In this study, we empirically investigate the relevance of relative valuation models in the
Japanese stock market. Using various multiples such as Price Earnings Ratio (PER), Price Book
Value Ratio (PBR), Price Sales Ratio (PSR), and Price Cash Flow Ratio (PCR), we study which valuation model is the best in forecasting stock prices, and in identifying portfolios which generate higher returns. We find that in terms of prediction accuracy, PBR is the best, while in portfolio selection results vary across the industry.

I.
In Japan, as in other advanced countries, fundamentals of corporate performance play a key role in the valuation of firms by the markets. Although the popular press has often discounted the role of fundamentals in the Japanese equity market, recent academic research demonstrates that the Japanese stock prices do react to fundamental news. These findings are consistent with the view that the globalization of Japanese financial markets has made them more efficient.
Three different approaches to firm valuation are usually mentioned in the literature. They are discounted cash-flow (DCF) method, relative valuation method (multiple method), and contingent claims valuation method. DCF relates the value of the asset to the present value of the expected future cash flow on that asset, and is widely used in the United States. The relative valuation model estimates the value of the asset by looking at the pricing of ‘comparable’ assets relative to variables like earnings, cash flow, book value or sales. The relative valuation model is easy to apply, and for that reason in Japan analysts prefer relative valuation to DCF. In the early 1990s when the Japanese stock market was at the initial stage of globalization, the accuracy of relative valuation was good enough to be accepted by market analysts. Recently, however, with increased competition in global markets, the relative valuation model is believed to be far less accurate than in early 1990s.
2

In relative valuation, the value of an asset is compared to the value assessed by the market for comparable assets. To implement relative valuation, first we need to identify comparable assets and obtain market values for them. The next step is to convert these market values into the standardized values because absolute prices cannot be compared. This process of standardization results in price multiples.
Lastly, we compare the standardized values or multiples for the asset that we are interested in to the standardized values for comparable assets, after controlling any differences between firms that may affect the multiples, and we conclude whether the asset is fairly valued.
The purpose of this paper is to test how effective the relative valuation model is in identifying undervalued or overvalued stocks in the Japanese stock market. To address the issue of predicting accuracy, we empirically analyze and compare the forecast errors calculated by various multiples. By comparing the forecast errors calculated by various multiples, we can tell which multiple is the best predictor of the stock price. Since we believe that the results will be quite different across the industry we compare the forecast errors within the same industry. Furthermore, we investigate which relative valuation method is the best in generating higher returns in the Japanese stock market. We will formulate two portfolios, one undervalued and the other overvalued, and will apply a zero-net investment strategy.
By comparing zero-net portfolios’ returns, we can find out which multiple is related with the best investment strategy.
The remainder of the paper is organized as follows. In section 2 we describe the sample companies
3

and data. In section 3, we investigate which multiple is the best predictor and gives rise to the best investment strategy. Section 4 concludes this paper.
The initial sample is from the PACAP(Pacific-Basin Capital) Market Research Center database. We select non-financial companies (with March fiscal year) traded on the Japan Stock Exchange from January 1990 to December 1999. Since we need to divide firms into two groups according to the levels of multiples, we exclude industries with less than 10 firms. As a result we end up with 195 firms from 10 industries. Our sample includes construction; machinery and equipment; wholesale and retail trade; textiles and apparel; motor vehicles and transport equipment; food and beverage; electrical machinery and apparatus; radio,
TV and communication equipment; basic metals; and chemicals and chemical products.
For each firm, we collect sales, earnings, earnings per share (EPS), book value of equity per share (BPS) and cash flow. Daily closing stock prices are retrieved from the Japan Securities Research Institute (JSRI) database. To minimize estimation errors, as the monthly stock price we use the average of daily stock prices rather than the month-end stock price. To be more specific, we define variables as follows.
4

