Lessons From Capital Market History

Chapter 12

Created by David Moore, PhD

Topics

  1. Historical returns
  2. First Lesson: Average Returns
    • Risk Premium
  3. Second Lesson: Variability of Returns
  4. Arithmetic vs Geometric Returns
  5. Capital Market Efficiency

Overview: Risk, Return and Financial Markets

  • Lessons from capital market history
    • There is a reward for bearing risk
    • The greater the potential reward, the greater the risk
    • This is called the risk-return trade-off


How should we measure risk and return?

First Lesson: Average Return

Historical Record

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Ranking Returns

  1. Small cap stocks
  2. Large cap stocks
  3. Long-term government bonds
  4. Treasury Bills
  5. Inflation


Why wouldn't you just buy small cap stocks?
RISK!!!!

Calculating Returns

  1. Total Dollar Return

    • $Return = Dividends + Capital Gains

  2. Total Percent Return

    • %Return = $\frac{\$Return}{\$Invested}$

Example: Returns

You just invested in "You call that a Donut! Inc" for $\$$25, after one-year the price is $\$$35. Each share paid out a $\$$2 dividend. What was your total return?

Dollar Return Percent Return
Dividend 2 $\frac{2}{25}=8\%$
Capital Gains 35-25=10 $\frac{35-25}{25}=40\%$
Total Return 2+10=12 $\frac{10+2}{25}=48\%$

Percent Returns: Formulas

Dividend Yield
$DY=\frac{D_{t+1}}{P_t}$

Capital Gains Yield
$CGY=\frac{P_{t-1}-P_t}{P_t}$

$\%Return=\frac{D_{t+1}+P_{t+1}-P_t}{P_t}$

Historical Average Returns


$HistoricalAverageReturn=\frac{\sum\limits_{i=1}^TReturn_i}{T}$

Large cap stocks average return from 1926 to 2010: 11.9%

Your best guess about the size of the return for a year selected at random is 11.9%.

Historical Average Returns: 1926-2010

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Practice: Average

Returns: -6, 8, 12, -15, 6

Average = 1

Returns: -1, 2, -1, 1, 4

Average = 1

Risk Premium

The excess return required from an investment in a risky asset over that required from a risk free investment.
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U.S. Treasury bill is considered risk-free return

Historical Average Risk Premium

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First Lesson Takeaways

Risky assets, on average, earn a risk premium

Large company stocks have a historical average risk premium of 8.6%

What determines size of risk premium?

Second Lesson: Return Variability

Measuring Return Variability

  • Variance or $\sigma^2$
    • Common measure of return dispersion
  • Standard deviation or $\sigma$
    • Sometimes called volatility
    • Same "units" as the average

Example

Two companies have the following returns:
Wildcat Inc: 13,15,12,10,8,10,2,19,10,10,8
Cardinals Corp: 12,17,8,12,7,15,24,9,13,3,8

Wildcats Inc. Cardinals Corp.
Average 10.6 11.6
Standard Deviation 4.3 5.7

Graphical Representation

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Steph vs LeBron (Points in 2016 Playoffs)

Steph Curry (9 games leading into finals):40,29,26,28,24,19,31,31,36.
LeBron James (9 games leading into finals):27,24,21,24,23,24,29,23,33.

Steph LeBron
Average 29.33 25.33
Standard Deviation 6.25 3.71

Return Variability

  • Return Variance:


$VAR(R)=\sigma^2=\frac{\sum\limits_{i=1}^T(R_i-\bar{R})^2}{T-1}$

  • Standard deviation:


$STD(R)=\sigma=\sqrt{VAR(R)}$

Practice: Standard Deviation

Returns(A): -6, 8, 12, -15, 6

Average = 1
Standard deviation = 11.18

Returns(B): -1, 2, -1, 1, 4

Average = 1
Standard deviation = 2.12

Graphing Returns

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Example

Year Return (%) Average Return (%) Difference Squared Difference
1926 11.14 11.48 -.034 0.0012
1927 37.13 11.48 25.65 657.82
1928 43.31 11.48 31.83 1013.02
1929 -8.91 11.48 -20.39 415.83
1930 -25.26 11.48 -36.74 1349.97
Variance 859.19
Standard Deviation 29.31

Normal Distribution

A symmetric bell-shaped frequency distribution that is completely defined by its mean and standard deviation.
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Arithmetic vs. Geometric Mean

Think about returns...

