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Week 6

Lecture 6

Ross, Westerfield and Jordan 7e

Chapter 12

Some Lessons from Capital Market History

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Last Week..

• Capital Budgeting Techniques• NPV, IRR, PI• Payback, Discounted Payback, AAR

• Non-Conventional Cash Flows

• Mutually Exclusive Projects

• Cash Flows

• Equivalent Annual Cost - EAC

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Chapter 12 Outline

• Returns• Holding period returns• Return statistics: AM & GM• Risk• Variance & Standard Deviation• Historical risk and returns on various types

of investments• Lessons from history• EMH

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Returns

• Dollar Returns (Investment Profit)

the sum of the cash received and the change in value of the asset, in dollars.

Time 0 1

Initial investment

Ending market value

Dividends

•Percentage Returns

the cash received and the change in value of the asset divided by the original investment.

Dollar Return = Dividend + Change in Market Value

Returns

yieldgains capital yielddividend

P

PP

P

C

P

)P(PCR

yieldgains capital yielddividend

value market beginning

value market in change dividend

value market beginning

return dollarReturn Percentage

1t

1tt

1t

t

1t

1tttt

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Example - Calculating Returns

• 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?

• Income = 30 + 30 = 60• Capital gain = 975 – 950 = 25• Total dollar return = 60 + 25 = $85

• What is the percentage return?• Total dollar return/ Beginning value• 85/950 = 8.95%

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Example – Calculating Returns

• You bought a stock for $35 and you received dividends of $1.25. The stock is now worth $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, dollar return/ beginning price:

6.25/35 = 17.86% (unrealised)

• Nominal v Real• Realised v Unrealised

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Holding-Period Returns

• The holding period return the return that an investor would get when holding an investment over a period of n years

Where r1, r2.. rn are yearly returns

1)r(1)r(1)r(1

Return Period Holding

n21

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Holding Period Return: Example

• Suppose your investment provides the following returns over a four-year period:

Your holding period return =

Year Return1 10%2 -5%3 20%4 15%

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Geometric Average

• An investor who held this investment would have earned an annual average compound return of 9.58%:

Geometric Average = GM =Rg = π[1+R]1/t -1

Rg = [(1+R1)x(1+R2)x(1+R3)x(1+R4)]1/t -1 =

Rg = [(1.10)x(0.95)x(1.20)x(1.15)]1/4 -1=9.58%

or

• So, our investor made 9.58% per year, for four years, earning a holding period return of 44.21%

• (1.095844)4 = 1.4421 – 1 = 0.4421 = 44.21%

Year Return1 10%2 -5%3 20%4 15%

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Arithmetic Average

• Arithmetic Average = AM= Ra

Year Return1 10%2 -5%3 20%4 15%

• Our investor earned 10% return in an average year, over the four year investment period.

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Example: Calculating AM and GM

• What is the arithmetic and geometric average for the following returns?• Year 1 5%• Year 2 -3%• Year 3 12%

• AM = (0.05 + (–0.03) + 0.12)/3 = 4.67%

• GM = (1+0.05)x(1-0.03)x(1+0.12)]1/3 – 1

= 0.0449 = 4.49%

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Arithmetic vs. Geometric Mean

• Arithmetic average – return earned in an average period over multiple periods (used as estimated return)

• Geometric average – average compound return per period over multiple periods

• The geometric average will be less than the arithmetic average unless all the returns are equal

• Which is better?• The arithmetic average is overly optimistic for long

horizons - use over short term• The geometric average is overly pessimistic for short

horizons - use over long term

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Risk

• Risk is the chance or possibility of loss

(Concise. Oxford.).

• Risk is the chance of things not turning

out as expected. (Economist).

• Risk is the uncertainty of future outcomes.

(Reilly&Brown)

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Risk Measurements

• Main Measures:• Variance (VAR) • Standard Deviation (SD).

• Variance = the average of the squared differences between the actual return and the average return.

