SOME STATISTICAL CONCEPTS Chapter 3 Distributions of Data Probability Distribution – Expected Rate of Return – Variance of Returns – Standard Deviation – Covariance – Correlation Coefficient – Coefficient of Determination Historical Distributions – Various Statistics Relationship Between a Stock and the Market Portfolio – The Characteristic Line – Residual Variance
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SOME STATISTICAL CONCEPTS Chapter 3 Distributions of Data Probability Distribution –Expected Rate of Return –Variance of Returns –Standard Deviation –Covariance.
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SOME STATISTICAL CONCEPTSChapter 3
Distributions of Data Probability Distribution
– Expected Rate of Return– Variance of Returns– Standard Deviation– Covariance– Correlation Coefficient
– Coefficient of Determination Historical Distributions
– Various Statistics
Relationship Between a Stock and the Market Portfolio– The Characteristic Line– Residual Variance
DISTRIBUTIONS OF DATA When evaluating security and portfolio returns, the
analyst may be confronted with:– 1. possible returns in some future time period
(probability distributions of possible future returns), or
– 2. past returns over some historical time period (sample distribution of past returns).
The same statistics may be used to describe both types of distributions (probability and sample). For each type of distribution, however, the procedures for calculating the various statistics vary somewhat.
In the following examples, statistics are discussed first with respect to probability distributions, and then with respect to sample distributions of historical returns.
PROBABILITY DISTRIBUTION(Evaluating Possible Future Returns)
Probability (hi)
_________
Possible Return (%) (ri)
_________ .05 .10 .20 .30 .20 .10 .05
-20 -10 5
30 55 70 80
PROBABILITY DISTRIBUTION(Continued)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
-20 -10 5 30 55 70 80
Probability
Possible Return (%)
Expected Rate of Return (Best Guess)
E(r) = .05(-20) + .10(-10) + .20(5) + .30(30)
+ .20(55) + .10(70) + .05(80)
= 30%
Variance of Returns (Potential for deviation of the return from its expected value)