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An Analysis of “Testing Benjamin Graham’s net current asset value model”


The focus of this article is the research paper “Testing Benjamin Graham’s net current asset value model” by Chongsoo An, John J. Cheh , and Il-woon Kim published in Journal of Economic & Financial Studies (2015). The objective of the paper was to examine the performance of securities that were trading at less than their Net Current Asset Value (NCAV) during the 14 year period from January 2, 1999 to August 31, 2012 in the US market.

Our objective was to analyze the study itself; determine its reliability, draw our own conclusions and glean, if any, actionable advice for the practitioner of the NCAV method of investing.

We have previously published a number of posts with regard to securities trading less than their Net Current Asset Value including:

Key Methodology

  • Valuation metric:

“According to Benjamin Graham, net current assets are defined as current assets minus total liabilities (and preferred stock if any)”

i.e. Net Current Asset Value = Current Assets – (Liabilities + Preferred Shares)

While the authors did not expressly state that they used the formula specified above we assume they did so.

“To test the Graham’s net current asset value method, the ratio of the net current asset value to market value (NCAV/MV) was employed in this study as the criterion in selecting stocks…“all securities that satisfied the primary condition “NCAV/MV > market price” were selected.”

  • Weighting of holdings: Not specified.

  • Purchase/rebalance date: Not specified.

  • Holding period: “the returns of different holding periods were tested: one year, six months and four months”.


Studies can suffer from a number of issues which reduce their reliability. Below we address potential concerns around sample size, return calculation methodology, data sources and common biases that may afflict research:

1. Valuation criteria, sample size and firm characteristics

“The analysis of stock performance was conducted in two stages. First, all securities that satisfied the primary condition “NCAV/MV > market price” were selected. The 126 selected securities were then pooled into three different portfolios using the secondary condition “market price×N; N=1, 2, & 5” as follow:

Portfolio 1: NCAV/MV > market price×1 [i.e. trading at less than NCAV]

Portfolio 2: NCAV/MV > market price×2 [i.e. trading at less than 50% of NCAV]

Portfolio 3: NCAV/MV > market price×5 [i.e. training at less than 20% of NCAV]

The final sample size for each portfolio was 84 firms, 32 firms, and 10 firms for Portfolio 1, Portfolio 2, and Portfolio 3, respectively. N was the weighing factor for the market price. For example, N=5 indicated that the NCAV/MV ratio was higher than five times the market price.”

There is a discrepancy between the portfolio formation criteria and the narrative; firms that met the criteria for inclusion in Portfolio 3 would also meet the specified criteria for Portfolio 2 and Portfolio 1. However, given the number of firms that were specified to be contained in each portfolio the authors actually tested firms trading at greater than the specified NCAV/MV cut off for the relevant portfolio, but less than the NCAV/MV cut off for the next portfolio.

With regard to sample size, only 126 firms traded at less than their NCAV (i.e. NCAV>MV) in the 14 year test period. Furthermore, the sample size was not specified by year. Presumably, there would have been years where few firms met the criteria as markets rose, and as markets fell more firms would have met the necessary criteria. For perspective, the approximate “average” number of holdings for Portfolio 1, 2 and 3 over the 14 years was 6, 2 and 1 (rounding up) respectively. Consequently, one needs to be cautious when interpreting results, especially those pertaining to Portfolio 2 and 3.

Significantly, no minimum market capitalization was specified. Consequently, the inclusion of the smallest firms can distort results as even when investing relatively modest sums the securities of the very smallest firms are virtually untradeable.

2. Return calculation methodology

The authors calculated the “Annualized returns” (i.e. geometric mean) and the “Average returns” (i.e. arithmetic mean).

It should be noted that in a dependant return series that exhibits volatility (like stock returns) the arithmetic mean will, as a matter of mathematical law, overstate returns relative to the more practitioner oriented geometric mean.

We will examine this further in the next section.

3. Survivorship bias

The authors used Portfolio123 who state that their financial data is free from survivorship bias.[i]

4. Look Ahead bias

As in the case of survivorship bias Portfolio123 state that their data is free from look ahead bias.[ii]

5. Time period bias

The study spans 14 years and we classify this as a “somewhat reliable” period.

For reference:

· < 10 years; inadequate/unreliable

· 11 to 20 years; somewhat reliable

· > 20 years; more reliable

· > 40 years; most reliable

The authors also acknowledge concerns with regard to the time period studied stating “extending the study period and adding more sample firms will definitely improve the relevance of the study.”

