1. Slide 1 W. Suo

2. Slide 2 W. Suo The Investor’s Goal  Goal is to maximize what is earned relative to the amount put into an investment Maximize either the Rate of return Investment’s terminal value Equivalent

3. Slide 3 W. Suo Rate of Returns  One period rate of return is called a random variable Returns tend to fluctuate randomly from period to period  Risk is associated with the variability of return Total risk can be measured with variance or standard deviation This chapter divides total risk into components

4. Slide 4 W. Suo The Basic Random Variable  Ways to calculate one-period rate of return Unmargined returns Reflects price change and any cash flow income Margined returns Reflects price change, any cash flows and interest paid on borrowed funds  Transaction costs (TC) can include Interest on borrowed funds Taxes Commissions

5. Slide 5 W. Suo Wealth Indices for Average U.S. Investments in Different Asset Classes Compared to Inflation, 1926-99  If you had invested $1 on December 31, 1925 in each of the following, you would have

6. Slide 6 W. Suo Average Annual Rate of Return and Risk Statistics for Asset Classes and Inflation in the U.S., 1926-99

7. Slide 7 W. Suo Uncertainty  Characterized by probability  How to interpret probability  Random variables  Expected value Most likely value vs expected value  Variance  Covariance & standard deviation  Correlation

8. Slide 8 W. Suo Example:  If we held the investment for 2 years, the following outcomes exist: T=0 T=1T=2 $100 $120 (50%) $90 (50%) $81 (25%) $108 (50%) $144 (25%)

9. Slide 9 W. Suo Historical Estimation  Histograpm  Average return: Arithmetic average return Geometric mean return  Variance/standard deviation  Correlation  Spreadsheet examples IBM & MCD

10. Slide 10 W. Suo GMA vs AMA  The geometric mean (GMR) differs from the arithmetic mean (AMR) in that the geometric mean Considers the compounding of rates of return GMR usually less than AMR

11. Slide 11 W. Suo Geometric Mean Example  Example: Given the following asset prices, calculate the geometric mean of the annual returns YearPrice Begin Price End 2001$40$60 2002$60$40

12. Slide 12 W. Suo Contrasting AMR and GMR  GMR should be used for Measuring historical returns that are compounded over multiple time periods  AMR should be used for Future-oriented analysis where the use of expected values is appropriate

13. Slide 13 W. Suo Example: GMR vs AMR  An investment costs $100 and it is equally likely to Lose 10% or Earn 20%  The probability distribution of such an investment is: OutcomeProbabilityRate of ReturnProduct Up50%+20%10% Down50%-10%-5% Total100%E(r) = 5%

14. Slide 14 W. Suo Example: GMR vs AMR  Expectations about the future should use the E(r) If $100 is compounded at 5% annually for two years, the expected terminal value is $110.25  If the investment actually grew to $108, the multi-period historical returns should be averaged using GMR ($108/100) 1/2 –1 = 0.03923 = 3.923%

15. Slide 15 W. Suo Compounding Returns over Multiple Periods  Various periodic price relatives can be compounded to obtain a new rate of return for the entire period 3 monthly returns can be compounded to determine 1 quarterly return 12 monthly returns can be compounded to determine 1 annual return, etc.

16. Slide 16 W. Suo Example: Compounding Returns over Multiple Periods  An investment earned the following returns over the last three years: YearReturn 111.1% 2-2.2% 33.3% GMR = (1.111)(0.978)(1.033) 1/3 –1 = 1.1224 1/3 – 1 = 3.92% annual return. The total 3-year return is 12.24%. AMR = 11.1% + -2.2% + 3.3% = 12.2%  3 = 4.07%

17. Slide 17 W. Suo Historical Estimation  Histograpm  Average  Variance/standard deviation  Correlation  Spreadsheet examples IBM & MCD

18. Slide 18 W. Suo Linear Regression  Brief review  Example