P i , t

N j
 i

1
, t
P i , j , t
N i , t
P i , t
: average stock price of firm i in June of year t
P i , j , t
: closing stock price of firm i at day j of June in year t
N i , t
: number of trading days of firm i in June of year t
We use industry medians of price earnings ratio (PER), price book value ratio (PBR), price sales ratio (PSR), and price cash flow ratio (PCR) to calculate the forecasted stock price.
1 We believe there are some anomalous factors that can explain a temporary gap between the fundamental value and the actual market price of the stock. In other words, there is a tendency that in the long run stock prices adjust themselves in a way to make the multiples the same across the firm in the same industry.
Accounting information on March fiscal year firms is officially announced in May or June, and therefore we use the average daily stock prices in June to calculate the forecasted prices.
The multiples we use are as follows.
PER
PSR i i , t
, t

 p i p i , t
, t
EPS i , t
SPS i , t
PBR i , t
 p i , t
BPS i , t
PCR i , t
 p i , t
CPS i , t
1 By using medians instead of means, we can avoid spurious effects by serious outliers.
5

Under Gordon’s constant growth model, PER is expressed as [payout ratio*(1+g)]/(r-g). PER varies across the industry and across the firm because of the differences in fundamentals. Usually, higher growth translates into higher PE ratios. When comparisons are made across the firm, differences in risk, growth rates and payout ratios have to be controlled explicitly. Thus we use other firms in the same industry as a control group.
2
PBR is the ratio of the market price to the book value of a share. Using Gordon’s growth model with the definition of ROE=EPS
0
/(Book value of equity), PBR equals {[ROE*(Payout Ratio)*(1+g)]/(r-g)}. It provides a relatively stable and intuitive measure of value which can be compared to the market price.
Even firms which have negative earnings and therefore cannot be valued with PER, can be evaluated if
PBR is used.
Unlike PER and PBR which can be negative, in which case they are meaningless, PSR is available for the most troubled firms.
Besides, while PER and PBR are easily influenced by accounting decisions on depreciations or inventory and extraordinary charges, PSR is more reliable for valuation purposes because sales are relatively difficult to manipulate. Under Gordon’s growth model with the definition of Profit
Margin=EPS
0
/(sales per share), PSR becomes (profit margin)*(Payout Ratio)/(r-g).
2 Sometimes this approach may not be the best one when firms in the same industry have very different business mixes and risk and growth profiles.
6

PCR is the ratio of the stock price to cash flow per share. The cash flow per share is net income plus depreciation divided by the number of shares outstanding.
When we address the issue of predicting accuracy, we use industry medians rather than industry means. The forecasted stock price is derived by multiplying the industry median of the multiple with each firm’s denominator in the multiple. For example, when we use PER, the forecasted stock price is defined as follows.
P i , t f
= [ Industry Median of PER ] i,t

EPS i,t
[ Industry Median of PER ] i,t
denotes year t’s median of PER for firms in the industry to which firm i belongs. For each company and for each year, we compute an absolute percentage forecast error in the stock price, defined as the absolute value of the difference between forecasted and actual stock prices, divided by the forecasted price. These absolute forecast errors are then averaged across the firm to construct a mean absolute percentage forecast error (MAPE). The MAPE represents the average ability of multiple in forecasting stock prices. Companies with absolute percentage forecast errors above 1.0
7

(100%) are assigned a value of 1.0 to keep outliers from distorting the reported average.
3
MAPE j , t
 i n
 j

1
P i , t r 
P i , t f p i f
, t n j
MAPE j , t
: forecast error for industry j at year t
In this section, we focus on the forecast accuracy by examining the mean absolute percentage errors for each industry. Using each multiple, we calculate the MAPE for ten industry groups as shown in section (a) of <Table 1>.
<Table 1> Insert Here
Initially, we expected that the best predictor among various multiples would differ depending on the industries. But it turns out that PBR is almost always the best predictor except for the food and beverage industry, for which we get the least MAPE with PCR. Globally, PBR is the best predictor of stock price
3 We use a MAPE rather than a mean squared error because the latter gives heavy weights to large errors. Use of the MAPE and the convention of assigning a maximum of 100 percent help us to avoid assigning too much weight to a few very large forecast errors.
8

