Value Investing

# Cheap Stocks; Defining Cheap Valuations [ANALYSIS]

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People say that stocks with low valuation (low P/E, low P/BV, low P/S) are better investments than expensive ones. Is it true? And what does it mean that a stock is cheap? Is P/S = 1 cheap? Or maybe P/S = 2 is cheap? Where is the border of cheapness? Today we’re going to find answers to these questions. To do this I performed a test. I divided all stocks from the market into 10 portfolios. Let’s call them:

1. Extremely cheap stocks
2. Very cheap stocks
3. Cheap stocks
4. Quite cheap stocks
5. Slightly cheap stocks
6. Slightly expensive stocks
7. Quite expensive stocks
8. Cheap stocks
9. Very expensive stocks
10. Extremely expensive stocks

I started from the first date in my database which is July 28, 2006. For each stock present on the market that day, I checked what the value of P/S indicator was at that moment. Here is a little piece of the table which I created. Whole has 350 non-trust stocks. (That is the number of all non-trust stocks in FTSE All Share for July 28, 2006. Now it’s over 400).

Later I sorted such created table according to P/S value in such way that the cheapest stocks (e.g. P/S = 0.1) were at the top of ranking and the most expensive stocks (e.g. P/S = 50) were at the bottom. After sorting, I divided all available stocks into 10 portfolios in such way, that first 10% of the cheapest stocks (which was 35 stocks) went to portfolio “extremely cheap stocks,” second 10% of stocks to portfolio “very cheap stocks,” third 10% to “cheap stocks,” and so on. After that in each of 10 portfolios there were 35 stocks. Each stock had the same position size, so each was not bigger that 3% of its portfolio.

Next I checked how much such folios would earn in next 4 weeks, so between July 28, 2006 and August 25, 2006. I wrote the results down and sold all stocks from all folios. Later one more time I checked what were the current values of P/S for all stocks for August 25, 2006 and on that basis, I created rank and again I divided 10% of stocks to each folio, in the same way as at the first time. After another 4 weeks I checked how much did stocks earn. I did this for each month since July 28, 2006 up to current date.

Thanks to such folios construction rules, in each there were socks which fitted well to its name. For example:

At the beginning stock X had P/S = 0.5. According to rank from July 28, 2006, it was the 30th cheapest stock on the market (for total of 350 stocks). It means that stock X was allocated to folio nr. 1 “extremely cheap stocks.” In the next month price of stock X rose +50%, which caused P/S ratio increased to 0.75. Stock X was not as cheap as before. Now according to P/S rank, it was at 120th place (for total of 350 stocks), so for the next month it was placed in “quite cheap stocks” folio.

Thanks to this approach, I didn’t have to set fixed criteria for allocating stocks to folio
(e.g. P/S < 1) and that is good because for now we don’t know which value can be called “cheap” and which an “expensive” one. Additionally, ranks gave us great diversification of each folio (average position size in each folio is 3%). Thanks to that a single disobedient stock won’t be able to disrupt out results. What is more, such way of dividing stocks gave us guarantee, that all folios will be completely filled with stocks, independently of current place in economic cycle (bull/bear market). Additionally to keep high credibility of results, I deleted:

• Stocks with very low trading volume (min. trades sum for last week should be greater than £80K.
• Stocks with very low prices (stock price should be greater than 20 p).

These are the capital curves for each portfolio:

Portfolio 1: Extremely cheap stocks:

Portfolio 2: Very cheap stocks:

Portfolio 3: Cheap stocks:

Portfolio 4: Quite cheap stocks:

Portfolio 5: Slightly cheap stocks:

Portfolio 6: Slightly expensive stocks:

Portfolio 7: Quite expensive stocks:

Portfolio 8: Expensive stocks:

Portfolio 9: Very expensive stocks:

Portfolio 10: Extremely expensive stocks:

The curves show very nicely that cheap stocks (first four portfolios) regained their value after the bear market in 2008 faster than expensive stocks.

While comparing folios, we should focus on annual profit. (In such test we skip transaction costs and spreads, because we only seek for trend in data. It’s not a real strategy test). Best folio gain 13.24% annual profit. To check if it’s high or low, we shouldn’t look at absolute values. Better way is to compare it with annual profit of portfolio consisted of all stocks.

Let’s create such portfolio. This single test took my computer about 30 min to generate and I was losing hope if it will succeed, but finally it did. In this test I took all stocks available at current date (starting at July 28, 2006) and gave them equal position size in portfolio (average position size for single stock was 0.35% of whole capital). It was like creating a non-weighted index of all stocks. Of course here I also deleted stock with very low trading volume and/or very low price. This is a capital curve for such non-weighted index:

Annual profit for non-weighted index was 10.9%, and this will be our reference lever for portfolios profits comparison. A chart below shows annual profit for each of 10 folios in comparison with non-weighted index:

It seems that:

• First five (cheap folios) earned more than last five (expensive folios).
• Best results were achieved in folios nr. 2 and 3 (cheap stocks, but not as cheap as
folio nr. 1).
• Expensive stocks (folios nr 8 – 10) earned less than our non-weighted index.

