Category Archives: Quantitative Value Investing

What is the best measure of quality?


In an earlier post, I examined the performance of different value metrics. My conclusion was simple: cheap stocks beat expensive stocks.

Most value investors don’t simply look for cheap alone. They try to find companies that are both cheap and good. Good is typically defined as companies that can earn high returns on their capital.

Finding these companies is a worthwhile pursuit but it is difficult to pull off systematically because companies earning high returns on capital are going to attract significant competition. I think it is far more difficult to do this than most value investors appreciate. Mean reversion, fueled by competition, inevitably pulls these returns down. Finding the rare birds that don’t succumb to this is hard.  These companies usually have a “moat“, which is hard to identify. Needless to say, this kind of investing requires a touch of genius that I don’t have. When investing, I operate under the assumption that every company succumbs to mean reversion.

With that said, finding these rare opportunities certainly pays off over the long run. You can park money in a company like Coca-Cola or Nike and earn high returns over long stretches of time, while reducing taxes and transaction costs.

The Magic Formula 

Joel Greenblatt sought out a systematic quantitative method to find companies that are simultaneously cheap and earn high returns on capital. The result was The Little Book that Beats the Market. In the book, Greenblatt demonstrated that simultaneously buying cheap companies that earn high returns on invested capital will outperform. He calls this the magic formula and generously maintains a free screener here.

Tobias Carlisle took this a step further in Deep Value and discovered that the quality metric of high returns on invested capital actually reduces returns from the magic formula. He explains in Deep Value how mean reversion tends to bring these returns down. Cheap alone is better than cheap plus good. In other words, it takes qualitative insight to determine which companies have a moat that will allow them to sustain high returns on capital. Tobias maintains a free large cap screen for this here.

I would recommend reading both The Little Book That Beats the Market and Deep Value.

Backtesting Quality Metrics

I decided to test the returns for myself and try to see which “quality” metric works best when combined with a value factor. The test I ran is limited to Russell 3000 components. My definitions of cheapness were:

  • EBITDA/Enterprise Value is higher than 20%
  • Price to free cash flow is less than 15
  • Price to sales is less than 1
  • Earnings Yield is over 10% (i.e., P/E is less than 10)
  • Price to book less than 1
  • Price to tangible book less than 1

In addition to examining metrics that define high returns on capital, I also included metrics for financial quality, such as the debt to equity ratio and the Piotroski F-Score. Below is a summary of all of the quality metrics that I tested.

Return on Equity – This is the oldest and most simple method of corporate quality. It is simply the company’s net income divided by equity (assets – liabilities). For the purposes of the test, I define high ROE as over 20%.

Return on Invested Capital – Joel Greenblatt’s preferred measure of quality. This is earnings before interest and taxes divided by invested capital. Invested capital is defined as working capital plus net fixed assets. For the purposes of the test, I define high ROIC as over 15%.

Gross Profits/Assets – Robert Novy-Marx created a very simplistic measure of quality, gross profits/assets. He found that this  method works extremely well, because it uses profits further up of the income statement where it is more difficult for a firm to manipulate the numbers. You can read his paper on the subject here. For the purposes of the test, I define good gross profitability as over 30%.

Debt/Equity – This is another simplistic measure of financial quality. It is simply total debt divided by equity (assets-liabilities). For the purposes of the test, I define a good debt/equity ratio as under 50%.

F-Score – This is a more complex measure of financial quality designed by Joseph Piotroski, who is currently a professor at Stanford. Piotroski designed a 9 point scale of financial quality in a paper written back in 2000. Piotroski backtested combining this measure of financial quality with price to book and found that the results greatly exceeded the market. Each component adds to the score. A perfect F-Score would be a 9. It’s too bad F-Scores don’t go up to eleven. The components of the F-Score are defined below.

