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Lessons from Capital Market History: Risk-Return Trade-off

Explore the rewards and risks of investing in financial markets and learn how to calculate dollar returns, percentage returns, and risk premiums. Understand the importance of financial markets in providing access to capital and information about required returns.

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Lessons from Capital Market History: Risk-Return Trade-off

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  1. Some Lessons from Capital Market HistoryChapter 12 • We can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets We can learn lessons from capital market history: • There is a reward for bearing risk • The greater the potential reward, the greater the risk • Hence, there is a risk-return trade-off

  2. $ - Dollar Returns Total dollar return = income from investment + capital gain (loss) due to change in price Example: • You bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. • What is your total dollar return? • Interest Income = 30 + 30 = 60 • Capital gain = 975 – 950 = 25 • Total dollar return = 60 + 25 = $85

  3. % - Percentage Returns • It is generally more intuitive to think in terms of percentages than in dollar returns • Dividend yield = income / beginning price • Capital gains yield = (ending price – beginning price) / beginning price • Total percentage return = dividend yield + capital gains yield

  4. Calculating Returns • You bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40. • What is your dollar return? • Dollar return = 1.25 + (40 – 35) = $6.25 • What is your percentage return? • Dividend yield = 1.25 / 35 = 3.57% • Capital gains yield = (40 – 35) / 35 = 14.29% • Total percentage return = 3.57 + 14.29 = 17.86%[ or 6.25/35 = .1786 ]

  5. The Importance of Financial Markets • Financial markets allow companies, governments and individuals to increase their utility • Savers have the ability to invest in financial assets so that they can defer consumption and earn a return to compensate them for doing so • Borrowershave better access to the capital that is available so that they can invest in productive assets • Financial markets also provide us with informationabout the returns that are required for various levels of risk

  6. FIGURE 10.4A $1 investment in different types of portfolios: 1925–2014 (year-end 1925 = $1) FIGURE 10.4A $1 investment in different types of portfolios: 1925–2014 (year-end 1925 = $1)

  7. ACTUAL RETURNS IN THE MARKET STOCKS vs. LONG GOVERNMENT BONDS vs. T-BILLS Large Stock Returns Bond Returns T-bill Returns http://www.investorsfriend.com/stocksriskierthanbonds.htm

  8. Year-to-Year Total Returns Large-Company Stock Returns 1926-2014 Swings up and down of 40% occur

  9. Small-Company Stock Returns 1926-2014 Notice Wilder Swings of 50%

  10. Total Return on Bonds and T-Bills 1925-2014

  11. Year-to-Year Inflation Rates 1926 – 2014 Deflation is uncommon but serious Deflation

  12. Returns by Year

  13. Historical Average Returns • Historical Average Return = simple, or arithmetic average • Using the data in Table in slide 12: • Sum the returns for large-company stocks from 1926 through 2014, you get about 1077% / 89 years = 12.1%. • Your best guess about the size of the return for a year selected at random for large company stock is 12.1%.

  14. Average Returns 1926 - 2014

  15. Risk Premiums • The expected return on asset i is Ri. • Treasury bills are considered to be risk-free (Rf) • The risk premium is the return over and above the risk-free rate • Risk Premium = Ri - Rf

  16. Historical Risk Premium Calculations Table for 1926-2014 • Large Stocks: 12.1 – 3.5 = 8.6% • Small Stocks: 16.7 – 3.5 = 13.2% • L/T Corporate Bonds: 6.4 – 3.5 = 2.9% • L/T Government Bonds: 6.1 – 3.5 = 2.6% • U.S. Treasury Bills: 3.5 – 3.5 = 0 • EAFE Index 9.5 – 3.5 = 6.0% • Europe Australasia and Far East (1970-2009)

  17. Average Annual Returns and Risk Premiums Whydo these risk premia vary?

  18. Fig 12.13 Risk Premiums for 17 Countries Perhaps 8.2% US risk premium is too high. Here it is 7.4% and above average. Data ending 2007.

  19. Frequency Distribution of Returns1926 - 2018 2017 Stock Market Returns 26 negative years 67 positive years 67/93 = 72%positive 2018 2016 2015

  20. The Normal Distribution Fig 12.11

  21. Variance and Standard Deviation • Variance and standard deviation measure the volatility of asset returns • The greater the volatility, the greater the uncertainty • Historical (or sample) variance = sum of squared deviations from the mean / (number of observations – 1) • Standard deviation = square root of the variance s measured in units similar to the average

  22. Return Variability: The Statistical Tools forHistorical Returns • Return variance: (“T" =number of returns) • Standard Deviation:

  23. Finding the Standard Deviation • The variance is the sum of the squared deviations, .0270, divided by the number of returns less 1. Let Var(R), or σ2 (read this as “sigma squared”), stand for the variance of the return: • The standard deviation is the square root of the variance. So, if SD(R), or σ, stands for the standard deviation of the return:

  24. Calculating Std. Dev. with Integers or Decimals • If your data is in decimals, such as .05, .10, and 15, the standard deviation will also be decimals, such as s = .05 • If your data is in integers, such as 5%, 10%, and 15%, the standard deviation will also be in integers, as in s = 5% • Variances are often weirdly large or weirdly small. Use standard deviations.

