**Abstract**

In the article the two approaches to the market's valuation are considered. The first one is based on using of the model of alternative investments, which is the second approximation for the Fed's model. The role of the model of alternative investments has increased for last 25 years since it allows describing of about 88% of results. It is interesting to note that the Fed's model itself describes only 73% of the results during the last 25 years. The second approach is based on a new method of valuation - Relative Earnings Accumulation Rate. This method is put in practice in order to describe the concept of earnings accumulations for the stock market. It allows estimating a difference between relative rates of growth of earnings and market. It is shown that during periods of essential earnings accumulation, when the meaning of REAR exceeds 100%, the market's growth is moderate enough. But such conditions create the basis for further great long-term growth of the market. The latest reading of REAR shows that the market's growth is supported by REAR's growth. It is a positive sign. However, in order to keep the process of earnings accumulation in the future and to create the base for the long-term bull trend the earnings growth should essentially outstrip growth of the market. As the earnings growth in the coming decade could appear moderate enough, the potential for growth of the market can be sufficiently limited as well. All the above indicates the cyclic nature of the current bull trend of the market.

**1. Introduction**

The US economy showed essential growth in 2003. So the GDP grew on impressive 8.2% in the third quarter and 4.1% in the fourth quarter. As a consequence, the companies' earnings surged.

In accordance with analysts' estimates the earnings will continue to grow in 2004 though should fall of last year's rate. For market's participants one of the main questions is how earnings growth will be translated into market's prices.

Certainly, earnings growth is one of the main engines of equity market. This factor had the greatest influence on prices dynamics in 2003.

But equity market is a complex system. It means that other parameters of system could enter into the game in this year.

As it was shown in [1], the year-to-year change of S&P 500 does not depend on profits cycle, i.e. on short-term change in earnings. The more important factor is the long-term earnings growth rate. So, the nominal earnings, dividend and market growth rate in the period since 1871 up to 1948 followed 1.5 % per year growth curve [2]. In the second half of last century (since 1949 up to 2004) the earnings growth rate was speed up and followed 5.5% per year growth curve. At the same time the growth of S&P 500 outstripped earnings growth and followed 8% per year growth curve. Such divergence of earnings growth and the market growth have already resulted in high value of earnings multiple ratio.

But even the high meaning of P/E ratio can become higher if market's participants want to reduce equity risk premium further. It is really a challenge to try predicting how long the sentiments of market's participants will keep the equity risk premium at the low level. But it is possible to describe the direction of main forces, which should at the end switch these sentiments.

**2. Discussion**

In accordance with the model of alternative investments [3] (which is the second approximation for the Fed's model) the current real earnings yield (reciprocal of P/E ratio) correlates with 10-Y Treasury bond yield and 10-year average of CRB Spot Index yield by the following way:

(1) **CREY(pred)=a+b _{t}·TBY+b_{c}·VTBY_{p},**

*CRBY _{p}=CRBY-TBY*

where

* CREY(pred)* is the current real earnings yield predicted by the model,

* TBY* is the 10-Y Treasury bond yield,

* CRBY* is the 10-year average of CRB Spot Index yield.

* a* is the constant,

* b_{t}* is the value of the response of CREY for TBY,

* b_{c}* is the value of the response of CREY for "pure" yield of CRB Index (i.e. its part which does not depend on TBY),

I have repeated the procedure of statistical estimation of the model described in [3].

To calculate the coefficients in expression (1), the statistical method of multiple regression is applied. Data for 183 quarters since March 1958 till September 2003 are used.

As a consequence, the following statistical results were obtained:

Regression Summary for Dependent Variable: CREY | |||||

R= 0.889 R-sq= 0.791 Adjusted R-sq = 0.788 | |||||

F(2,180)=340.34 p<0.0000 Std.Error of estimate: 1.28 | |||||

BETA | St. Err.of BETA | B | St. Err.of B | t(180) | |

Intercept | 3.99 | 0.321 | 12.4 | ||

TBY | 0.68 | 0.034 | 0.73 | 0.036 | 19.8 |

CRBY_{p} | 0.53 | 0.034 | 0.52 | 0.033 | 15.7 |

(2) **CREY(pred)=3.99+0.73·TBY+0.52·CRBY _{p},**

I used further the described above statistical procedure for an estimation of parameters of the model for the last 25 years (since December 1978 till September 2003).

