Wednesday, September 19, 2018

Regression Specification Issues for Stock Price Equation


Regression Specification Issues for Stock Price Equation

The issue discussed here is how variations in regression model specifications impact estimated coefficients and conclusions reached from a model

Question:  A post on my finance blog considered share price as a function of earnings per share, sales per share, and a dummy variable set to one if the firm pays dividends. 

Do Dividend Affect Firm Value?




The estimates from this regression model are presented below.

Regression Results for Share Price Equation
Earnings Per Share
10.5
2.36
Sales Per Share
0.2
3.63
Dividend Dummy
-331.0
-4.27
_cons
385.6
4.92
R2
0.66
N
67.0


The model suggests that dividend paying firms have a lower stock price than firms that do not pay dividends.

Around half of the firms used to estimate this model are growth firms and half of the firms are value firms.  How did the dividend policy of growth firms differ from the dividend policy of value firms in this sample?

After accounting for the difference in dividend policy between growth and value firms what can we say about whether the decision to pay dividends affects share price?

The Incidence of Dividend Payments for Growth and Value Firms:

Dividend Policy Growth and Value Firms
Growth Firms
Value Firms
No Dividends
9
0
Dividends
25
33
Total
34
33

Observations:

All 33 firms in the value firm sample pay some dividends.   We cannot estimate a model with the div dummy in the value firm sample because the div dummy would be perfectly correlated with the constant term.

Estimated Coefficients from the Growth Model:



Share Price Equation for Growth Firms
Coef.
t
earnings per share
11.8
1.53
Sales Per share
0.17
2.14
Dividend Dummy
-328.2
-2.77
_cons
377.4
3.26
R2
0.64
N
34


Observation: 

 The estimated coefficients for the growth-only sample are similar to the combined sample.

The earnings per share coefficient is no longer significantly different from zero.

The dividend dummy is negative. 

Concluding Remark: 

Growth firms that do not pay dividends appear to have higher share prices than dividend paying growth firms.

We can’t conclude anything on this issue about value firms from our sample because all 33 value firms in our sample pay dividends



Monday, September 10, 2018

Financial Ratio Math



 How can one use forward and trailing PE ratios and PEG ratios to measure projected growth of earnings?

Question:   The table below has information on the trailing PE ratio, the forward PE ratio, and the PEG ratio for four firms.  Two of the firms AAPL and AMZN are considered growth firms.   Two of the firms GS and NEE are value firms.


Financial Ratios for Four Firms
Trailing PE
Forward PE
PEG
APPL
20.05
16.31
1.46
AMZN
154.59
76.94
2.46
GS
18.68
9.21
0.3
NEE
9.96
20.56
2.37

Show how these three financial ratios can be used to measure expected earnings growth?

Discussion:

These financial statistics can be used to create three measures of earnings growth. 

Caution: The growth measures only make sense when earnings is positive.  The PE ratio is a nonsensical statistic when earnings are negative.  Also, when earning are very close to 0 the PE ratio will be very large and earnings growth estimate will be sensitive to small changes in earnings.

The first growth measure is based on the ratio of trailing PE to forward PE.  This ratio simplifies to EF/ET where EF is forward earnings and ET trailing earnings because the same stock price is in the numerator of both PE ratios. 

 It follows that 100*((EF/ET) -1) is the projected growth rate in earning because EF is projected earnings next year and ET is earnings in the current year.

The second measure of projected growth is the ratio of the trailing PE ratio to the PEG ratio.  The third projected growth ratio is the ratio of the forward PE ratio to the PEG ratio.

The PEG ratio is defined as PE ratio divided by growth in earnings over some period.   The ratio of PE to PE over growth in earnings simplifies to growth in earnings.

I don’t know whether the reported PEG ratios in yahoo finance, the source of my data, use trailing or forward PE.  Also, I don’t know the time frame of the earnings growth used in the denominator of the PEG.

My approach is to present all three measures of projected growth for the four firms.

Calculations:

 Here are my calculations of the three projected growth statistics for the four stocks.



Projected Growth Rate in Earnings
Trailing PE to Forward PE
Trailing PE to PEG
Forward PE to PEG
APPL
22.9
13.7
11.2
AMZN
100.9
62.8
31.3
GS
102.8
62.3
30.7
NEE
-51.6
4.2
8.7

Observations on the growth projections

On all three measures AMZN and GS are virtually tied as having the highest projected growth rates in earnings.  The rank orders of the projected growth estimates for the four companies, while not identical, are similar.

One company NEE (Nextera Energy) has projected negative growth because the forward earnings estimate is less than current earnings estimate.

The ratio of trailing to forward PE ratios lead to the higher projected growth rate for three of the four companies.   The one exception is NEE.


Concluding Remarks:

These projected growth statistics can be used to measure expectations in the market. Large projected growth in earnings could indicate that analysts are excessively optimistic.   This currently appears to be the case for several highly-traded tech firms.



Go to my finance blog for an example looking at these ratios for a comparison between PE ratios from a growth ETF and a value ETF.   The results are somewhat surprising.  Most analysts are concerned about the valuation of tech stocks but the negative PE ratio of a significant number of value firms appears to be a larger concern.

https://financememos.com/2018/09/12/valuation-of-growth-and-value-stocks-with-pe-ratios/