compared to PER, PSR, and PCR. Considering the fact that the book value of equity is historically the most stable, we can easily understand why the MAPE of PBR is smaller than those of the other multiples.
We divide the sample period into bear and bull market periods, and compare forecast accuracies to check the robustness of results.
4 The results are summarized in sections (b) and (c) of <Table 1>. The differences of results in sections (b) and (c) from (a) are: In the bull market period, PCR is the best predictor in textiles/apparel, food/beverage, and Radio/TV/communication equipment industries;
During the bear market period PSR is, if marginally, the best predictor in the textiles/apparel industry, and
PCR is the best in the food/beverage industry. Comparing forecast errors in (b) and (c), we find that forecast errors in the bull market are generally smaller than those in the bear market. This finding is related with the argument that fundamental information of Japanese firms plays a more active role in the bull market period.
According to <Table 1>, the range of forecast errors with PBR is generally the smallest, but that does not mean employing PBR in the investment strategy will provide higher returns than when other multiples are used. It only tells us that PBR generates the least variance within the industry. Therefore we further investigate whether there is a mean reversion effect in the multiples. We dynamically calculate the investment returns of various investment strategies to find the best portfolio selection method.
4 Based on the annual stock market performance (from June to next May), we call a positive(negative) TOPIX return period as bull(bear) market. This criterion classifies 1992, 1993,
1995 and 1998 as the bull market period, and 1990, 1991, 1994, 1996 and 1997 as the bear market period.
9

We adopt a zero net investment strategy where the amount invested in the long portfolio is the same as that invested in the short portfolio. For each multiple, we create a long (short) portfolio with the stocks of the firms belonging to the top(bottom) 20% group. We invest the equal amount to each firm, i.e., we create an equally weighted portfolio. Finally, we measure the portfolio performances by Jensen index which allows for embedded risks in the portfolio.
5
<Table 2> Insert Here
<Table 2> compares the performances of investment strategies based on various relative valuation models. From section (a) we can see that annual average returns for most portfolios are positive.
Compared with other multiples, PSR offers the best results both in terms of the annual average return and in terms of Jensen index in six out of 10 industry groups. Also it is surprising that contrary to the belief of the popular press, PER is the worst multiple in 8 industry groups. The investment strategy based on PER generates negative annual average returns in 6 industry groups.
The above results are consistent with the view that the investment strategy based on fundamental values can generate higher returns in the Japanese stock market.
6 The result that PSR is the best multiple in 6 out of 10 industry groups is quite different from the conclusion we draw from the analysis of forecast error comparison in <Table 1>. It leads us to conclude that while PBR is a stable multiple within the same
5 Jensen index measures the abnormal return in excess of the risk-adjusted return. To calculate
Jensen index we need the beta of each firm, and for it we use 36 monthly stock returns.
6 According to <Table 3>, the Jensen index of every portfolio is very close to the annual portfolio return. It means that betas of zero net investment portfolios are close to 0.
10

industry, there is no tendency for a high or low PBR to revert to the industry median.
Sections (b) and (c) in <Table 2> show the performances of investment strategies in bull and bear market periods. It is interesting to see that PER, which results in the worst performances in most industry groups for the whole period, turns out to be the best multiple for 3 industry groups in the bear market period. From this, we suspect that PER is a better multiple in the bear market than in the bull market.
We test whether the relative valuation model is effective in identifying undervalued and overvalued stocks in the Japanese equity market. To address the issue of predicting accuracies, we empirically analyze and compare the forecast errors based on various multiples. Based on our expectations that results would be different across the industry, we compare the forecast errors within the same industry. By comparing the forecast errors generated by various multiples, we find that PBR gives rise to least prediction errors.
Next, we investigate which relative valuation method is the best in generating higher returns in the
Japanese stock market. We form two portfolios, undervalued and overvalued, and opt for a zero-net investment strategy. By comparing zero-net portfolios’ returns, we find that PSR is related to the best investment strategy in the whole period, but PER is a reasonably good multiple in the bear market period.
11

