Damodarian's Valuation and Dividend Implied Equity Premium
In the book On Valuation by Damodarian. Some normative models are used to define the equity premium and help with comparison accross companies and countries.
- equity premium through dividend yield and dividend growth points to a long term premium of equity 3% over 10Y bonds, which is reasonnable
- for cross companies comparison, the CAPM model is proposed, although this is not supported by data
- for cross country comparison, a country premium is proposed, which is also not supported by data, unless the country premium is just the expected monetary debasement in that country relative to the USD
So one out of three formula appears to be useful. The book has a bias towards what can be taught rather than what has been tested to have predictive value.
Laer sections of the book focuses on analysing company cashflows and cashflow to equity. The argument made is that the value is that 0 is a pessimistic value for a company for Tencent or Amazon, so Damodarian makes the point for optimistically valuing the cashflows that the firm did not give back to the investor at 100% instead of 0% of their value. The truth is probably a value in between, but Damodarian works seems focused on models that are teachable, not necessarily on validating them with statistics.
Our article below focuses on statistical data relevant to the simpler dividend based valuation.
Dividends and Equity Premium
The gordon model is proposed to infer the equity premium from dividend yield:
$$ P = \frac{D}{r-g} = \frac{P r_d}{r-g} $$ Hence the relationship between the equity discount rate $r$ and the dividend yield $r_d$: $$ r = r_d + g$$
This calculation can be made on individual stocks or as an aggregate on an index such as SP500 whose dividend yield was published by SP until their website changed in september 2023.
Equity Premium and CAPM
The equity premium is defined as the average equity return $\bar{r}$ over bond yields $y_0$. While $\bar{r} = \alpha + \beta (\bar{r} - y_0)$ is tautological for $\alpha=y_0, \beta=1$, the CAPM assumes that a statistical estimation $\alpha$ should give $y_0$, while the market should require a higher return for high $\beta$ stocks: $$ E(r_i) = y_0 + \beta_i (\bar{r} - y_0) $$
It is a well documented fact since 1972 that this relation does not hold and high $\beta$ stocks have a negative $\alpha$ (lower implied rate), and yet, valuation textbooks still suggest a formula based on stocks $\beta_i$ for discounting future cashflows.
We show the graph of $r$ vs $\beta$ for the 500 top worldwide stocks:
The equity dividend return $r=y_d+g$ has not been adjusted for dividend withholding tax although companies include Microsoft, Aramco, Novo Nordisk, Nestle and Toyota Motor.
Equity Premium and Foreign Country Risk
Damodarian suggests that an additional country risk premium $c_0$ be added to $r$: $$ r = y_0 + c_0 + \beta (\bar{r} - y_0)$$
or that it be integrated to $\beta$ if this is a country equity market premium: $$ r = y_0 + \beta (\bar{r} - y_0 + c_0)$$
or that a separate country risk multiplier be added, which depends on how much the company is linked to the country: $$ r = y_0 + \beta (\bar{r} - y_0) + \lambda c_0$$
We know that FX currency for most currencies in the world except the G10 include a strong devaluation trend. We use dividend growth measured in USD In the table below, there is then little in the way of consistently positive country premium.
For correctness, the return has been adjusted for the withholding tax $w$ of a Hong Kong investor $r = r_d (1-w) + g$. This tax depends on the investor location.