The following results were obtained:

Regression Summary for Dependent Variable: CREY | |||||

R= 0.94 R-sq = 0.88 Adjusted R-sq = 0.878 | |||||

F(2,97)=357.73 p<.00000 Std.Error of estimate: 1.1361 | |||||

BETA | St. Err.of BETA | B | St. Err.of B | t(97) | |

Intercept | 1.37 | 0.441 | 3.1 | ||

TBY | 0.82 | 0.035 | 0.97 | 0.042 | 23.3 |

CRBY_{p} | 0.39 | 0.035 | 0.48 | 0.043 | 11 |

(3) * CREY(pred)=1.37+0.97·TBY+0.48·CRBY_{p}*,

The role of the model has increased for the last 25 years since it allows describing about 88% of results. It is interesting to note that the Fed's model itself describes only 73% of the results during the last 25 years. Particularly TBY plays the larger role in the last 25 years as its beta has grown from 0.68 up to 0.82 while pure CRBY beta has decreased from 0.53 up to 0.39.

These data specify that in the course of time the market displaces the priorities. Therefore, there are no universal laws at the equity market.

In Figure 1 the dynamic (on a quarterly base) of CREY, TBY and CREY predicted by the model of the alternative investments (2) for the whole period of testing is shown.

In Figure 2 the dynamic of above mentioned factors and CREY predicted by the model of the alternative investments (3) for 25-years period is shown.

On March, 30 2004 S&P500's P/E ratio is 23 (based on preliminary estimates for Q4 earnings) and corresponding CREY is 4.35. In accordance with the expression (2) CREY predicted by the model of alternative investments is 5.80 (the meaning of TBY is 3.902 and CRBY(pure) is -1.99). So, the market is overvalued on 33%. But the market is fairly valued in accordance with the expression (3) as meanings of predicted CREY is 4.20%.

Let's consider the factors of the model of the alternative investments in details.

I think that there are a lot of reasons to move bond yield higher this year.

The first reason is the correlation of 10-Y Treasury bond yield with the year-to-year change of GDP and earnings. As it is shown in the Figure 3, bond yield (left scale) tends to grow when GDP (left scale) and earnings (right scale) are growing.

The second reason is the influence of economic growth on FED policy in relation of Federal Funds rate. So, one of the most important parameters of economic activities is Industrial commodity prices (CRB Raw Industrial Sub-Index). As it is shown in the Figure 4, FED made shift from accommodation to aggressive tightening when Industrial commodity prices grew (see also [4]).

Thus GDP, earnings and commodities growth should lead to growth both Federal Funds rate and 10-Y Treasury bond yield.

The second factor of the model is the 10-year average of CRB Spot Index yield. This factor is expected to continue its growth as CRB Spot Index (right scale) closely correlates with both row industrials components (right scale) and the price of gold (left scale). The Figure 5 shows these correlations.

Resuming growth of the global economy is expected to result in further rise in prices of row industrials components and gold.

Thus, the 10-year average of CRB Spot Index yield will surge this year.

As a result, the current earnings yield will grow as well. It is possible only in case when the growth of equity market will be limited.

In [1] the concept of phase of earnings accumulations as periods of significant outstripping of earnings growth over the market growth is introduced.

To define the concept of earnings accumulation in the form of the numerical expression I used the following procedure:

- the average meanings of earnings and S&P 500 for the last 25 years are calculated,
- the deviations (expressed in percentages) of earnings and S&P 500 from their respective average are calculated,
- the difference between the above deviations is found

Let's name the above-described expression as Relative Earnings Accumulation Rate (REAR)

(4) *REAR=RER-RMR*

* RER* is the relative earnings rate (expressed in percentage deviation of the earnings from the average meaning for 25 years)

* RMR* is the relative market rate (expressed in percentage deviation of S&P 500 from the average meaning for 25 years)

* REAR* can be calculated for other time periods and market's benchmarks as well.

In Figure 6 two curves are shown. First is the Relative Earnings Accumulation Rate calculated according to the expression (4). The second curve is the more smoothed. For this curve calculation it is used the difference between deviations of 4 year averages of earnings and S&P 500 from their respective averages for 25 years.