• Standard Deviation = square root of Variance

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Example – VAR and SDYear Actual Return

R

Average Return

Rmean

Deviation from the Mean

R - Rmean

Squared Deviation

(R – Rmean)2

1 0.15 0.105 0.045 0.002025

2 0.09 0.105 -0.015 0.000225

3 0.06 0.105 -0.045 0.002025

4 0.12 0.105 0.015 0.000225

TotalsAverage

0.420.42/4=0.105

0.00 0.0045 ∑

Variance = 0.0045 / (4-1) = 0.0015 Standard Deviation = √0.0015 = 0.03873 = 3.87%

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Example - Standard Deviation

• SD = 3.87%

• 68% of possible outcomes will lie between 6.63% and 14.37%

-3σ -2σ -1σ mean +1σ +2σ +3σ6.63% 10.5% 14.37%

68%

95%

99%

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Historical Return Statistics

• The history of capital market returns can be summarized by describing • The average return• The standard deviation of those returns • The frequency distribution of the returns

• Roger Ibbotson and Rex Sinquefield show historical annual rates of return starting in 1926 for five important types of financial instruments in the United States:• Large-Company Common Stocks• Small-company Common Stocks• Long-Term Corporate Bonds• Long-Term U.S. Government Bonds• U.S. Treasury Bills

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Figure 12.4 – FV of $1 investment in 1925

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Historical Returns, 1926-2003

Source: © Stocks, Bonds, Bills, and Inflation 2004 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.

– 90% + 90%0%

Average Standard Series Annual Return DeviationDistribution

Large Company Stocks 12.4% 20.4%

Small Company Stocks 17.5 33.3

Long-Term Corporate Bonds 6.2 8.6

Long-Term Government Bonds 5.8 9.4

U.S. Treasury Bills 3.8 3.1

Inflation 3.1 4.3

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Rates of Return – stock, bonds, bills

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95 2000

Common Stocks

Long T-Bonds

T-Bills

Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.

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Stock Market Volatility

0

10

20

30

40

50

60

Source: © Stocks, Bonds, Bills, and Inflation 2000 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.

The volatility of stocks is not constant from year to year.

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Lessons from Capital Market History

• U.S. data reflects two features often observed in financial markets.

• There is a reward for bearing risk.• The larger the potential reward, the larger

the risk.

• This is called the risk-return trade-off.

• There is a positive relationship between risk and return.

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The Risk-Return Tradeoff

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Risk Premium

• The “extra” return earned for taking on risk• The risk premium is the return over and above

the risk-free rate• Average Return – Risk-free Rate = Risk Premium• What is a risk free rate?• Treasury bills are considered to be risk-free. Can

use Government bonds as well.• Considered risk free in terms of ability of pay

interest obligations

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Table 12.3 Average Annual Returns and Risk Premiums

Investment Average Return Risk Premium

Large stocks 12.4% 8.6%

Small Stocks 17.5% 13.7%

Long-term Corporate Bonds

6.2% 2.4%

Long-term Government Bonds

5.8% 2.0%

U.S. Treasury Bills 3.8% 0.0%

E.g. Large stocks premium = 12.4% - 3.8% = 8.6%

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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

• Efficient Market Hypothesis or EMH Eugene Fama – 1970, Journal of Finance

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Figure 12.12 - Stock Price Reaction

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Common Misconceptions about EMH

• An efficient market doesn’t mean “you can’t make money”!!!

• It means that, on average, 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

• Three forms: weak, semi-strong and strong

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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

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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

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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

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Lecture 6 - Summary

• Returns• Arithmetic Mean• Geometric Mean

• Risk• Variance• Standard Deviation

• Lessons from Capital Market history• There is a reward for bearing risk

• EMH• Weak, Semi-strong, Strong

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Next Week..

• No Lecture and No tutorials next week!

• Tutorial questions from Week 6 lecture are due in Week 8.

• I will be available for consultation as usual: Thursday 2-4pm G06_2.22

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End Lecture 6