## Portfolio Construction Based On Fundamental Ratios

**Highlights**

- Relative valuation is one of the basic concepts of stock evaluation that allows us to determine undervalued stocks.
- The Treynor-Black model enables us to construct a portfolio with active and passive investment parts.

**Principles of Relative Valuation**

The objective of relative valuation is to value assets based upon how similar assets are currently priced in the market. There are two components to relative valuation. The first one is to value assets on a relative basis by converting prices into multiples of earnings, sales, or book value. The second one is to find comparable companies, which could be difficult to do, since there are no two identical companies, and companies in the same business can still differ on risk, growth potential, and cash flows. Relative valuation has its pros and cons. Valuation based upon multiple and comparable companies can be completed with far fewer assumptions and far more quickly than discounted cash flow valuation. Relative valuation is also much more likely to reflect the current mood of the market because it is an attempt to measure relative and not intrinsic value. In fact, relative valuations will generally yield values that are closer to the market price than discounted cash flow valuations.

However, the strengths of relative valuation are also its weaknesses. Pulling together a multiple and a group of comparable companies can also result in inconsistent estimations of value where key variables such as risk, growth, or cash flow potential are ignored. Moreover, the fact that multiples reflect the market mood also implies that applying the relative valuation method to estimate a stock value can result in values which are too high when the market overvalues comparable companies, or too low when it undervalues these companies.

Relative valuation is one of the basic concepts of stock evaluation with its pros and cons. However, even if we can determine undervalued stocks based on price ratios, there is a question of how to effectively incorporate a stock that is supposed to be undervalued in an investment portfolio to also get benefits from diversification, and it is where the Treynor-Black model can help to find the balance between active and passive investment. The Treynor-Black model is a portfolio-optimization model that seeks to maximize a portfolio’s Sharpe ratio.

**Constructing Portfolio Based upon P/E Ratio**

Let us evaluate two companies from the energy sector based on the P/E ratio: Occidental Petroleum Corporation (OXY) and Marathon Oil Corporation (MRO). OXY and MRO have stock prices of $60.10 and $25.17 and Earning Per Share in TTM of $6.59 and $2.86 on May 11th, 2022. I have chosen the next comparable companies: APA Corporation (APA ), Devon Energy Corporation (DVN), Coterra Energy Inc. (CTRA), Continental Resources, Inc. (CLR), Pioneer Natural Resources Company (PXD), Diamondback Energy, Inc. (FANG), and EOG Resources, Inc. (EOG).

According to Figure 1, the fair P/E ratio based upon comparable companies is 11.13, which provides fair prices for OXY and MRO of $73.35 and $31.83, respectively. Therefore, OXY and MRO look like very good investments but we need to determine how many OXY and MRO stocks we should have in our portfolio, and it is where the Treynor-Black model becomes helpful. The Treynor-Black model is a portfolio-optimization model that seeks to maximize a portfolio’s Sharpe ratio. The model calls for two portfolio segments: an actively-managed component built from select mispriced securities; and a passively-managed index component. The Treynor-Black model assumes that all correlation between products is captured by the systematic risk factors, leaving specific risks to be distributed independently from company to company.

Firstly, I assume that a price needs 24 months to converge to a fair valuation. The alpha is an abnormal return related to the fact that OXY and MRO stocks are undervalued. For example, OXY’s alpha of 0.83% means that on average OXY is expected to outperform the market by 0.83% per month. The market beta, which shows how a stock is exposed to the market index, is calculated based on the log return of monthly adjusted close prices for the last sixty months. The idiosyncratic variance is a variance of monthly abnormal returns, which are calculated per month as a stock total return minus the product of a beta and a stock market return. The idiosyncratic risk is a risk that is inherent to a particular company that is associated with events happening within the company that are impactful for this stock alone. As opposed to the systematic risk, the idiosyncratic risk can be eliminated by diversification. The appraisal ratio is how much a stock is overvalued or undervalued in terms of idiosyncratic variance. The active weight is a proportion of an actively managed capital proportional to appraisal stocks ratios. We can see that 43.73% of our actively managed capital should be invested in OXY, and 56.27% of the capital should be invested in MRO. So, the active alpha of our portfolio is 0.92% as the sum product of the alpha and the active weight of both stocks. At the same time, the active beta is the sum product of the beta and the active weight of both stocks. Finally, the active volatility is the sum of the product of the idiosyncratic variance and our active weight squared portfolio (there is an assumption that the specific risk is distributed independently from stock to stock).

In figure 3 we estimate stock market parameters. The market return is a geometric mean for sixty months. I assumed the annual risk-free rate is equal to 3% corresponding to the current yield on the 10-year US Treasury note. The excess market return is a difference between a monthly market return and a monthly risk-free rate.

The uncorrected active weight is the performance of active investment adjusted for the risk compared to the performance of the stock market adjusted for the risk. The corrected active weight is the uncorrected active weight adjusted by the Beta of our active portfolio. When we find the active weight of our portfolio, which is 32.84%, we can find the weight of the passive part of 67.16%. Thereafter, we find the weight of OXY and MRO in our active weight portfolio as the product of the corrected active weight and the active weights of OXY and MRO from Figure 3. Finally, we get the investment portfolio where we need to invest 67.16% of our capital in S&P500 and 14.36% and 18.48% of our capital in OXY and MRO, respectively.

**Stock Selection **

As we have seen before, the relative valuation method assumes that overall the stock market correctly evaluates stocks but sometimes some stocks can be evaluated incorrectly. Therefore this method does not allow us to correctly estimate stocks in the period when the stock market as a whole is underpriced or overpriced. Moreover, price ratios have two sides. On the one hand, a stock with price ratios higher than average is recognized as overvalued and vice versa. On the other hand, a high price ratio could provide evidence that company earnings, sales, or other financial metrics will increase in the future, and the current high price represents this expectation. Therefore, the correct price ratio interpretation is a key to distinguishing promising stocks from losing investment.

The I Know First predictive algorithm is a successful attempt to discover the rules of the market that enable us to make accurate stock market forecasts. Taking advantage of artificial intelligence and machine learning and using insights of chaos theory and self-similarity (the fractals), the algorithmic system is able to predict the behavior of over 10,500 markets. The key principle of the algorithm lays in the fact that a stock’s price is a function of many factors interacting non-linearly. Therefore, it is advantageous to use elements of artificial neural networks and genetic algorithms. How does it work? At first, an analysis of inputs is performed, ranking them according to their significance in predicting the target stock price. Then multiple models are created and tested utilizing 15 years of historical data. Only the best-performing models are kept while the rest are rejected. Models are refined every day, as new data becomes available. As the algorithm is purely empirical and self-learning, there is no human bias in the models and the market forecast system adapts to the new reality every day while still following general historical rules.

**Conclusion**

Relative valuation is one of the basic concepts of stock evaluation with its pros and cons, and the Treynor-Black model can help to construct an effective portfolio with active and passive investment parts. However, an incorrect stock selection based on multiples can transform good-looking stocks into losing investments.

I Know First provides the Fundamental Stocks Package which allows us to select the most promising stocks based on the fundamental ...

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