  25. Example: Calculating Historical Variance and Standard Deviation Using data from Table for large-company stocks:

  26. Excel Works Well for Standard Deviations • Sample standard deviation in Excel is @stdev(observations). • Sample variance in Excel is @var(observations) Notice that the mean is 10% and the standard deviation is 5%. These describe the distribution compactly.

  27. Arithmetic vs.Geometric Mean Arithmetic average – return earned in an average period over multiple periods • Arithmetic average = (R1 + R2 +… + RN ) / N Geometric average – the average compound return per period over multiple periods {holding period return} • Geometric average = [(1+R1)(1+R2)…(1+RN)]1/N - 1 • geometric average < arithmetic average • unless all the returns are equal, when they are the same

  28. Which is Better? • The arithmetic average is overly optimistic for long horizons • The geometric average is overly pessimistic for short horizons • So the answer depends on the planning period under consideration. The book suggests: • 15 – 20 years or less: use arithmetic • 20 – 40 years or so: split the difference between them • 40 + years: use the geometric • Prof Marcus likes GEOMETRIC as reflecting what your holding period return was regardless.

  29. Example: Computing Averages • What is the arithmetic and geometric average for the following returns? Year 1 5% Year 2 -3% Year 3 12% Arithmetic average= (5 + (–3) + 12) /3 = 4.67%(higher) Geometric average = [(1+.05)*(1-.03)*(1+.12)]1/3 – 1 = .0449 = 4.49% (lower) RA > RG

  30. My Favorite Extreme Example • Two years • Lose 50% in first year and gain 100% in two periods. • Arithmetic return = 25%. • Geometric return = (.5)(2)½ – 1 = 0% • If invest $1000, then at end of year 1 have only $500, and by end of year 2 have $1,000. • Which reflects my true holding period return?

  31. Efficient Capital Markets • Stock prices are in equilibrium or are “fairly” priced • If this is true, then you should not be able to earn “abnormal” or “excess” returns • Efficient markets DO NOT imply that investors cannot earn a positive return in the stock market

  32. Figure 12.14

  33. What Makes Markets Efficient? • There are many investors out there doing research • As new information comes to market, this information is analyzed and trades are made based on this information • Therefore, prices should reflect all available public information • If investors stop researching stocks, then the market will not be efficient

  34. Efficient Market Hypothesis (EMH) – some misconceptions • Efficient markets do not mean that you can’t make money • They mean that you will earn a return that is appropriate for the risk undertaken and there is not a bias in prices that can be exploited to earn excess returns • Market efficiency will not protect you from wrong choices if you do not diversify – you still don’t want to put all your eggs in one basket

  35. Strong Form Efficiency • Prices reflect all information, including public and private • If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed • Empirical evidence indicates that markets are NOT strong form efficient and that insiders could earn abnormal returns

  36. Semistrong Form Efficiency • Prices reflect all publicly available information including trading information, annual reports, press releases, etc. • If the market is semistrong form efficient, then investors cannot earn abnormal returns by trading on public information • Implies that fundamental analysis will not lead to abnormal returns

  37. Weak Form Efficiency • Prices reflect all past market information such as price and volume • If the market is weak form efficient, then investors cannot earn abnormal returns by trading on market information • Implies that technical analysis will not lead to abnormal returns • Empirical evidence indicates that markets are generally weak form efficient

  38. Review • Which of the investments discussed have had the highest average return and risk premium? • Which of the investments discussed have had the highest standard deviation? • What is capital market efficiency? • What are the three forms of market efficiency?

  39. 3 Problems • Your stock investments return 8%, 12%, and -4% in consecutive years. What is the geometric return? • (1.08 x 1.12 x .96)^.3333 – 1 = .0511 • What is the sample standard deviation of the above returns? • Mean = ( .08 + .12 + -.04) / 3 = .0533 • Variance = (.08 - .0533)^2 + (.12 - .0533)^2 + (-.04 - .0533)^2 / (3 - 1)= .00693 • Standard deviation = .00693 ^ .5 = .0833

  40. Continued Problems • Using the standard deviation and mean that you just calculated in #2, and assuming a normal probability distribution, what is the probability of losing 3% or more? • Z = (-03 - .0533)/(.0833) = 1 standard deviation.Probability of a 3% loss (return of -3%) lies one standard deviation below the mean. There is 16% of the probability falling below that point (68% falls between -3% and 13.66%, so 16% lies below -3% and 16% lies above 13.66%).

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