Section 8
Technical properties of
financial ratios
1
Learning objectives
After studying this chapter, you will understand:
• Why financial statement information is used in the ratio
form
• Assumptions in calculating financial ratios
• Why these assumptions are often violated
2
Why ratios?
• Financial data are usually summarized in a ratio form
– Financial statement numbers are divided by other financial
statement numbers
• Financial ratios control for the effect of firm size
accross firms and over time
Financial statement numbers are combarable across firms and
years
3
Why ratios?
•
Consider following example of summarizing financial
data in the ratio form:
Earnings:
Sales:
Profit margin
(Earnings/Sales):
•
•
Firm A
10 milj.
100 milj.
Firm B
2 milj.
8 milj.
10%
25%
Earnings of Firm A are higher than those of Firm B
However, Profit margin reveals the true profitability
4
Proportionality
• An important assumption in using financial ratios is the socalled proportionality between the numerator and
denominator
• Strict proportionality implicates that
1. there should exist a linear relationship between the numerator and
denominator of the ratio
2. this relationship should not contain any constant term
• Empirical evidence indicates that the proportionality
assumption is usually full-filled
5
Strict proportionality
• E = Earnings, S = Sales and r is the ratio of Earnins-toSales:
E r
S
 E  rS
• Under strict proportionality assumption, the relationship
between the numerator and denominator is linear and
there is no constant term in the relationship
6
Deviations from strict proportionality
assumption
1. Proportionality without constant
Earnings
3. Non-proportionality without constant
Earnings
Sales
Sales
2. Proportionality with constant
4. Non-proportionality with constant
Earnings
Earnings
Sales
7
Sales
Technical issues in calculating financial
ratios
• Small or zero denominators
– If the denominator of the financial ratio is equal to zero, the ratio
cannot be calculated
– If the value of the denominator is close to zero, the ratio is close
to infinity
– If the denominator fluctuates a lot across years or firms, the
values of ratio fluctuate a lot, too
• Following example of P/E- and E/P-ratios illustrates the
problem of small or zero denominators
8
Technical issues in calculating financial
ratios
• Outliers refer to the extreme values of a given financial
ratio
– Outliers are inconsistent with the remaining data
• There may be several reasons for outlier observations
– Data recording errors
– Technical issues such as close to zero denominators
– True indication of the extreme state of the underlying firm
characteristic (e.g. bankcuptcy firms)
• Outlier observations are usually deleted from the data,
but one should be very careful when doing so
– Important information may be lost, if the outlier reflects the true
economic state of the firm
9
Common-size analysis
• Common-size analysis refers
to the standardization of
items in income statement
and balance sheet
– Financial items are expressed as
percentage of a chosen item that
measures the scale of the
operations
– Common-size analysis helps
comparing financial statements
10
Example: the common-size analysis
EUR
%
Sales
31191 100.0
Operating expenses -19787
-63.4
Operating income
-2985
-9.6
Depreciations
-3443
-11.0
EBIT
-714
-2.3
Interest payments
-80
-0.3
Tax
-518
-1.7
Net profit
-302
-1.0
Distributional properties of financial
ratios
• Financial ratios are compared across firms and years
• This comparison requires some knowledge on the
distributions of ratios
– Financial analysts may intuitively use a prior distribution of
the variable that is of interest
– Some of the analyses methods such as credit rating or
bankruptcy prediction are based on statistical tools that
assume a certain distribution
– Financial data can also be summarized by calculating
averages or other parameters of the ratio distributions
11
Normal distribution
• Distributions can have many different type of shapes
• We often focus on the normal distribution
• Normal distribution can be described by only two
variables
– Mean
– Standard deviation
• Some of the frequently used statistical tools used to
analyze financial variables assume that the data are
normally distributed
12
Empirical evidence on ratio distributions
• Empirical evidence indicates that financial ratios are
often non-normally distributed
• Typical reasons for non-normality include:
– Strict proportionality assumption between the numerator and
denominator of the ratio may cause skewness
– Some financial ratios have technical limits, e.g. in zero
• Current ratio, Quick ratio
– Some financial ratios may have economic limits
• Accounts receivables turnover
– Outlier observations may cause peaked distributions
13
How to achieve normality?
• Non-normal ratio distributions can be converted to
normal ones by using at least following methods
– deleting observations that deviate most from normality
– resetting extreme observations to less extreme values
– transforming ratios with a certain function
•
•
•
•
square root transformation
cubic root transformation
logarithmic transformation
inverse transformation
– recognize non-normality in decision making without attempting
to transform distribution
14
Example: Square root transformation
Value of the original
financial ratio
1
2
3
4
5
6
7
8
15
Value of the
transformed financial ratio
1,00
1,41
1,73
2,00
2,24
2,45
2,65
2,83
Evidence on ratio distributions
• Kallunki (1998) reports empirical evidence on the impact
of transformation to the normality of the financial ratios:
Year
1989
1990
1991
1992
1993
ROI
0.90***
0.97
0.98
0.96
0.85***
Year
ROI
1989
1990
1991
1992
1993
0.98
0.86***
ETS
CR
QR
INT
0.84***
0.81***
0.87***
0.85***
0.90***
0.79***
0.82***
0.87***
0.83***
0.92***
0.82***
0.77***
0.73***
0.81***
0.80***
ETS
CR
QR
INT
0.97
0.96
0.92***
0.98
0.97
0.95*
0.98
0.97
0.98
0.98
0.97
0.97
0.97
0.96
0.99
0.97
0.97
0.99
0.85***
0.98
0.97
0.94**
0.91***
Notes: The numbers in the table are the values of the Shapiro-Wilk’s test statistic for
testing the normality of financial ratios. * significant at level of 10 percent, ** significant
at level of 5 percent *** significant at level of 1 percent
16
’Raw’ data
Transformed data
Summary
• Financial data are usually summarized in a ratio form to
control for size of the firm
• There should be a proportionality between the
numerator and denominator of the financial ratio
• Outliers are often a problem in ratio analysis
• We need to have some idea about the distribution of the
financial ratio
• Financial ratios are transformed to achieve a better
distribution