3
4
5
1
2
6
7
8
9
10
MAPE (Mean Absolute Percentage Error) under Various Relative Valuation Model a. Whole Period (1990-1998) (unit : %)
Industry PER PBR PSR PCR
1
4
5
6
7
2
3
8
9
10
39.87
42.64
53.94
58.47
52.44
51.12
53.48
45.89
48.34
37.56
30.84
17.39
22.98
29.04
24.53
39.85
29.88
31.46
27.29
25.43 b. Bull Market Period (1992, 1993, 1995, 1998)
Industry PER PBR
36.97
36.55
63.37
38.55
47.82
33.98
39.98
38.64
49.20
39.73
35.66
32.05
43.59
44.30
36.02
30.50
32.90
39.41
39.35
30.46
(unit : %)
52.78
58.29
56.87
52.55
59.76
49.81
51.32
44.75
43.73
36.72
28.78
11.63
19.76
27.71
19.19
34.55
19.63
25.33
19.64
25.34
PSR
31.79
29.48
48.65
29.29
42.10
36.12
34.32
41.70
33.45
29.32
PCR
33.52
32.51
51.65
23.52
32.30
33.09
29.06
25.25
32.66
34.16
12

c. Bear Market Period (1990, 1991, 1994, 1996, 1997)
Industry PER PBR
4
5
6
7
1
2
3
8
9
10
61.34
30.58
43.51
61.32
45.28
40.28
60.42
54.26
43.54
42.27
Industry Code:
1.
Construction
2.
Machinery and equipment
3.
Wholesale and retail trade
4.
Textiles and apparel
5.
Motor vehicles and transport equipment
6.
Food and beverage
7.
Electrical machinery and apparatus
8.
Radio, TV and communication equipment
9.
Basic metals
10.
Chemicals and chemical products.
34.28
19.35
23.67
36.53
27.48
37.29
29.46
30.75
34.64
30.16
13
(unit : %)
PSR
42.68
49.73
68.57
35.63
45.36
37.49
51.64
37.24
47.81
40.45
PCR
40.12
33.68
39.54
58.42
38.51
27.57
33.51
45.96
37.68
39.45

<Table 2> The Comparison of Portfolio Performance of Investment Strategy
Using Various Relative Valuation Model a. Whole Period (1990-1998) (unit : %)
Industry PER PBR PSR PCR
1
Annual Average
Return
28.34
*** 14.49
*** 37.34
*** 29.35
***
31.45 16.21 39.23 31.11
2
3
4
5
6
7
8
9
10
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
-15.23
-12.10
-10.12
-9.12
-22.33
-21.19
-12.11
-22.09
-19.34
***
-10.22
-20.88
-18.17
0.21
1.24
-2.13
1.01
***
***
***
***
***
-2.09
-0.11
22.96
***
23.55
15.23
***
14.94
10.13
22.12
23.37
6.32
***
12.81
31.10
***
35.11
5.21
*
6.19
22.09
21.76
6.98
26.19
*
27.12
***
***
***
59.22
***
58.84
36.13
***
38.11
29.12
***
31.24
21.12
***
20.39
21.19
***
24.12
42.12
***
43.73
29.12
***
32.04
0.23
1.32.
32.71
***
35.01
29.23
29.77
32.11
34.13
-7.43
-5.73
16.97
17.99
47.60
49.30
-15.73
-12.76
22.19
23.75
18.12
21.01
31.18
***
***
***
***
***
***
***
***
33.12
* Significant at 10% level
** Significant at 5% level
*** Significant at 1% level
14

