these shares for $19 per share. You received no dividends. What is your return? What is your annualized return? • Return: (Pt+1 – Pt) / Pt = ($19 - $18) / $18 = .0556 = 5.56% This return is known as the holding period percentage return. • Effective Annual Return (EAR): The return on an investment expressed on an “annualized” basis. Key Question: What is the number of holding periods in a year? 1-20 Annualizing Returns, II 1 + EAR = (1 + holding period percentage return)m m = the number of holding periods in a year. • In this example, m = 4 (12 months / 3 months). Therefore: 1 + EAR = (1 + .0556)4 = 1.2416. So, EAR = .2416 or 24.16%. 1-21 $1 Invested in Different Portfolios: 1926-2009 Investment Ending Value ($) Small-Company Stocks 12,971.38 Large-Company Stocks 2,382.68 L-T Govt. Bonds 75.33 U. S. Treasury Bills 22.33 Inflation 12.06 22 A $1 Investment in Different Types of Portfolios, 1926—2009 The Historical Record: Total Returns on Large-Company Stocks The Historical Record: Total Returns on Small-Company Stocks The Historical Record: Total Returns on Long-term U.S. Bonds The Historical Record: Total Returns on U.S. T-bills The Historical Record: Inflation Holding Period Return (HPR) • “The total return earned from holding an investment for a specified holding period (usually 1 year or less).” HPR I (V e V b ) Vb 30 S & P 500 Annual Returns Year Total Return (%) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 +37.58 +22.96 +33.36 +28.58 +21.04 -9.10 -11.89 -22.10 +28.69 +10.88 S & P 500 Annual Returns Year Total Return (%) 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 +28.69 +10.88 + 4.91 +15.79 + 5.49 - 37.00 +26.46 +15.06 + 2.05 +16.00 S & P 500 Annual Returns Year Total Return (%) 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 +10.88 + 4.91 +15.79 + 5.49 - 37.00 +26.46 +15.06 + 2.05 +16.00 ?????? S & P 500 Annual Returns Year Total Return (%) 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 +10.88 + 4.91 +15.79 + 5.49 - 37.00 +26.46 +15.06 + 2.05 +16.00 +32.40 Historical Average Returns • A useful number to help us summarize historical financial data is the simple, or arithmetic average. • Using the data in Table 1.1, if you add up the returns for large-company stocks from 1926 through 2009, you get about 987 percent. • Because there are 84 returns, the average return is about 11.75%. How do you use this number? • If you are making a guess about the size of the return for a year selected at random, your best guess is 11.75%. • The formula for the historical average return is: n Historical Average Return yearly return i1 n 1-39 Average Annual Returns for Five Portfolios and Inflation Table 1.3: Historical Returns & Risk Premiums (1926-2009) Investment Avg. Return Premium Large Co. Stocks 11.7% 7.9% Small Co. Stocks 17.7% 13.9% L-T Corp. Bonds 6.5% 2.7% L-T Govt. Bonds 5.9% 2.1% U. S. T-bills 3.8% 0.0% Average Returns: The First Lesson • Risk-free rate: The rate of return on a riskless, i.e., certain investment. • Risk premium: The extra return on a risky asset over the risk-free rate; 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 by large-company stocks was 7.9%! – Is 7.9% a good estimate of future risk premium? – The opinion of 226 financial economists: 7.0%. – Any estimate involves assumptions about the future risk environment and the risk aversion of future investors. Why Does a Risk Premium Exist? • Modern investment theory centers on this question. • Therefore, we will examine this question many times in the chapters ahead. • We can examine part of this question, however, by looking at the dispersion, 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 the risk. 1-46 Return Variability: The Statistical Tools • The formula for return variance is ("n" is the number of returns): R N VAR(R) σ 2 i R 2 i1 N 1 • Sometimes, it is useful to use the standard deviation, which is related to variance like this: SD(R) σ VAR(R) Return 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 frequency distribution that can be described with only an average and a standard deviation. • Does a normal distribution describe asset returns? Frequency Distribution of Returns on Common Stocks, 1926—2009 Historical Returns & Standard Deviations, 1926-2009 Series Avg. Return Std. Dev. Large Co. Stocks 11.7% 20.5% Small Co. Stocks 17.7% 6.5% 5.9% 5.6% 3.8% 3.1% 37.1% 7.0% 11.9% 8.1% 3.1% 4.2% L-T Corp. Bonds L-T Govt. Bonds Int.-Term Govts. U. S. T-bills Inflation (CPI) 52 Historical Returns, Standard Deviations, and Frequency Distributions: 1926—2009 The Normal Distribution and Large Company Stock Returns Arithmetic Averages versus Geometric Averages • The arithmetic average return answers the question: “What was your return in an average year over a particular period?” • The geometric average return answers the question: “What was your average compound return per year over a particular period?” • When should you use the arithmetic average and when should you use the geometric average? • First, we need to learn how to calculate a geometric average. 1-56 Arithmetic Averages versus Geometric Averages • The arithmetic average tells you what you earned in a typical year. • The geometric average tells you what you actually earned per year on average, compounded annually. • When we talk about average returns, we generally are talking about arithmetic average returns. • For the purpose of forecasting future returns: – The arithmetic average is probably "too high" for long forecasts. – The geometric average is probably "too low" for short forecasts. Compound Annual Return • Geometric mean return GM n (1 r1 )(1 r2 )...( 1 rn ) 1 59 Compound Annual Return on the S&P 500, 1995-99 GM 95 99 5 (1 . 37 )( 1 . 23 )( 1 . 33 )( 1 . 28 )( 1 . 21 ) 1 60 Compound Annual Return on the S&P 500, 1995-99 GM GM 95 99 5 (1 . 37 )( 1 . 23 )( 1 . 33 )( 1 . 28 )( 1 . 21 ) 1 95 99 5 3 . 4711 1 61 Compound Annual Return on the S&P 500, 1995-99 95 99 5 (1 . 37 )( 1 . 23 )( 1 . 33 )( 1 . 28 )( 1 . 21 ) 1 GM 95 99 5 3 . 4711 1 GM 95 99 1 . 2826 1 28 . 26 % GM 62 Risk and Return • The risk-free rate represents compensation for just waiting. • Therefore, this is often called the time value of money. • First Lesson: If we are willing to bear risk, then we can expect to earn a risk premium, at least on average. • Second Lesson: Further, the more risk we are willing to bear, the greater the expected risk premium. 1-64 Historical Risk and Return Trade-Off A Look Ahead • This textbook focuses exclusively on financial assets: stocks, bonds, options, and futures. • You will learn how to value different assets and make informed, intelligent decisions about the associated risks. • You will also learn about different trading mechanisms and the way that different markets function. 1-69 Useful Internet Sites • cgi.money.cnn.com/tools/millionaire/millionaire.html (millionaire link) • finance.yahoo.com (reference for a terrific financial web site) • www.globalfinancialdata.com (reference for historical financial market data—not free) • www.robertniles.com/stats (reference for easy to read statistics review) 1-70 Assignment • Calculate the compound annual return (geometric mean) of the Standard & Poor’s 500 Stock Index for the period 2004-2013. • S&P 500 Return2004-2013 = ??? Problems: Chapter 2 • 2.19 • 2.20 • 2.25