There has been great debate recently around the notion that passive ETFs are distorting valuations and reducing price discovery. As more investment denominations have flown into passive funds trying to chase popular named stocks or sectors, this has created upward pressure on less popular or otherwise not fundamentally justified stocks along with it, therefore removing price discovery and distorting valuations. With that in mind we’ve decided to value the S&P 500 using relative valuation, to get a sense of where we stand today. While we find the S&P 500 and developed economies are approaching overvalued territory, potential value opportunities in the global financial sector, automotive and airline industries still exist. The point of this research piece is to highlight current valuations, specify possible areas of undervaluation and to present a case for future research into certain sectors and companies.

We’ll begin with valuing the S&P using the Fed model and Yardeni Model. From there we will look at the cyclically adjusted price-to-earnings ratio of the S&P relative to its past. Lastly we will get a sense of valuations around the globe using price-to-earnings ratios and price-to-book ratios.

### **Fed Model**

A somewhat controversial model in use that attempts to value the S&P 500 is the Fed Model. The model tries to predict the return on the S&P 500 based on the relationship between forecasted earnings yields and yields on bonds. Specifically it relates the earnings yield of the S&P 500 to the yield to maturity on 10-year US Treasury bonds.

The idea is that the when the earnings yield of the S&P 500 is higher than the 10-year Treasury yield, equities are undervalued and are an attractive investment. If the reverse is found, equities are overvalued and unattractive. The intuition is that Treasury bonds are a risk-free asset versus stocks, a riskier asset. Therefore if yields are higher on Treasury bonds versus stocks, more money is being poured into equities than fixed income, signifying overvaluation.

As we can see in the chart below, according to this model anyway, equities are significantly undervalued.

Source: S&P 500 Earnings Yield vs 10 Year T Bond Yields

A major criticism and caveat to consider of the Fed model is that it is not forward looking and only states the present environment. Another criticism and probably more important is the idea that lower bond yields have been financially engineered by the U.S. Federal Reserve, through the manipulation of the Federal Funds rate and quantitative easing. Many would argue the Fed model is not a good representation of valuations today because of the financial engineering of the Federal Reserve.

### **Yardeni Model**

Sometimes referred to as a more robust model to the Fed model is the Yardeni model. This model incorporates a forward growth estimate of earnings. We can calculate the Yardeni model as follows:

CEY = CBY - b x LTEG + Residual

If you’ll notice, the model above is a linear regression model we all can remember from school as y=mx+b.

Where,

CEY is the current earnings yield, CBY equals an A rated corporate bond yield, b is the coefficient that measures the weight the market gives to five-year earnings projections and LTEG equals the consensus 5 year earnings growth forecast. Residual is the error term of the regression equation.

The current earnings yield CEY, can also be stated as E/P, so if we take the inverse of this we form the expression to find P/E, the price-to-earnings ratio:

Justified P/E = 1 / CBY - b x LTEG

We use the word justified here to state, with our assumptions included, what should be the P/E value of the S&P 500.

Therefore, using the above equation, we find that higher corporate bond yields (CBY) imply a lower justified P/E and higher expected long-term earnings growth (LTEG) result in a higher justified P/E.

Contrary to how the Yardeni model is traditionally used, we wanted to experiment with different variables using the past derive our P/E value. In deriving these assumptions to use in the model, we have presented variables under different economic environments below.

Average of Past 5 Years | Prior 5 Year Arithmetic Mean ending at start of Great Recession*** | Prior 5 year Arithmetic Mean ending at start of Early 2000 Recession*** | Post 5 Year Arithmetic Mean from beginning of Great Recession | Post 5 Year Arithmetic Mean from beginning of Early 2000 Recession | |

CBY* | 3.92% | 5.56% | 7.17% | 4.85% | 5.95% |

b** | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 |

LTEG | 2.25% | 8.62% | 22.29% | 42.08% | 10.72% |

P/E | 27.06 | 21.29 | 20.24 | 155.76 | 20.50 |

Source: *CBY found here Moody's Seasoned Aaa Corporate Bond Yield©

**According to Yardeni, the coefficient b has averaged 0.10, but reported weights that have been used include 0.10, 0.20 and 0.25.

***We find define the starting and ending of the Great Recession and Early 2000 Recession here. List of recessions in the United States - Wikipedia and S&P 500 earnings yield found here. S&P 500 Earnings Growth Rate by Year

Using the table above as a base, below are our assumptions.

CBY of 3.68 - This is the current corporate bond yield found here.

b of 0.10 - We use the average coefficient found by Ed Yardeni.

LTEG of 2.25% - We use the 5 year mean earnings growth of the last 5 years assuming the naive outlook that the past will represent the future.

Using this model and the assumptions above we derive a justified P/E for the S&P 500 of 28.95. If we compare this value to todays P/E ratio of 25.89 we can judge that the S&P is most likely approaching fair value.

However, when compared to the mean of the S&P 500 using data from 1871 to present of 15.66, we look to be overvalued. Of course different time periods justify different averages of earnings growth and P/E values.