b. Bull Market Period (1992, 1993, 1995, 1998)
Industry PER PBR
1
2
3
4
5
6
7
8
9
10
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
23.12
-19.84
-3.12
-2.76
-12.88
-22.13
-11.19
**
-10.39
22.39
***
-7.34
***
24.89
-14.18
***
-13.12
-9.12
*
-8.76
-21.77
-13.71
-23.19
***
***
***
25.01
*
-6.99
15.12
13.88
*
16.12
34.17
39.95
23.12
-9.22
10.73
28.12
28.98
25.67
***
35.78
***
41.23
***
25.12
*
-8.39
***
11.09
***
***
25.65
***
14.12
33.72
***
34.87
(unit : %)
PSR
29.17
31.98
1.35
2.28
23.09
***
25.48
18.91
***
19.63
19.65
23.17
***
19.76
***
25.73
-2.21
-1.72
21.76
***
22.98
17.74
***
18.45
21.69
**
22.72
PCR
19.12
13.89
***
20.14
***
14.59
38.83
***
40.32
-8.12
**
-9.43
28.76
29.01
32.87
***
***
33.82
3.88
4.01
25.76
***
25.99
21.74
***
22.73
18.34
***
19.05
* Significant at 10% level
** Significant at 5% level
*** Significant at 1% level
15

c. Bear Market Period (1990, 1991, 1994, 1996, 1997) (unit : %)
Industry PER PBR PSR PCR
1
2
3
4
5
6
7
8
9
10
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
Annual Average
Return
Jensen Index
-8.32
17.87
*
2.78
3.01
7.98
**
8.23
*
-8.22
1.83
1.88
27.34
***
27.59
2.78
3.15
-24.48
-12.24
18.98
32.74
***
33.98
-13.87
***
***
***
-12.78
2.93
4.32
-26.34
***
-23.99
14.78
15.21
12.34
14.78
45.89
46.87
10.75
12.34
23.89
***
***
***
***
***
25.73
24.30
***
22.99
5.43
5.99
-5.87
*
-6.32
17.21
18.12
23.35
-21.74
8.87
-11.87
***
***
25.84
4.66
3.99
*
9.10
6.54
7.01
-10.43
27.33
***
15.98
***
4.65
5.12
***
-23.32
**
28.23
16.98
9.87
18.73
1.99
-26.20
19.45
***
20.65
-17.74
13.77
*
11.74
15.03
28.07
3.89
4.17
***
19.98
1.83
-25.87
***
***
-16.89
***
16.87
***
18.88
24.78
***
* Significant at 10% level
** Significant at 5% level
*** Significant at 1% level
16

Basu, S., "The Investment Performance of Common Stocks in Relation to Their Price-Earnings Ratio",
Journal of Finance June 1977, pp. 951-970
Breen, W., "Low Price Earnings Ratios and Industry Relations", Financial Analysts Journal , July/August,
1968, pp. 23-34
Chan, K.C., Y. Hamao, and J. Lakonishok, Fundamentals and Sock Returns in Japan, Journal of Finance
1991, pp. 1739-1789
Conroy, R., R. Harris, and Y. Park, “Published Analysts’ Earnings Forecasts in Japan: How accurate are they?”, Pacific-Basin Finance Journal 1993. pp 127-137
Fama, E. and K. French, “The Cross-section of Expected Stock Returns”, Journal of Finance 1992, pp. 427-465
Fisher K., "Price Sales Ratios : A New Tool for Measuring Stock Popularity", American Association of
Individual Investors Journal , June. 1984, pp.13-17
Goodman D. A. and J. W. Peavy, "The Significance of P/E for Portfolio Returns", Journal of Portfolio
Management , 1983, pp 34-57
Lee, J. and Y. Ahn, “Performance Analysis of Investment Strategy in the Korean Stock Market,” The
Journal of Korean Securities Association, 2002, pp 33-72
Malkiel B. and J. Craig, "Expectation and the Structure of Share Price," American Economic Review (Sep.
1970). pp. 601-617
Park, Y. and G. Lee, “The Opening of Korean Stock Market and Stock Price Behavior: From View Point of Co-Movements by Business Group and Industry”, The Journal of Korean Securities Association , 2000, pp 27-63
Senchack J. and J. Martin, "The Relative Performance of PSR and PER Investment Strategies", Financial
Analysts Journal , March-April, 1987, pp.46-56
17

Whitbeck V. S. & M. Kisor, "A New Tool in Investment Decision Making", Financial Analysts Journal
(May-June 1963), pp. 55-62
18