measure risk
SECURITY ANALYSIS AND POR TFOLIO MANAGEMENT
LESSON 6:
MEASUREMENT & EVALUATION OF RISK
How does we Measure Risk?
Understanding the nature of the risk is not adequate unless the investor or analyst is capable of expressing it in some quantitative terms. Expressing the risk of a stock in quantitative terms makes it comparable with other stocks. Measurement cannot be assures of percent accuracy because risk is caused by numerous factors as discussed above. Measurement provides an approximate quantification of risk. The statistical tool often used to measure is the standard deviation.
Standard Deviation: It is a measure of the values of the variables around its mean or it is the square root of the sum of the squared deviations from the mean divided by the number of observances. The arithmetic mean of the returns may be same for two companies but the returns may vary widely. This can be illustrated with an example.
Now let us take two companies A and B to calculate the expected returns.
COMPANY A
standard deviation is affected by the association of movement of returns of two securities. Covariance of two securities measures their co-movement.
How do we Calculate Co-variance?
There are three steps involved I the calculation of covariance between two securities;
Determine the expected returns for securities Determine the deviation of possible returns from the expected return for each security. Determine the sum of the product of each deviation of returns of two securities and probability.
Let us consider the data of two securities X and Y.
State of economy
Probability
X
Returns
Y
A
0.1
-8
14
COMPANY B
ri
Pi
Piri
ri
Pi
Piri
B
0.2
10
-4
6
0.10
0.6
4
0.1
0.4
C
0.4
8
6
7
0.25
1.75
6
0.2
1.2
D
0.2
5
15
8
0.30
2.4
8
0.4
3.2
E
0.1
-4
20
9
0.25
2.25
10
0.2
2.0
10
0.10
1.00
LESSON 6:
MEASUREMENT & EVALUATION OF RISK
How does we Measure Risk?
Understanding the nature of the risk is not adequate unless the investor or analyst is capable of expressing it in some quantitative terms. Expressing the risk of a stock in quantitative terms makes it comparable with other stocks. Measurement cannot be assures of percent accuracy because risk is caused by numerous factors as discussed above. Measurement provides an approximate quantification of risk. The statistical tool often used to measure is the standard deviation.
Standard Deviation: It is a measure of the values of the variables around its mean or it is the square root of the sum of the squared deviations from the mean divided by the number of observances. The arithmetic mean of the returns may be same for two companies but the returns may vary widely. This can be illustrated with an example.
Now let us take two companies A and B to calculate the expected returns.
COMPANY A
standard deviation is affected by the association of movement of returns of two securities. Covariance of two securities measures their co-movement.
How do we Calculate Co-variance?
There are three steps involved I the calculation of covariance between two securities;
Determine the expected returns for securities Determine the deviation of possible returns from the expected return for each security. Determine the sum of the product of each deviation of returns of two securities and probability.
Let us consider the data of two securities X and Y.
State of economy
Probability
X
Returns
Y
A
0.1
-8
14
COMPANY B
ri
Pi
Piri
ri
Pi
Piri
B
0.2
10
-4
6
0.10
0.6
4
0.1
0.4
C
0.4
8
6
7
0.25
1.75
6
0.2
1.2
D
0.2
5
15
8
0.30
2.4
8
0.4
3.2
E
0.1
-4
20
9
0.25
2.25
10
0.2
2.0
10
0.10
1.00