### **Cyclically Adjusted Price-To-Earnings Ratio**

A popular measure of market valuations, made famous by John Y Campbell and Robert Shiller is the cyclically adjusted price-to-earnings ratio or CAPE ratio. This takes form as the ratio of the current price of the S&P 500 and the 10 year average of past earnings, adjusted for inflation. The premise for taking the long term average of earnings is that it smooths out volatility from short-term events and business cycles. We can compare the CAPE ratio to its past to get a sense of where we stand today. As seen below we have approached overvalued territory. If we believe the CAPE ratio is mean reverting, we should expect lower equity returns into the future.

Source: Shiller P/E

### **Price-to-Earnings Ratio**

The price-to-earnings ratios or P/E ratio is one of the most common and widely recognized ratios used in valuation today. As we know, earnings growth and power is a main driver of investment value. The denominator in the P/E ratio, earnings-per-share or EPS, is arguably the principal attention and focus of investors. According to empirical research, P/E ratios may have a relationship to differences in long-run average returns. In the chart below we use the P/E ratio to find specific under and overvalued sectors and companies.

Source: Finviz P/E ratios

You don’t have to be a genius to know that a whole sea of red may be a sign investors are getting ahead of themselves, or just that investors are extremely optimistic about future earnings growth. Fortunately you’ll notice there are some pockets of potential value left. Financials seem to be an area still open for opportunity, as well as the automotive industry within consumer goods, and if you look closely right in the middle of the services sector, a few squares of green, those are airline companies.

Now you may disagree with me and say that these sectors are priced below market for a reason, and you would be smart to think that. The automotive sector for example is beginning to see a major disruption in what cars are being manufactured and demanded, i.e. electric and other alternative energy cars. Many investors feel the incumbent car manufacturers, such as General Motors, are too behind or slow to act. The demand for ride sharing has also dampened shares of auto companies. We may be seeing the beginning of fewer cars on the road just because people don’t want the hassle of keeping and maintaining a car.

As in all investing and valuation, the present value of a company is a factor of its future growth in cash flows and its risk. In future research articles we will present a case for investing or not investing in automotive.

Potential disadvantages of the P/E ratio is that earnings-per-share, EPS, can be zero, negative or insignificantly too small relative to the price of the stock. When EPS is insignificantly small it does not make any economic sense when compared to other companies. A possible solution to this is to use the earnings yield E/P to compare companies. A yet even more discerning issue of P/E ratios is the application of different accounting standards across different companies. Corporate managers will choose different accounting applications and estimates in reporting earnings. Therefore EPS may be distorted across different sectors, industries and companies. In other cases corporate managers will either be too conservative or aggressive in reporting earnings, further manipulating EPS and making it harder to compare “apples to apples”.

### **Price-to-Book Ratio**

Another popular measure of value is the price-to-book ratio or P/B. Book value in this case represents the investment that common shareholders have made in the company. It is defined as taking shareholders equity (total assets minus total liabilities) and since we are looking to value common shareholders only, we will subtract preferred shares. The P/B ratio offers several advantages over its cousin P/E. For one, even when EPS is zero or negative, book value is usually positive. Book value per share is generally more stable than EPS, which makes it easier to compare companies, even through volatile earnings environments. There is also evidence that P/B ratios may have a relationship with differences in long-run average returns, which makes sense as they are less susceptible to volatile changes in earnings and book value is a cumulative balance sheet amount.

Lets now take a look at the landscape using the P/B ratios.

Source: Finviz P/B ratios

If we focus on just the financial, basic materials, and utilities sectors, potential value may be available and will require further research.

A major disadvantage to using the P/B ratio is it does not recognize critical factors such as human capital i.e. the value of knowledge and talents of the workforce. One could argue this should be represented as an operating expense in the selling, general and administration (SG&A) line item. The fact that workers are paid for their knowledge and talents should be addressed in the balance sheet, obviously this may not be the case and the balance sheet may or may not take into affect future labor contributions.

### **Global Price-to-Earnings Ratios**

Let’s move abroad and use relative valuation ratios to get a sense of what parts of the world are under or overvalued.

Source: Finviz Global P/E ratios

It may be hard to see, but if you look closely, many of the “cheapest” companies on a P/E basis, in no particular order, seem to reside in Japan, South Korea, Brazil and South Africa.

Again you would be smart to question what does cheap or undervalued really mean here. For example, South Korea, geographically being closer to the political turmoil of its neighbor North Korea, many would argue is too risky of an investment. Again value is a function of future growth in cash flows and risk. If we assume in our models that the political uncertainty in North Korea will subside, and growth will continue in that region, this may be a great value play. Going forward we will investigate this economy in future research.

Lastly we will end with CAPE ratios around the world. Given the assumption that economies with higher CAPE ratios versus lower CAPE ratios will revert towards their means, we can use the CAPE ratio to rank countries. Star Capital provides a great resource for valuing economies by its CAPE ratio which you can find here.

Simply put in order from 1 through 10, the highest ranked countries by lowest CAPE ratio include South Korea, Austria, Czech, Hungary, Italy, Poland, Portugal, Turkey, Spain, Russia, and China.

In the next piece we will dig deeper into the banking equities around the world and take a deep dive into specific company fundamentals.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.