As it follows from Figure 6 for last 60 years there were two primary ascending trends of REAR and two primary descending trends. The results are shown in the tables below:

Table 1

REAR direct. | Period | REARRange | Duration(years) | S&P 500 Chng. % | S&P 500 Chng. %Per Year | Earn. Chng.% | Earn. Chng. %Per Year | Earn. Rate- S&P500 Rate |

Up Trend | 06/30/46 - 06/30/49 | -55% + 126% | 3 | -25% | -7.7% | +186% | +41.9% | +49.6% |

Up Trend | 12/31/61 - 03/31/80 | -120% + 122% | 18.5 | +46% | 2.1% | +379% | +8.8% | +6.8% |

As it follows from the Table 1, the market's growth is moderate enough during the periods of essential earnings accumulation, when the REAR meaning exceeds 100% level, (see columns 5 and 6 of the table). Simultaneously, the rate of annual earnings growth essentially outstrips the appropriate rate of the market (see last column of the table).

As a consequence, such conditions create a basis for further great long-term growth of the market. As it follows from the Table 2, during the periods of REAR fall, the averaged market growth rate was 14% per year, while earnings showed moderate growth rate.

Table 2

REAR direct. | Period | REARRange | Duration(years) | S&P 500 Chng. % | S&P 500 Chng. %Per Year | Earn. Chng.% | Earn. Chng. %Per Year | Earn. Rate- S&P500 Rate |

Down Trend | 06/30/49 - 12/31/61 | +126% -120% | 12.5 | +414% | +14% | +33% | +2.3% | -11.7% |

Down Trend | 03/31/80 - 03/31/99 | +122% -196% | 19 | +1124% | +14.1% | +150% | +4.9% | -9.2% |

The last long-term period, when REAR has fallen from +122 % up to -196 %, lasted 19 years since March 1980 till March 1999 (see Figure 7). During this period market grew on 1124% (or 14.1% per year), while earnings grew only 150% (or 4.9% per year).

It is necessary to note that against a background of primary down trend of REAR (and contrary market's up trend) there were five secondary counter-trends.

The resent action of REAR specifies transition in long-term up trend. So the absolute minimum of REAR at the level of -196 % was registered in March 1999. The following minimum of the REAR in December 2001 was__ __already at higher level (-142 %).

The latest reading (red arrow on the chart) shows that the market's growth is supported by REAR's growth. It is a positive sign.

However, in order to keep the process of earnings accumulation in the future and to create the base for the long-term bull trend the earnings growth should__ __essentially outstrip growth of the market.

As the earnings growth in the coming decade could appear moderate enough (see [2], [5]), the potential for market growth can be sufficiently limited as well. All this specifies on the cyclic nature of the current bull trend of the market.

**3. Conclusion**

It is shown that the role of the model of alternative investments (which is the second approximation for the Fed's model) has increased for the last 25 years since it allows describing about 88% of results. At the same time there was a shift in the extent of responses (measured as betas) of the model's factors. Particularly, TBY plays the larger role in the last 25 years as its beta has grown__ __from 0.68 up to 0.82, while CRBY (less TBY) beta has decreased from 0.53 up to 0.39. These data show that in the course of time the market displaces the priorities. Therefore, there are no universal laws at the equity market. It is shown that the absolute value of the factors of model should grow. As the result the current earnings yield should grow as well. It is possible only in that case if the grows of market will be limited. In the article the expression for Relative Earnings Accumulation Rate is entered. REAR is described the concept of earnings accumulation for the stock market. Particularly during periods of essential earnings accumulation, when the meaning of REAR exceed 100% the market's growth is moderate enough. The latest reading shows that the market's growth is supported by REAR's growth. However, in order to keep the process of earnings accumulation in the future the earnings grows should essentially outstrip growth of the market.

**References:**

[1] "Playing On Profits Cycle?", Dmitry Baryshevsky, Gold - Eagle, October 27, 2003,

[2] "The Speed", Dmitry Baryshevsky, Safe Haven, July 14, 2003,

[3] "What is hidden in the Fed's model? The second approximation", Dmitry Baryshevsky, Gold - Eagle, August 21, 2003,

[4] "What If The Fed Tightens?", Investment Strategy, Dr. Edward Yardeni, October 22, 2003, Prudential Equity Group, Inc.

[5] " Thoughts On The Equity Risk Premium And Expected Equity Returns", Quantitative Strategy, Edward Keon and others, February 6, 2004, Prudential Equity Group, LLC.