Thanks to this analysis we can be sure that in matter of P/S, cheap stock earns more for the investor than expensive stocks.

At the chart I also wrote standard P/S values, which had stocks inside each portfolio. These aren’t accurate values, because boundaries in each folio depend on current market situation. During bull market all stocks are basically expensive, so a stock with P/S = 1 could be seen as a cheap one. During bear market all stocks are basically cheap, so a stock with P/S = 1 could be seen as an expensive one.

To create intervals I checked values of P/S for all stocks, which were bought inside the portfolio which we are looking at. Next I sorted all the values (To make it easier, let’s assume that there were 100 transactions in portfolio) and checked what the values at positions nr 25 and nr 75 (from total 100 transactions) were. Expertly it is called lower quartile and upper quartile, but it’s just about estimation of P/S values which can be found in each portfolio.

I could just use an average from P/S values, but it could be easily distorted by single outlier. For example if many stocks have P/S between 1 and 2 and there will be one stock with P/S = 1000, the average P/S could be somewhere near to 3, which is a poor measurement for the real distribution of P/S values. In such situation quartiles seems to be quite good solution.

These are the values of P/S which could be found in portfolios:

The best results are generated in first four folios. Upper quartile of fourth folio is equal to P/S = 0.91. Poor results start in 8th folio. Lower quartile of this folio is equal to P/S = 2.19. Of course these borders are not strict, but if would have to divide stocks into: cheap, normal and expensive we would say that:

• Stocks with P/S below 0.91 are cheap and allow us to earn more.
• Stocks with P/S over 2.19 are expensive and shouldn’t be bought.

What is interesting, the cheapest stocks from quartile nr. 1 earns money, but are worse than those in folios nr. 2 and 3. It could mean than even if cheap stocks earn more than expensive ones, it is not so important to get much below P/S = 0.91, because extra cheap stocks (P/S below 0,26) can be so cheap because of some real threats.

To confirm or disprove these discoveries I made another test from the other side. This time I started with finding all stocks, which were about to raise their prices at least 50% in next year. As it was historical data (from July 2006 to June 2014) I could easily check were the prices will be after 12 months. I found totally 357 such moments in time for all stocks (some stocks were rising 50% per year many times. Each 50% per year rise was counted separately). For each of these 357 moments I checked what the P/S for the stock was. Thanks to that I collected a set of 357 P/S values, which characterized pearl stocks.

Next I checked what the distribution of these values is. How many of these pearl stocks had low P/S? To check this I dividend these 357 values into 10 groups according to our borders from the table which were:

 1 Extremely cheap P/S from 0 to 0.29 2 Very cheap P/S from 0.29 to 0.49 3 Cheap P/S from 0.49 to 0.675 4 Quite cheap P/S from 0.675 to 0.885 5 Slightly cheap P/S from 0.885 to 1.19 6 Slightly expensive P/S from 1.19 to 1.645 7 Quite expensive P/S from 1.645 to 2.15 8 Expensive P/S from 2.15 to 3.05 9 Very expensive P/S from 3.05 to 5.17 10 Extremely expensive P/S greater than 5.17

These are the result of such division:

If P/S would have zero influence into finding pearls, the distribution would approximately show 10% for each group. From our chart we can see that first three groups (P/S from 0 to 0.675) allow us to find 40% of all pearls from the market. It means that in these 3 cheapest groups the distribution of pearls is denser than it should be if P/S wouldn’t matter.

We can make similar analysis for poor performers. This time I was looking for stocks which will lose at least -50% in the next year.

Distribution for bad stocks (poor performers) is not as linear as for pearls. We have two places where it’s easier to find poor performing stock than it should be if P/S didn’t matter.

• First is for group nr. 9 and 10, which is quite obvious. It means that within very expensive stocks (P/S > 3.05) there is greater probability to find poor performing stocks.
• Second place is for group nr. 1 and 2, which can be quite surprising. It looks like within very cheap stocks (P/S < 0.49) there are many hiding poor performers.

Let’s combine these two charts to see what is the ratio of pearls (50% in year) to poor performers (-50% in year) in each group.

The chart is very liner (omitting group nr. 1), which means that in general it is much better to look for cheap than expensive stocks (in matter of P/S). Lower result for the first group is caused by very high number of poor performing stocks. It looks like group nr. 1 (the cheapest stocks) is the place where it’s easy to find both pearls and poor performers. There is a little room for stock with neutral trend. When we compare this chart with the one generated during the first test, we can see that they are both very similar, so the second test confirmed results from the first.