country | divyield | divgrowth | count | mktcap | wht | r | |
---|---|---|---|---|---|---|---|
0 | United States | 0.013882 | 0.062972 | 4842 | 4.552017e+13 | 0.3 | 0.072689 |
1 | China | 0.026602 | 0.083033 | 2533 | 9.527179e+12 | 0.1 | 0.106975 |
2 | Japan | 0.020218 | 0.008545 | 3872 | 6.225274e+12 | 0.15 | 0.02573 |
3 | United Kingdom | 0.032981 | 0.001114 | 826 | 5.181922e+12 | 0.0 | 0.034095 |
4 | India | 0.008942 | 0.022857 | 1523 | 4.456707e+12 | 0.05 | 0.031352 |
5 | France | 0.024787 | 0.044636 | 568 | 3.457746e+12 | 0.25 | 0.063226 |
6 | Saudi Arabia | 0.031152 | 0.048900 | 229 | 2.968482e+12 | 0.05 | 0.078495 |
7 | Canada | 0.022856 | 0.063289 | 1996 | 2.758667e+12 | 0.15 | 0.082717 |
8 | Switzerland | 0.026171 | 0.033391 | 229 | 2.724169e+12 | 0.35 | 0.050403 |
9 | Germany | 0.022942 | 0.033720 | 481 | 2.449960e+12 | 0.1 | 0.054368 |
10 | Taiwan | 0.031188 | 0.127480 | 969 | 2.369955e+12 | 0.21 | 0.152118 |
11 | Australia | 0.037399 | 0.042232 | 1796 | 1.898344e+12 | 0.3 | 0.068412 |
12 | South Korea | 0.015098 | 0.108507 | 807 | 1.887738e+12 | 0.15 | 0.121341 |
13 | Hong Kong | 0.019335 | 0.057582 | 1405 | 1.667610e+12 | 0.0 | 0.076917 |
14 | Brazil | 0.053900 | 0.011873 | 406 | 1.644365e+12 | 0.0 | 0.065774 |
15 | Netherlands | 0.014413 | 0.168435 | 95 | 1.574975e+12 | 0.0 | 0.182848 |
16 | Ireland | 0.013935 | 0.064182 | 58 | 1.154320e+12 | 0.0 | 0.078118 |
17 | Sweden | 0.019094 | 0.035461 | 647 | 1.045870e+12 | 0.3 | 0.048826 |
18 | Denmark | 0.014932 | 0.087391 | 159 | 9.717430e+11 | 0.275 | 0.098217 |
19 | Spain | 0.031525 | 0.009748 | 139 | 8.120395e+11 | 0.19 | 0.035284 |
20 | Italy | 0.028483 | 0.053912 | 375 | 8.119027e+11 | 0.1 | 0.079546 |
21 | Indonesia | 0.026866 | -0.139784 | 874 | 7.087751e+11 | 0.1 | -0.115604 |
22 | Mexico | 0.035903 | 0.109782 | 125 | 6.665680e+11 | 0.0 | 0.145686 |
23 | Belgium | 0.025691 | -0.030855 | 86 | 5.510959e+11 | 0.15 | -0.009017 |
24 | Singapore | 0.037972 | 0.043640 | 393 | 5.165128e+11 | 0.0 | 0.081611 |
25 | Thailand | 0.038464 | 0.023244 | 884 | 4.822688e+11 | 0.1 | 0.057862 |
26 | Turkey | 0.012009 | 0.012782 | 533 | 4.325922e+11 | 0.1 | 0.02359 |
27 | Norway | 0.021681 | -0.111988 | 199 | 4.004372e+11 | 0.25 | -0.095727 |
28 | Malaysia | 0.029048 | 0.007387 | 758 | 3.889432e+11 | 0.0 | 0.036435 |
29 | Russia | 0.053867 | 0.089574 | 86 | 3.867150e+11 | 0.15 | 0.135361 |
30 | Israel | 0.014221 | 0.057931 | 462 | 3.604961e+11 | 0.22 | 0.069024 |
31 | South Africa | 0.029489 | 0.014682 | 224 | 3.330064e+11 | 0.2 | 0.038273 |
32 | Finland | 0.026097 | 0.046477 | 98 | 2.911277e+11 | 0.1 | 0.069965 |
33 | Luxembourg | 0.012189 | 0.085743 | 55 | 2.533710e+11 | 0.1 | 0.096712 |
34 | Vietnam | 0.017380 | 0.024177 | 337 | 2.087371e+11 | 0.1 | 0.039819 |
35 | Bermuda | 0.023175 | 0.050781 | 57 | 2.073252e+11 | 0.0 | 0.073956 |
36 | Poland | 0.026415 | 0.144183 | 307 | 1.845841e+11 | 0.19 | 0.165579 |
37 | Chile | 0.023100 | 0.051612 | 163 | 1.805444e+11 | 0.35 | 0.066627 |
38 | Austria | 0.028145 | 0.083437 | 73 | 1.723833e+11 | 0.1 | 0.108767 |
39 | Qatar | 0.036076 | 0.021138 | 51 | 1.627576e+11 | 0.0 | 0.057214 |
40 | Kuwait | 0.030238 | 0.070329 | 144 | 1.382336e+11 | 0.05 | 0.099055 |
41 | Colombia | 0.050836 | 0.054003 | 23 | 9.796259e+10 | 0.35 | 0.087047 |
42 | Uruguay | 0.000678 | NaN | 4 | 9.665977e+10 | 0.07 | NaN |
43 | Greece | 0.024061 | 0.006618 | 150 | 9.222828e+10 | 0.05 | 0.029476 |
44 | Argentina | 0.005102 | 1.293891 | 77 | 8.726615e+10 | 0.35 | 1.297207 |
45 | New Zealand | 0.022350 | 0.015250 | 55 | 8.014322e+10 | 0.15 | 0.034248 |
46 | Cayman Islands | 0.008813 | 0.086408 | 63 | 7.437165e+10 | 0.0 | 0.095221 |