6. Data source

As the initial sample, we used all stocks in Portfolio123 (about 6,000 firms) which are supplied by Compustat, Standard & Poors, S&P Capital IQ, and Interactive Data.

Presumably the data sources covered stocks listed across all the major US exchanges.

No mention was made with regard to the treatment of dividends; presumably returns included dividends in light of the reputable data sources used in the study.

7. Human error

There is nothing specified in the research methodology that would make us believe this study is at greater risk of suffering from human error.

8. Journal rating/credibility[iii]

This study was not, to our knowledge, published in a top tier academic journal and therefore cannot be granted the “additional credibility” that may come with such publication.

Reliability Assessment: Due to the relatively short time period (14 years), sample size concerns and the absence of a minimum market capitalization requirement for the securities examined the study does not appear to be reliable.

Results and Analysis

Annualized and Average Returns

The authors calculate and present the “annualized returns” (i.e. compound annual growth rate/geometric mean) which represent the gross returns a practitioner could have actually achieved.

“The annualized returns of three portfolios and S&P 500 during the study period are presented in Exhibit 2. Annualized returns are the returns that should have been realized every year to earn total returns during the study period. Theoretically, the stocks with a higher NCAV/MV value should be generating annualized returns higher than the stocks with a low value. The results of this study, however, are mixed. Portfolio 1 (4.15%) and Portfolio 2 (2.49%) beat the market with a big margin as shown in Exhibit 2, while Portfolio 3 (0.51%) does not do well compared to the S&P500 (0.96). It is also puzzling to see in Exhibit 2 that the returns are decreasing as the value of N is increasing from 1 to 2 and to 5. We believe that these mixed results are due to the fact that the number of firms in each portfolio is decreasing from 84, to 31 and to 10. As the sample size is getting smaller, the results of the study are getting less reliable and sometimes inconsistent.”

It is interesting to note the that the Portfolio returns were in the opposite sequence to that which was expected. “It was expected that the stocks with a higher NCAV/MV value (e.g., N=5) would be generating returns higher than the stocks with a low value (e.g., N=1).”

One wonders how the returns impacted the narrative; had the returns been in accordance with expectation would less emphasis have been placed on the small sample size and instead would the returns have been taken as “evidence” that “cheapness” drives returns?

Sample size concerns aside, it is noteworthy that the very cheapest stocks did not even beat the market. We suggest that the results provide food for thought; perhaps cheapness alone cannot be relied on when dealing in securities trading below NCAV. Rather, further criteria may need to be considered when making investment decisions.

What is particularly interesting about these results is the low level of absolute return outperformance relative to the market when compared to other studies examining the returns to firms trading below NCAV. For example, Portfolio 1, the best performing portfolio, the absolute outperformance relative to the S&P 500 was just 3.19% (4.15%-0.96%). Furthermore, net of fees and commissions the absolute return outperformance would have been even lower. Indeed, the annualized return of three-month Treasury bills over the 14 year period was approximately 2.3%[iv]; a figure reasonably comparable to the net of fee and commission return likely to have been achieved. Furthermore, net of taxes (and effort) investing in firms with a NCAV > MV (i.e. trading at a discount to NCAV) appears to have been a forlorn endeavour in the US market over the test period.

The authors (with a focus on demonstrating the results of their “hedging strategy”) also present the “average” (i.e. arithmetic mean) returns. As mentioned in the “Reliability” section above, in a dependant return series that exhibits volatility (like stock returns) the arithmetic mean will, as a matter of mathematical law, overstate returns relative to the more practitioner oriented geometric. We examined this phenomena in more detail in An Analysis of “Graham’s Net-Nets: Outdated or Outstanding?”. Furthermore, we also discussed this point in An Analysis of “Testing Benjamin Graham’s Net Current Asset Value Strategy in London” along with how “confirmation bias” may impel an investor to believe the arithmetic mean could be used to “reasonably estimate” the geometric mean (i.e. the return potentially attainable in practice) and warned against such an endeavour.

This study demonstrates objectively the reason for such warning.

The “average” (i.e. arithmetic mean) returns are reported as follows:

Recall the annualized return (compound annual growth rate/geometric mean) for Portfolio 1, 2 3 and the S&P 500 was 4.15%, 2.49%, 0.51% and 0.96% respectively. In contrast the “simple averages [i.e. arithmetic mean] of all rebalancing returns realized in backtesting using Portfolio 123 with one year holding period” for Portfolio 1, 2 3 and the S&P 500 was 17.17%, 17.78%, 14.87% and 2.91% respectively.

