1 A History of Risk and Return - PowerPoint Presentation

1. 1A History of Risk and Return

2. Careers in FinanceCorporate financeInvestment, Money ManagementBanking (commercial banking, investment banking)InsuranceReal estate financeInternational financeDerivatives (e.g., futures, options, swaps, etc)Risk managementFinancial planning and personal finance……..2

3. 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 risks of various important types of investments.The relationship between risk and return.Learn: normal distribution, kurtosis, geometric average, fat tails, 3

4. Measuring returns4

5. 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.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 will kick in $250 per monthOver the last 81 years, the S&P 500 Index return was about 12%5

6. Dollar ReturnsTotal dollar return is the return on an investment measured in dollars, accounting for all interim cash flows and capital gains or losses.Total percent return is the return on an investment measured as a percentage of the original investment.The total percent return is the return for each dollar invested.6

7. Example: Calculating Total Dollar and Total Percent ReturnsSuppose 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 sharesCapital gain: 40 shares times $14 = $560Dividends: 40 shares times $1.40 = $56Total Dollar Return is $560 + $56 = $616What was your total percent return?Dividend yield = $1.40 / $35 = 4%Capital gain yield = ($49 – $35) / $35 = 40%Total percentage return = 4% + 40% = 44%R = + = + = 4% + 40% = 44% Note that $616 divided by $1400 is 44%.7

8. Compounding Realized Returns Problem: Suppose you purchased Microsoft stock (MSFT) on Nov 1, 2004 and held it for one year, selling on Oct 31, 2005. What was your annual realized return? 8

9. Annualizing ReturnsYou buy 200 shares of Lowe’s Companies, Inc. at $48 per share. Three months later, you sell these shares for $51 per share. You received no dividends. What is your return? What is your annualized return?Return: (Pt+1 – Pt) / Pt = ($51 - $48) / $48 = .0625 = 6.25% 6.25% * 4 = 25.00% (1 + .0625)4 – 1 = 1.2744 – 1 = .2744 or 27.44% Which one is right? Both!!!This return is known as the holding period percentage return.9

10. Annualizing ReturnsThere are two ways to annualize the holding period return.Annual Percentage Return (APR)Effective Annual Return (EAR)APRNominal return or the holding period return times mReturn that ignores the compoundingEARReturn that investors actually earnedReturn that considers the compoundingEAR = (1+ )M – 1 Where M = 1, 2, 4, 12, or 365 10

11. Annualizing ReturnsEffective 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 + EAR = (1 + holding period percentage return)m m = the number of holding periods in a year.In this example, m = 4 (there are 4 3-month holding periods in a year). Therefore:1 + EAR = (1 + .0625)4 = 1.2744. So, EAR = .2744 or 27.44%. 11

12. Annualizing ReturnsYou made five stock investmentsReturn from Boeing = 10% for 3-monthReturn from Intel = 12% for 6-monthReturn from Citi = 15% for 1-yearReturn from Exxon = 7% for 70-dayReturn from ebay = 25% for 2-yearWhich stock performed best???Annualized R (Boeing) = 1.14 -1 = 46.41%Annualized R (Intel) = 1.122 – 1 = 25.44%Annualized R (Citi) = 1.151 -1 = 15.00%Annualized R (Exxon) = 1.07(365/70) – 1 = 42.30%Annualized R (ebay) = 1.25(1/2) -1 = 11.80%12

13. A brief history of return and risk"The four most dangerous words in investing are: 'this time it's different.'"   - Sir John Templeton"History is the version of past events people have decided to agree upon."  - Napoleon Bonaparte13

14. A Brief History of Risk and ReturnOur 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.14

15. A $1 Investment in Different Typesof Portfolios, 1926—2006 & 1926 – 2009 & 1926 -201515

16. Dow Jones Industrial AverageBull Market, Bear MarketsSource: Google Finance16

17. The Historical Record:Total Returns on Large-Company Stocks17

18. The Historical Record: Total Returns on Small-Company Stocks18

19. The Historical Record: Total Returns on Long-term U.S. Bonds19

20. The Historical Record: Total Returns on U.S. T-bills20

21. The Historical Record: Inflation21

22. Historical Average ReturnsA 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 2015, you get about1,067 percent.Because there are 90 returns, the average return is about 11.9%. 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 11.9%.The formula for the historical average return is:This formula says:Starting with the first one, add up each yearly return (S says “sum”) and divide by the number of years, n 22