  • A net decline in long-term debt for the current year.
  • A net increase in the current ratio in the current year. The current ratio is current assets/current liabilities. It measures the liquidity of the company’s balance sheet to meet short-term obligations.
  • A positive increase in gross margins in the current year.
  • Faster asset turnover in the current year.
  • The total number of shares outstanding is flat or decreasing. In other words, the company isn’t issuing new equity and diluting the current pool of shares.
  • Return on assets is positive.
  • Operating cash flow is positive.
  • Return on assets for the current year is higher than the previous year.
  • Operating Cash Flow/Total Assets is higher than return on assets.

The results of the backtest are below. The results are in the Russell 3000 universe with annual rebalancing beginning in 1999.


The High Return Metrics – ROE, ROIC, GP/Assets

Measures for returns on capital – ROE, ROIC and GP/Assets – actually detract from the performance of EBITDA/Enterprise Value. They add performance to the other valuation metrics slightly, with Gross Profits/Assets being the best.

The middling performance of high return quality metrics is due to mean reversion, or the propensity for high return businesses to eventually succumb to the pressures of competition.

With that said, if you are trying to identify high return businesses, the best metric to use appears to be Gross Profits/Assets.

Financial Quality (The Debt/Equity Ratio and the F-Score)

In contrast, measures of financial quality, such as the debt/equity ratio and the F-Score, supercharge all of the valuation metrics that are examined here. Why is this?

Cheap stocks are only cheap because they are in some kind of trouble. There is an “ick” factor. Any time you run a value screen, you will scratch your head and think “Do I really want to invest in this garbage?”

This is why financial quality metrics are more useful than business quality metrics. If a company has a good balance sheet and is financially healthy then it has time to resolve its problems. Managers have time to implement a new strategy that can turn things around. Even without a new strategy, time will help the financially healthy company. For instance, if the company is in a crowded, competitive industry, the financially healthy company can weather the storm while the highly leveraged firms will go out of business first. Less firms means less competition. Less competition means that future returns in the industry will improve.

This is the essence of the simple Graham method that I follow with my own portfolio. I am looking for cheap companies that have the financial ability to weather the storm that they’re in.

This is also why the high return metrics add a little to the other valuation metrics but detract from the EBITDA yield. Unlike the other valuation metrics tested here, the EBITDA yield is the only one here that uses Enterprise Value in the calculation. Enterprise Value brings balance sheet health into the valuation ratio. For EBITDA/Enterprise Value to result in a high yield, the company must have little debt and a lot of cash on hand. In other words, valuation metrics that use Enterprise Value will identify companies that are both cheap and have safe balance sheets.

RadioShack vs. Best Buy

This reminds me of an article I read over at the Motley Fool. The author explains why Radio Shack fell apart and Best Buy was able to turn around.

Radio Shack had numerous problems, including asking for your phone number when you buy batteries.

Best Buy’s problem is that it basically became a showroom for Amazon. The referenced article explain how Best Buy successfully turned things around by cutting costs, emulating the Apple Store, expanding the Geek Squad and improving their website.

I have a more simplistic explanation for why Best Buy was able to recover and Radio Shack fell apart. Radio Shack had a lot of debt and Best Buy didn’t. Radio Shack’s debt to equity ratio was over 670%. Best Buy’s debt to equity ratio was 41% a few years ago and is 29% today.

Best Buy’s balance sheet gave them an edge: time. They had time to work through their problems and try to find a solution. If Best Buy had Radio Shack’s debt levels, the CEO would have never been able to pursue the turnaround strategy. All troubled companies are trying to turn things around, but only those with financial strength will have the time to do so.

Screening for High F-Scores and EBITDA Yield

One of the most robust combinations tested was the F Score and the EBITDA Yield, with a 17.69% rate of return since 1999. I ran a screen for companies with an EBITDA yield over 20% and an F-Score of 8 or higher. This combination of criteria is very stringent. It only returned 5 results out of the entire Russell 3000. Best Buy actually comes up in this screen, implying that it is still a financially healthy bargain. Output from the screen is below.


I am not going to buy positions in these companies, but wanted to share the results of what I found. Hopefully this will give you some useful leads that are worthy of further research.

PLEASE NOTE: The information provided on this site is not financial advice and it is for informational and discussion purposes only. Do your own homework. Full disclosure: my current holdings.  Read the full disclaimer.