Using Portfolio 1 as an example, that represents a 13.02% return differential. To illustrate the magnitude of that differential, compounding $100,000 at the Portfolio 1 annualized return rate of 4.15% yields $176,696 (100,000*(1.0415)^14-1) over 14 years (the length of the study period). In contrast, wrongly assuming that one could “compound” at the (arithmetic) average rate of 17.17% per Portfolio 1 would result in a mistaken belief that a terminal value of $784,537 (100,000*(1.1717)^14-1) was achievable. That represents a $607,841 (or 77.5%) difference in potential expectation.

The Hedging Strategy

“As an attempt to improve the performance in the down market, a hedging strategy was implemented for each portfolio. The strategy was that the market condition should be favorable before any stocks were purchased. Understanding that the Federal Reserve Board tends to increase interest rates during a growth period and that the yield of corporate stocks would fall, the specific rule in this study is to buy stocks when the10-year Treasury yield are no higher than the yield 20 trading days ago.” (“CEY = TBY, where CEY is Current Estimated Yield (S&P current year estimates divided by S&P price) and TBY - Treasury Note Yield (10 year).”)

This hedging strategy materially improved the annualized returns and reduced the standard deviation.

Prima facie the hedging strategy appears to possess utility. However, from our analysis of other studies such as An Analysis of “Benjamin Graham’s Net Current Asset Values: A Performance Update”, An Analysis of “Testing Benjamin Graham’s Net Current Asset Value Strategy in London” and Examining Greenblatt’s “How the small investor can beat the market” we know the number of firms trading below NCAV tends to wax and wane. This tendency leads to periods of high and low concentration in the number of firms trading below NCAV. Given we do not know how many firms met the criteria for investment in each year of the study, it is possible (probable) that the majority of candidates were found in the minority of years. Consequently the proposed “hedging strategy” may have benefitted from providing a “buy signal” at an opportune time and without suffering from being return reducing in periods where a “false” buy signal was created due to the relatively low number of firms meeting the necessary criteria for investment. Indeed, with the overall small sample size the hedging strategy signal may not have had many opportunities to have its hypothesized efficacy tested robustly enough to be considered reliable. Furthermore, technically speaking, we would not consider the proposed “hedging strategy” as truly providing a “hedge”; rather it appears to be merely “market entry signal” without a corresponding “market exit signal” which would be required for it to be considered a “hedging strategy”.

The authors also suggest that further work is required on the hedging strategy stating, “Using different benchmarks, new buy-and-sell rules can be created and tested on the relationship between earnings and market conditions.”

Holding Periods

The authors also examined the annualized returns achieved by Portfolio 1, 2 and 3 over three holding periods: 1 year, 6 months and 4 weeks. Observing the annualized returns “without hedging” (not reproduced here) we note that a consistent pattern does not emerge with regard to the various holding periods for any Portfolio. For instance, Portfolio 1 generated fluctuating annualized returns of 4.15%, 0.96% and 4.00% over the 1 year, 6 month and 4 week holding periods respectively.


“Testing Benjamin Graham’s net current asset value model” was an interesting 14 year study commencing in 1999 and concluding in 2012 that examined portfolios of US listed firms whose NCAV was greater than its “market value”(MV) (i.e. traded at a discount to NCAV). Despite the quantification of annualized returns, the study cannot be considered reliable as no minimum market capitalization was specified for the securities examined. Consequently, the inclusion of all firms may have unduly influenced the results as even when investing relatively modest sums the securities of the very smallest firms are virtually untradeable. In addition, the particularly small sample size of securities meeting the necessary criteria was also of concern.

Interestingly, the authors also presented the arithmetic average returns which provided an objective lesson into why attempting to estimate the geometric mean (i.e. annualized return/compound annual growth rate) from the arithmetic mean is an inadvisable action. While Portfolio 1 generated an annualized return of 4.15% the practically unattainable arithmetic average return for the Portfolio was far greater at 17.17%.

With regard to return performance, the “best” performing portfolio, Portfolio 1, generated an annualized return (i.e. compound annual growth rate) of only 4.15%, an absolute excess return of just 3.19% over the S&P 500 which returned only 0.96% over the 14 year period. We say “only” and “just” due to both the relative and absolute outperformance reported in other studies (of variable reliability) examining firms trading below NCAV, as well as the historical return achieved by firms forming the S&P 500 index.

Reliability concerns notwithstanding, the study demonstrated that even over a 14 year period investing in firms trading below NCAV may not provide immunity from a low return environment - a sobering realization.



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