0. Week 6 Lecture 6 Ross, Westerfield and Jordan 7e Chapter 12
Some Lessons from Capital Market History

1. Last Week.. Capital Budgeting Techniques Non-Conventional Cash Flows
NPV, IRR, PI
Payback, Discounted Payback, AAR
Non-Conventional Cash Flows
Mutually Exclusive Projects
Cash Flows
Equivalent Annual Cost - EAC

2. 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

3. Returns
Dollar Returns (Investment Profit)
the sum of the cash received and the change in value of the asset, in dollars.
Dividends
Ending market value
Time 1
Initial investment
Percentage Returns
the cash received and the change in value of the asset divided by the original investment.

4. Returns
Dollar Return = Dividend + Change in Market Value

5. 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 = = 60
Capital gain = 975 – 950 = 25
Total dollar return = = $85
What is the percentage return?
Total dollar return/ Beginning value
85/950 = 8.95%

6. 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 = (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 = = 17.86%
Or, dollar return/ beginning price:
6.25/35 = 17.86% (unrealised)
Nominal v Real
Realised v Unrealised

7. 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

8. Holding Period Return: Example
Suppose your investment provides the following returns over a four-year period:
Your holding period return =

9. 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%
( )4 = – 1 = = 44.21%

10. Arithmetic Average Arithmetic Average = AM= Ra
Our investor earned 10% return in an average year, over the four year investment period.

11. 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 = ( (–0.03) )/3 = 4.67%
GM = (1+0.05)x(1-0.03)x(1+0.12)]1/3 – 1
= = 4.49%

12. 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

13. 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)

14. 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

15. Deviation from the Mean
Example – VAR and SD
Year
Actual Return R
Average Return
Rmean
Deviation from the Mean
R - Rmean
Squared Deviation
(R – Rmean)2 1
0.15
0.105
0.045 2
0.09
-0.015 3
0.06
-0.045 4
0.12
0.015
Totals
Average
0.42
0.42/4=0.105
0.00 ∑
Variance = / (4-1) =
Standard Deviation = √ = = 3.87%

16. Example - Standard Deviation
SD = 3.87%
68% of possible outcomes will lie between 6.63% and 14.37%
68%
95%
99%
-3σ -2σ -1σ mean +1σ +2σ +3σ
6.63% 10.5% 14.37%

17. 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

18. Figure 12.4 – FV of $1 investment in 1925

19. Historical Returns,
Average Standard Series Annual Return Deviation Distribution
Large Company Stocks 12.4% 20.4%
Small Company Stocks
Long-Term Corporate Bonds
Long-Term Government Bonds
U.S. Treasury Bills
Inflation
– 90% 0%
+ 90%
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.

20. Rates of Return – stock, bonds, 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.

21. Stock Market Volatility
The volatility of stocks is not constant from year to year.
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.

22. 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.

23. The Risk-Return Tradeoff

24. 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

25. 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%

26. 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

27. Figure 12.12 - Stock Price Reaction

28. 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

29. 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

30. 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

31. 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

32. Lecture 6 - Summary Returns Risk Lessons from Capital Market history
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

33. 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

34. End Lecture 6