How to Overvalue a Company: Use Discounted Cash Flow Analysis


Discounted Cash Flow Rationale

Discounted cash flow (DCF) analysis is the most popular method of business valuation.  It is taught extensively in most finance classes.  The goal is to find a reasonable price for a future stream of cash flows and compare it to a risk-free rate of return, usually US treasuries.

It’s also fraught with peril because it usually results in overvaluing businesses.  It is the preferred method of valuation in investment banking.  I suspect this is because investment bankers can easily game the numbers and make companies appear more valuable than they actually are.  Allow me to explain.

Apple Valuation (AAPL)

To show the power of assumptions, let’s try a real world valuation example.  Let go with Apple (AAPL) using this method.

Free Cash Flow

Let’s start with a fact: in the 2016 fiscal year, Apple’s free cash flow was: $65.844 billion in operating cash flow – $13.548 billion in capital expenditures = $52.296 billion in free cash flow

At the end of the 2016 fiscal year, there were 5.336 billion shares of Apple common stock.

$52.296/5.336 = $9.80 of free cash flow per share of Apple stock.

So what’s the value of $9.80 in discounted cash flow?  Let’s use DCF analysis to figure it out.

Zero Growth Example

For example 1, let’s take an extreme approach.  Let’s say Apple won’t grow at all (unlikely).  For the interest rate, we’ll use US treasuries.  The 10-year US treasury currently pays 2.38%.  Here is a link with a detailed explanation of the math.

If you want to do this quickly, Gurufocus has a calculator tool that you can use here.  Another nice shortcut is a formula that can be used in Microsoft Excel or in Google sheets.  Simply input the following formula into a cell:

=NPV(discount rate, cash flow 1, cash flow 2, etc.)

Now, let’s try to find the present value of a $9.80 stream of cash flows.  Based on no growth and 10 years of cash flows and using the 2.38% rate, we get a value for Apple of $86.30.

Growth and Different Discount Rates

2% Growth, 2.38% rate, 10 years = $96.02

What if instead of using the 10 year treasury as our base, we used the 10 year average AAA corporate bond yield, 2.96%

2% Growth, 2.96% rate, 10 years = $93.11

Terminal value

Most likely, Apple isn’t going to go out of business in 10 years.  For this reason, most DCF analysis adds a terminal value to the value after the 10 years of cash flows.  Let’s proceed with our assumption that there will be 2% growth for 10 years, then let’s say after 10 years the growth rate drops to 1%.

Present value of 10 years of cash flows + Terminal Value = $173.52

Now, what if we increased our assumptions?  Let’s say Apple grows by 5% a year, and then the terminal value grows earnings at 3% into the future?  Now the value goes up to $228.54!

With DCF analysis, you can make the data say whatever you want.  That’s great for investment bankers but it’s not very good for investors.


By messing around with different assumptions, I produced valuations for Apple that ranged from $86.30 to $228.54.  All of these assumptions are debatable.  You can’t say with any degree of certainty where interest rates are going, what Apple’s cost of capital will be, what their growth rate will be, how long the business will be viable, etc.  All of these are assumptions.  Also keep in mind that I produced this wide range of values with one of the the largest and most recognizable company in the United States.  If we can’t safely value Apple, how can we safely value a micro-cap stock?

For this reason, I avoid discounted cash flow analysis.  It is simply too easy to twist around the data with your assumptions and get the result you want.  If you want to find a margin of safety with DCF analysis, you’re going to find one.  I suspect that this is what the investment banking community does when they want to convince corporate managers to make acquisitions that may not be in the best interests of the acquirer.

A simple ratio (i.e., the stock trades at 10 times earnings) is a far more simplistic . . . and far more telling . . . statistic than DCF analysis.  The cheapness of something should hit you over the head and should be abundantly obvious.  If it’s not, move onto something else.  There are plenty of publicly traded companies.  Torturing the data to get the result you want is not a prudent path.

I prefer the Graham approach and focus on what’s actually known in the here and now without making so many assumptions about the future.  This is why the Grahamian balance sheet approach (because what’s more clear cut than the value of a balance sheet?) of net-net’s is a nearly foolproof method of investment.