47 | Kazakhstan | 5.770967 | 0.500639 | 23 | 6.604369e+10 | 0.15 | 5.405961 |
48 | Egypt | 0.034592 | 0.095803 | 107 | 5.351686e+10 | 0.1 | 0.126936 |
49 | Macau | 0.012093 | 0.070620 | 16 | 3.723540e+10 | 0.0 | 0.082713 |
50 | Peru | 0.018947 | 0.127478 | 5 | 2.124148e+10 | 0.05 | 0.145478 |
51 | Czech Republic | 0.080742 | 0.114490 | 2 | 1.888434e+10 | 0.05 | 0.191195 |
52 | Hungary | 0.026897 | 0.076654 | 7 | 1.881912e+10 | 0.0 | 0.103551 |
53 | United Arab Emirates | 0.006051 | NaN | 10 | 1.672457e+10 | 0.0 | NaN |
54 | Pakistan | 0.054592 | 0.043361 | 44 | 1.672302e+10 | 0.1 | 0.092494 |
55 | CuraƧao | 0.032810 | -0.029051 | 2 | 1.135348e+10 | 0.0 | 0.003759 |
56 | Philippines | 0.000000 | NaN | 2 | 1.080448e+10 | 0.25 | NaN |
57 | Jersey | 0.029850 | 0.374507 | 19 | 1.070466e+10 | 0.0 | 0.404357 |
58 | Guernsey | 0.021304 | 0.000277 | 17 | 1.032459e+10 | 0.0 | 0.021581 |
59 | Monaco | 0.027281 | -0.024298 | 7 | 9.972276e+09 | 0.0 | 0.002983 |
60 | Cyprus | 0.034446 | NaN | 15 | 9.071393e+09 | 0.0 | NaN |
61 | Morocco | 0.000000 | NaN | 1 | 8.722357e+09 | 0.15 | NaN |
62 | Lithuania | 0.032841 | -0.004305 | 27 | 6.735860e+09 | 0.15 | 0.023609 |
63 | Iceland | 0.000876 | NaN | 3 | 6.432646e+09 | 0.22 | NaN |
64 | Malta | 0.002760 | 0.202286 | 10 | 5.704080e+09 | 0.0 | 0.205046 |
65 | Panama | 0.030591 | -0.039770 | 2 | 5.030780e+09 | 0.2 | -0.015298 |
66 | Korea | 0.059375 | 0.048367 | 2 | 4.226763e+09 | 0.15 | 0.098836 |
67 | Liechtenstein | 0.033438 | NaN | 2 | 3.125880e+09 | 0.0 | NaN |
68 | Mauritius | 0.027886 | 0.306922 | 11 | 2.655469e+09 | 0.0 | 0.334808 |
69 | Georgia | 0.093977 | NaN | 2 | 2.517544e+09 | 0.05 | NaN |
70 | Portugal | 0.059703 | -0.014311 | 2 | 2.160375e+09 | 0.1 | 0.039422 |
71 | Isle of Man | 0.029794 | -0.100601 | 3 | 1.912501e+09 | 0.0 | -0.070808 |
72 | Cambodia | 0.004732 | NaN | 1 | 1.741099e+09 | 0.14 | NaN |
73 | Bahamas | 0.004161 | NaN | 3 | 1.587848e+09 | 0.0 | NaN |
74 | Mongolia | 0.000000 | NaN | 3 | 1.432329e+09 | 0.2 | NaN |
75 | Nigeria | 0.082395 | NaN | 2 | 1.174157e+09 | 0.1 | NaN |
76 | Bahrain | 0.115303 | NaN | 3 | 1.121561e+09 | 0.0 | NaN |
77 | Costa Rica | 0.000000 | NaN | 1 | 1.071350e+09 | 0.15 | NaN |
78 | Ukraine | 0.005447 | NaN | 3 | 8.553552e+08 | 0.15 | NaN |
79 | Gibraltar | 0.017322 | NaN | 2 | 7.961045e+08 | 0.0 | NaN |
80 | Gabon | 0.118473 | 0.058544 | 1 | 7.681614e+08 | 0.2 | 0.153323 |
81 | Barbados | 0.027512 | 0.362677 | 1 | 6.496557e+08 | 0.05 | 0.388814 |
82 | Papua New Guinea | 0.066818 | 0.054186 | 3 | 5.708338e+08 | 0.15 | 0.110981 |
83 | Jordan | 0.013339 | NaN | 1 | 5.506400e+08 | 0.1 | NaN |
84 | British Virgin Islands | 0.014644 | NaN | 9 | 4.173784e+08 | 0.0 | NaN |
85 | Zambia | 0.590843 | NaN | 1 | 2.515148e+08 | 0.2 | NaN |
86 | Macedonia | 0.038683 | NaN | 2 | 2.413775e+08 | 0.1 | NaN |
87 | Greenland | 0.040325 | NaN | 1 | 1.756165e+08 | 0.44 | NaN |
88 | Botswana | 0.000000 | NaN | 1 | 6.230961e+07 | 0.1 | NaN |
89 | Estonia | 0.000000 | NaN | 4 | 2.918222e+07 | 0.0 | NaN |
90 | Namibia | 0.000000 | NaN | 1 | 2.340950e+07 | 0.2 | NaN |
91 | Dominican Republic | 0.000000 | NaN | 1 | 2.113918e+07 | 0.1 | NaN |
92 | Kenya | 0.000000 | NaN | 1 | 1.240714e+07 | 0.05 | NaN |
93 | Liberia | 0.000000 | NaN | 1 | 4.660614e+06 | 0.15 | NaN |
94 | Bulgaria | 0.000000 | NaN | 1 | 3.344554e+06 | 0.05 | NaN |
95 | Zimbabwe | 0.013590 | NaN | 1 | 3.326523e+06 | 0.15 | NaN |
96 | French Guiana | 0.000000 | NaN | 1 | 7.554022e+05 | 0.25 | NaN |
97 | Martinique | 0.042074 | NaN | 1 | 6.478878e+05 | 0.25 | NaN |
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