Ch 02 Tool Kit
5/25/2002
Chapter 2. Tool Kit for Risk and Return
The relationship between risk and return is a fundamental axiom in finance.
Generally speaking, it is totally logical to assume
that investors are only willing to assume additional risk if they are adequately compensated with additional return.
This idea is
rather fundamental, but the difficulty in finance arises from interpreting the exact nature of this relationship (accepting that risk
aversion differs from investor to investor).
Risk and return interact to determine security prices, hence its paramount importance
in finance.
PROBABILITY DISTRIBUTION
The probability distribution is a listing of all possible outcomes and the corresponding probability.
Demand for the
Probability of this
Rate of Return on stock
company's products
demand occurring
if this demand occurs
Sale.com
Basic Foods
Strong
0.30
100%
20%
Normal
0.40
15%
15%
Weak
0.30
70%
10%
1.00
EXPECTED RATE OF RETURN
The expected rate of return is the rate of return that is expected to be realized from an investment.
It is determined as the weighted
average of the probability distribution of returns.
Demand for the
Probability of this
Sale.com
Basic Foods
company's products
demand occurring
Rate of Return
Product
Rate of Return
Product
Strong
0.3
100%
30%
20%
6%
Normal
0.4
15%
6%
15%
6%
Weak
0.3
70%
21%
10%
3%
1.0
EXPECTED RATE OF RETURN, r hat
15%
15%
MEASURING STANDALONE RISK: THE STANDARD DEVIATION
To calculate the standard deviation, there are a few steps.
First find the differences of all the possible returns from the expected
return.
Second, square that difference.
Third, multiply the squared number by the probability of its occurrence.
Fourth, find the sum
of all the weighted squares.
And lastly, take the square root of that number. Let us apply this procedure to find the standard deviation
of Sale.com's returns.
Demand for the
Probability of this
Deviation from r hat
Squared deviation
Sq Dev * Prob.
company's products
demand occurring
Sale.com
Strong
0.3
85%
72.25%
21.68%
Normal
0.4
0%
0.00%
0.00%
Weak
0.3
85%
72.25%
21.68%
Sum:
43.35%
Std. Dev.
= Square root of sum
65.84%
Sq. root can be
65.84%
found in two ways
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View Full DocumentProbability of this
demand occurring
Basic Foods
Strong
0.3
5%
0.25%
0.08%
Normal
0.4
0%
0.00%
0.00%
Weak
0.3
5%
0.25%
0.07%
0.15%
Std. Dev.
= Square root of sum
3.87%
Sq. root can be
3.87%
found in two ways
MEASURING STANDALONE RISK: THE COEFFICIENT OF VARIATION
The coefficient of variation indicates the risk per unit of return, and is calculated by dividing the standard deviation by the expected
return.
Std. Dev.
Expected return
CV
Sale.com
65.84%
15%
4.39
Basic Foods
3.87%
15%
0.26
PORTFOLIO RETURNS
The expected return on a portfolio is simply a weighted average of the expected returns of the individual assets in the portfolio.
Consider the following portfolio.
Stock
Portfolio weight
Expected Return
Microsoft
0.25
12.0%
General Electric
0.25
11.5%
Pfizer
0.25
10.0%
CocaCola
0.25
9.5%
Portfolio's Expected Return
10.75%
PORTFOLIO RISK
deviationsusually, it is much lower than the weighted average.
The portfolio's SD is a weighted average only if all the securities in it
are perfectly positively correlated, which is almost never the case.
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 Spring '10
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 Standard Deviation, Variance, The Market, Errors and residuals in statistics

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