If you invest in a hedge fund that loses 20% the first year, but makes 20% the second year, are you back to even?

  • NO!!!!!
  • Start with $\$$100
  • After year 1: you have $\$$80
  • After year 2, you have $96

Another example

Suppose you invest $\$$100 and it falls 50% in year one but gain 100% in year 2.

  • Year 0:100
  • Year 1:100*(1-0.50)=50
  • Year 2:50*(1+1)=100

Arithmetic vs. Geometric Mean

  • Arithmetic average:
    • Return earned in an average period over multiple periods
    • Answers the question: "What was your return in an average year over a particular period?"
  • Geometric average
    • Average compound return per period over multiple periods
    • Answers the question: "What was your average compound return per year over a particular period?"


Geometric average < Arithmetic average unless all the returns are equal

Geometric Average: Formula


$GAR=[(1+R_1)*(1+R_2)*...*(1+R_T)]^{\frac{1}{T}}-1$

Where:
$R_i$= return in each period
$T$ = number of periods

Geometric Average: Formula


$GAR=[\prod\limits_{i=1}^T(1+R_i)]^{\frac{1}{T}}-1$

Where:
$\prod$= Symbol for product (multiply)
$R_i$= return in each period
$T$ = number of periods in sample

Revisit Examples

If you invest in a hedge fund that loses 20% the first year, but makes 20% the second year.
Average Return: 0%
Geometric return: -2.02%

Suppose you invest $\$$100 and it falls 50% in year one but gain 100% in year 2.
Average Return: 25%
Geometric Return: 0%

Example

Year Return (%) (1+R) Compounded
1926 11.14 1.114 1.114
1927 37.13 1.3713 1.5241
1928 43.31 1.4331 2.1841
1929 -8.91 0.9109 1.9895
1930 -25.26 0.7474 1.4870
$(1.4870)^\frac{1}{5}$ 1.0826
Geometric return 8.26%

Capital Market Efficiency

Capital Market Efficiency

A market in which security prices reflect available information
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If true, cannot earn abnormal or excess returns.

Efficient Market Hypothesis

The hypothesis that actual capital markets are efficient.

  • Idea is competition among investors drives information into prices and thus the market becomes more and more efficient.
  • Stocks are all priced correctly

Finance version of "Dad Joke"

A student and a finance professor are walking down the hall when they both see a $\$$20 bill on the ground. The student bends down to pick it up.

The professor shakes their head slowly with a look of disappointment. And says…

"Don't bother, If it were really there, someone else would have picked it up already"

Forms of Market Efficiency

  1. Strong form: all information of every kind is reflected in the stock prices. Including public and private.
  2. Semi-strong form: all public information is reflected in stock prices.
  3. Weak form: Prices reflect all past trading information such as prices and volume.

Summary

  • No simple way to "beat" the market
  • Identifying mispriced stocks is very difficult (borderline impossible)
  • Prices do respond rapidly to information
  • Very difficult to predict future stock prices

Extra Practice

Example 1

One year ago, Avril purchased 3,600 shares of Lavigne stock for $\$$101,124. Today, she sold those shares for $\$$26.60 a share. What is the total return on this investment if the dividend yield is 1.7 percent?

Example 2

A stock has yielded returns of 6 percent, 11 percent, 14 percent, and -2 percent over the past 4 years, respectively. What is the standard deviation of these returns? 

Example 3

You purchased 1,300 shares of LKL stock 5 years ago and have earned annual returns of 7.1 percent, 11.2 percent, 3.6 percent, -4.7 percent and 11.8 percent. What is your arithmetic average return?What is the geometric return?

Key Learning Outcomes

  • First Lesson: Average Returns
    • Historical returns
    • Risk Premium
  • Second Lesson: Return Variability
    • Standard deviation
  • Arithmetic vs Geometric return
  • Capital market efficiency
    • Efficient market hypothesis

Next time

Chapter 13: Return, Risk, and the Security Market Line