For the goal of finding the present value of cash flows in analysis of stocks, I think a more useful metric is one that is more simple: price to free cash flow or enterprise value to free cash flow. If you can find a decent company like Apple trading at a price to free cash flow of 10 or less, then DCF analysis would likely yield a number close to the current price even with very conservative assumptions. It is probably then a good candidate worthy further research.

In the world of finance, there is a tendency to make things more complicated than they really are.  I like to keep things simple.

PLEASE NOTE: The information provided on this site is not financial advice and I am not a financial professional. I am an amateur and the purpose of this site is to simply monitor my successes and failures.  Full disclosure: my current holdings.

What is the Best Stock Valuation Ratio?


Value investors use a number of ratios to assess whether a stock is cheap.  Everyone has their favorite.  Everyone debates the merits of one versus the other.  I backtested some of the popular ratios to see how they would perform if you simply split the market up into deciles and compared the cheapest to the most expensive deciles.  The population I used for this analysis was the S&P 1500.  In this case, we are comparing the most expensive 150 stocks to the cheapest 150 stocks.  These are the total returns since 1999, with the 150 stocks re-balanced annually, because re-balancing monthly is impractical.

Below is a list of the ratios that I tested:

EBIT/Enterprise Value – This is the ratio identified by Joel Greenblatt in The Little Book that Beats the Market.  EBIT is “earnings before interest and taxes”.  Tobias Carlisle refers to this as the “Acquirer’s Multiple” in Deep Value

The Enterprise Value is the total cost of the firm to an acquirer.  Enterprise values are the total cost of the firm to an acquirer at the current market price.  In other words, if you were to buy this company in its entirety, you wouldn’t simply pay the market price.  You would also assume all of its debt obligations and would inherit all of its cash on hand.  It is the cost to acquire the entire company.  EV gives you a good idea of the true size of the business.  The calculation for Enteprise Value is:

EV = market value of common stock + market value of preferred equity + market value of debt + minority interest – cash and investments.

Price/Cash Flow – The price per share divided by the total trailing twelve month cash flow for the last calendar year.  In other words, how much total cash is the stock generating for what you are paying?

Price/Sales – The price per share divided by the total revenue per share.  This ratio was popularized by Kenneth Fisher in his 1984 book Super Stocks.

Price/Free Cash Flow – Free cash flow is the company’s operating income minus its capital expenditures.  Free cash flow strips away the company’s other financial performance variables and looks simply at how the core business is doing.  This ratio looks at how much free cash flow is being generated per share relative to the price of the stock.

Free Cash Flow/Enterprise Value – This is the same thing as price/free cash flow, but instead compares free cash flow to the total size of the business.

Price/Book Value – Book value is the total balance sheet value of the company.  It’s the simple equation Assets – Liabilities = Shareholder Equity.  The goal of many asset-based value investors is to buy company’s that are trading at or below book value.

Price/Earnings – This is the most basic and common valuation metric.  It takes the per share price of the stock and divides it by the earnings per share.

Price/Tangible Book Value – The same thing as price/book value, with a twist.  When calculating shareholder equity, intangible assets are taken out of total assets.  The goal here is to look at what assets can actually be sold and turned into cash.

The results are below:


I think it is best to look at the effectiveness of the ratio based on the difference in return between the cheapest and most expensive decile, rather than looking at its total return for the cheapest decile.  A ratio that is effective in identifying cheap stocks should be equally effective in identifying expensive stocks.  Based on the backtesting, the acquirer’s multiple popularized by Tobias Carlisle is the most effective.  Tobias maintains a nice screener here.

Here is a visualization of the value premium in chart form:


The important takeaway is that no matter which ratio you prefer, they all work to some extent and buying expensive stocks is a risky bet.  Value investors can debate about which ratio works best, but they all work!  No matter how you slice it, cheap beats expensive.

PLEASE NOTE: The information provided on this site is not financial advice and it is for informational and discussion purposes only. Do your own homework. Full disclosure: my current holdings.  Read the full disclaimer.