23. Average Annual Returns and Risk Premiums for Five Portfolios, 1926—2015 23

24. Average Returns: The First LessonRisk-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 1.4, we can see the risk premium earned by large-company stocks was 8.3%!Is 8.3% 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. 24

25. 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.25

26. Historical Returns and Standard Deviations for Select Asset Classes (1900–2014)26

27. Average Annual Stock Returns Around the World1900 - 2014(Source: Elroy Dimson, Paul Marsh, and Mike Staunton, Credit Suisse Global Investment Returns Sourcebook 2015, https://www.credit-suisse.com/investment_banking/doc/cs_global_investment_returns_yearbook.pdf.)27

28. World Stock Market CapitalizationMore than one third of the value of tradable stock is in the U.S.28

29. Measuring risk29

30. 2008: The Bear Growled and Investors Howled30

31. Good Times, Bad Times31

32. Risk: The Other Side of the CoinSources of RiskIn finance, there are two types of risks an investor must deal with. (1) Unsystematic risk (2) Systematic risk : measured by stock betaTherefore, Total Risk = Unsystematic risk + Systematic riskUnsystematic risk is diversifiable.Total risk: measured by standard deviation32

33. Risk: The Other Side of the CoinUnsystematic riskBusiness Risk: the degree of uncertainty associated with an investment’s earnings and the investment’s ability to pay the returns (interest, principal, dividends) that investors expect.Event Risk: occurs when an unexpected event has a significant and unusually immediate effect on the underlying value of an investment.Liquidity Risk: the risk of not being able to sell (liquidate) an investment quickly without reducing its price.Systematic riskPurchasing Power Risk: the chance that unanticipated changes in price levels (inflation or deflation) will adversely affect investment returns. Interest Rate Risk: the chance that changes in interest rates will adversely affect a security’s value.Tax Risk: The chance that Congress will make unfavorable changes in tax laws, driving down the after-tax returns and market values of certain investments.Market Risk: the risk that investment returns will decline because of factors that affect the broader market, not just one company or one investment33

34. Return Variability Review and ConceptsVariance 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.34

35. Return Variability: The Statistical ToolsThe formula for return variance is ("n" is the number of returns):Sometimes, it is useful to use the standard deviation, which is related to variance like this:The variance formula says: Starting with the first return, subtract the average return from it and then square the result. Continue to do so for all “N” returns. Add them all up (S says “sum”). Then, divide by N – 1.35

36. Example: Calculating Historical Variance and Standard DeviationLet’s use data from Table 1.1 for Large-Company Stocks.The spreadsheet below shows us how to calculate the average, the variance, and the standard deviation (the long way…).36

37. Frequency Distribution of Returns on Common Stocks, 1926—201537

38. The Normal Distribution and Large Company Stock Returns38

39. Historical Returns, Standard Deviations, and Frequency Distributions: 1926—201539

40. Returns on Some “Non-Normal” Days40

41. Kurtosis and “Fat Tail” Phenomenon The measure of the degree of “fat tails.”The fourth moment – a positive value of kurtosis implies a fat tailed distribution.Extreme values on either side of the mean at the expense of smaller fraction of moderate deviations.Called, “Black Swan” or “slender shoulders”Symmetry is still observed.A high kurtosis suggest a high frequency of extreme negative returns like Financial Crisis 2008.41

42. “Black Swan”42

43. Normal and Fat-Tailed Distributions43

44. Arithmetic average vs. geometric average44

45. Arithmetic Avg. vs. Geometric Avg.Ex.) Buy a stock for $100. 1st year: falls to $50 2nd year: rises to $100Historical Avg. Return = = = 25% ??? - 50%+ 100%0% or 25%?Geometric Avg. ReturnWhat was your avg. compound return per year?Arithmetic Avg. ReturnWhat was your returns in an average (≈ typical) year? 45

