slide 1 w. suo. slide 2 w. suo the investor’s goal goal is to maximize what is earned relative to...
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Slide 1 W. Suo
Measuring risk and returns: Measuring risk and returns:
Brief review of probabilityBrief review of probability
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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 of ValuePresent
Funds Invested of Value Terminal return of rate 1
• Investment’s terminal value
return of rate 1 ValuePresent Value Terminal
Equivalent
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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
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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 returnsReflects price change, any cash flows and
interest paid on borrowed funds Transaction costs (TC) can include
Interest on borrowed funds Taxes Commissions
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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
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Slide 6 W. Suo
Average Annual Rate of Return and Risk Statistics for Asset Classes and Inflation in the U.S., 1926-99
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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
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Slide 8 W. Suo
Example:
If we held the investment for 2 years, the following outcomes exist:
T=0 T=1 T=2
$100
$120 (50%)
$90 (50%)
$81 (25%)
$108 (50%)
$144 (25%)
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Slide 9 W. Suo
Historical Estimation
Histograpm Average return:
Arithmetic average return Geometric mean return
Variance/standard deviation Correlation Spreadsheet examples
IBM & MCD
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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
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Slide 11 W. Suo
Geometric Mean Example
Example: Given the following asset prices, calculate the geometric mean of the annual returns
Year PriceBegin PriceEnd
2001 $40 $60
2002 $60 $40
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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
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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:
Outcome Probability Rate of Return Product
Up 50% +20% 10%
Down 50% -10% -5%
Total 100% E(r) = 5%
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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%
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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.
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Slide 16 W. Suo
Example: Compounding Returns over Multiple Periods
An investment earned the following returns over the last three years:
Year Return
1 11.1%
2 -2.2%
3 3.3%
GMR = (1.111)(0.978)(1.033)1/3 –1 = 1.12241/3 – 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%
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Slide 17 W. Suo
Historical Estimation
Histograpm Average Variance/standard deviation Correlation Spreadsheet examples
IBM & MCD
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Slide 18 W. Suo
Linear Regression
Brief review Example