46. Arithmetic Avg. vs. Geometric Avg.Arithmetic Avg. = Geometric Avg. = [(1+R1)(1+R2)…(1+RN)]1/N -1= [(1-.5)(1+1)] 1/2 - 1= [(.5)(2)]1/2 -1= [1]1/2 – 1= 0%  46

47. Example: Calculating a Geometric Average ReturnHere’s how to calculate a geometric average return.47

48. Arithmetic Averages versusGeometric AveragesConceptual Differences: 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?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.48

49. Arithmetic versus Geometric Average49

50. Geometric versus Arithmetic Averages1926-20061926-201250

51. Geometric versus Arithmetic Averages, 1926—2015 51

52. Dollar-weighted average return52

53. Dollar-Weighted Average Returns, IThere is a hidden assumption we make when we calculate arithmetic returns and geometric returns.The hidden assumption is that we assume that the investor makes only an initial investment.Clearly, many investors make deposits or withdrawals through time.How do we calculate returns in these cases? 53

54. Dollar-Weighted Average Returns, IISuppose you had returns of 10% in year one and -5% in year two. If you only make an initial investment at the start of year one:The arithmetic average return is 2.50%.The geometric average return is 2.23%.Suppose you makes a $1,000 initial investment and a $4,000 additional investment at the beginning of year two.At the end of year one, the initial investment grows to $1,100.At the start of year two, your account has $5,100.At the end of year two, your account balance is $4,845.You have invested $5,000, but your account value is only $4,845.So, the (positive) arithmetic and geometric returns are not correct.54

55. Dollar-Weighted Average Returns and IRR55

56. Risk and ReturnThe 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.56

57. Quiz QuestionOver the past 200 years, U.S. Treasury bills have outperformed gold. A) True B) FalseThe 95 percent probability range is equal to the mean plus or minus three standard deviations. A) True B) FalseYou purchased a stock one year ago at $22 a share. The stock pays a quarterly dividend of $1.20. Today, you sold the stock for $24.50 a share. What is your total dollar return? A) $1.20B) $2.50 C) $3.70 D) $4.90 E) $7.3057

58. Quiz QuestionWhich one of the following never had a negative annual return during the period 1926- 2005? A) large-company stocks B) Consumer Price Index C) U.S. Treasury bills D) long-term government bonds E) small-company stocksSmall-company stocks have the _____ and the _____ for the period 1926-2005. A) highest average return; lowest risk premium B) lowest average return; greatest volatility C) highest average return; lowest volatility D) lowest average return; highest risk premium E) highest average return; greatest volatility58

59. Quiz QuestionThe average squared difference between the actual annual returns and the average return for a period of time is measured by the: A) variance. B) risk premium. C) risk-free rate. D) standard deviation. E) geometric average return.Which one of the following categories of investments would you expect to have the highest standard deviation of returns over a long period of time? A) U.S. Treasury bills B) large-company stocks C) short-term corporate bonds D) long-term corporate bonds E) small-company stocks 59

60. Quiz QuestionThe rate of return on Cherry Jalopies, Inc., stock over the last five years was 19 percent, 11 percent, -7 percent, 6 percent, and 9 percent. Over the same period, the return on Straw Construction Company’s stock was 16 percent, 20 percent, -3 percent, 3 percent, and 14 percent. Calculate the variances and the standard deviations for Cherry and Straw. Cherry: RA = 7.6%Var = 1/4[(0.19 − 0.076)2 + (0.11 – 0.076)2 + (-0.07 − 0.076)2 + (0.06 − 0.076)2 + (0.09 −0.076)2] = 0.00898Standard deviation = (0.00898)1/2 = 0.094763 or 9.48% Straw: RB = 10%Var = 1/4[(0.16 – 0.1)2 + (0.2 – 0.1)2 + (-0.03 − 0.1)2 + (0.03 − 0.1)2 + (0.14 − 0.1)2] = 0.00925Standard deviation = (0.00925)1/2 = 0.096177 or 9.62%60