This abridged version has been streamlined for readability. For the full technical exposition, please consult the complete paper at the link below.
https://economyandsociety.in.ua/index.php/journal/article/view/6237/6180
Benjamin Graham’s “intrinsic‑value” formula occupies a peculiar place in investment lore: it appears in virtually every edition of «The Intelligent Investor», yet Graham himself warned that it was provided only «for illustrative purposes». Written in an era of stable 4–5 percent bond yields and modest GDP growth, the formula condensed a stock’s value into three observable variables: earnings per share (EPS), the expected long‑run growth rate (g), and the prevailing yield on high‑grade corporate bonds (Y). More than six decades later, interest rates have traversed the zero lower bound, global equity markets are dominated by high‑growth technology firms, and quantitative easing (QE) has distorted the term structure of risk‑free rates. Unsurprisingly, modern practitioners who apply Graham’s constants mechanically obtain valuations that deviate sharply from market prices. Although the formula is, by definition, a relative-valuation tool rather than an intrinsic one, we still view it as a useful rule of thumb – an acid test for the preliminary valuation stage. The present study revisits the formula’s theoretical underpinnings and demonstrates how a parsimonious ‘rate‑adjusted’ adaptation can restore its usefulness as a first‑pass screening tool. Capital‑market conditions have diverged so radically from the mid‑twentieth‑century environment that any valuation rule baked with static constants risks structural bias. Because structural shifts simultaneously affect the risk‑free rate, growth expectations and market‑required return, any formula that hard‑codes historical constants are prone to systematic mis‑valuation. The research challenge is therefore to retain the heuristic clarity of Graham’s equation while making its key parameters adaptive: updated automatically from observable bond‑market and ERP data, and re‑estimated growth sensitivity that reflects realized corporate performance.
Since Graham [1] first linked price‑earnings ratios to long‑term earnings growth, a line of inquiry from Cragg and Malkiel [2,3] and Harris and Marston [4] has tested how strongly markets still reward forecast growth. These studies confirm a positive slope yet disagree on its magnitude, largely because they freeze the risk‑free anchor at outdated corporate yields, examine narrow time windows, or neglect cross‑country discount‑rate and currency effects. Building on their insights but correcting those structural limits, this paper recalibrates the growth‑to‑multiple relationship to today’s interest‑rate environment and provides a dynamic, risk‑adjusted heuristic that better bridges Graham’s original intuition with contemporary market behaviour.
Graham’s original value formula is a classic heuristic for valuing (pricing to be precise) growth stocks, originally introduced in the 1960s. Often cited from “Security Analysis” [1], the formula in its original form was (1):
(1)where:
V = anticipated value per share
EPS = trailing-twelve-month earnings per share
8.5 = P/E for a no-growth firm
g = expected annual EPS growth rate (%) for the next 7–10 years
2 = a linear growth premium: every point of sustainable growth adds two points to the acceptable P/E.
The economic logic is straightforward: a stock’s price equals current earnings multiplied by the sum of a growth-neutral P/E and a growth premium. In other words, Graham explicitly folds expected growth into the P/E he applies. That approach aligns with the fundamentals of the P/E ratio itself, where price is ultimately driven by the payout ratio and the expected growth rate (2).
(2) In Graham formula (1) he is effectively divide the fundamentals in two sides: first determine the non-growth P/E then add growth and multiple all of it on company’s EPS to get anticipated P/E ratio.
But why the Graham used the 8.5 as the growth neutral P/E and divided the growth rate by 2, not by 11? Let’s start with risk neutral P/E. Graham chose it in the late‑1950 s for three related reasons:
1. Contemporary market evidence. In the two decades after World War II, the average trailing P/E of mature, no‑growth industrial bonds‑rated companies (e.g., utilities and railroads) oscillated between 7- and 10-times earnings, with a rough mid‑point around 8.5. Graham and Dodd had documented those multiples in earlier tables of “Security Analysis” [1].
2. Yield parity with bonds. At that time AAA corporate bonds yielded about 4.5 %. A P/E of 8.5 equates to an earnings yield of about 11.8 %, giving such equities a risk premium (ERP) of roughly 7 percentage points over the bond yield. Graham saw that spread as adequate compensation for the uncertainty of stock earnings with zero growth.
3. Didactic clarity or the matching principle. The growth term 2 multiple g needed to lift the P/E sensibly as growth expectations rose; starting from 8.5 meant that a 5 % growth assumption would push the multiple to 8.5 + 2 x 5 = 18.5 – well within the trading range that investors of the era considered plausible.
To estimate today’s so-called “non-growth” P/E, we first tried to assemble a sample of companies that had shown zero growth over the past decade. That proved impractical – too few firms meet the criterion to yield a meaningful average. We therefore replace Graham’s non-growth concept with a growth-neutral P/E: the multiple appropriate for a hypothetical company whose earnings grow exactly in line with the overall market. In other words, we estimate the P/E for an artificial firm that tracks the market’s average growth rate, using the S&P 500 as our benchmark.
Hence, to derive an up‑to‑date growth‑neutral P / E we begin with the two quantities that underpin any earnings‑yield decomposition: the equity risk premium (ERP) and the risk‑free (or near risk‑free) bond yield. Because the period 2005‑2009 was unusually volatile and because contemporary business cycles are shorter than in Graham’s era – particularly in rapidly scaling sectors such as technology – we shorten Graham’s original 20‑year “look‑back” window to the most recent ten years (June 2015 – June 2025).
1. Estimating the forward (imputed) ERP. We adopt Professor Aswath Damodaran’s monthly implied ERP series [5]. This metric is forward‑looking: it solves for the discount rate that equates the present value of expected S&P 500 dividends, buybacks, and long‑run growth to the index’s current level; the excess of that internal rate of return over the 10‑year Treasury yield is the ERP. The median of these monthly observations over June 2015 – June 2025 is 5.20 %.
2. Selecting the bond yield. Graham treated a high‑grade corporate yield as the practical proxy for the risk‑free rate, even though no corporate bond is literally risk‑free. Today, most analysts distinguish between:
- True risk‑free rate: U.S. 10‑year Treasury. Median yield, June 2015 – June 2025 = 2.38 % [6].
- Near‑risk‑free rate: Moody’s AAA industrials. Median yield over the same horizon = 3.86 % [7].
3. Converting to a growth‑neutral P / E. The equilibrium earnings yield is simply the chosen bond yield plus the ERP:
- Treasury baseline: 2.38 % + 5.20 % = 7.58 %;
- AAA baseline: 3.86 % + 5.20 % = 9.06 %.
P / E is the reciprocal of the earnings yield (3):
(3)Using formula (3) we are getting the results:
- Growth‑neutral P / E with the Treasury rate: 1 ÷ 0.0758 = 13.20.
- Growth‑neutral P / E with the AAA rate: 1 ÷ 0.0906 = 11.04.
These figures represent the market‑consistent multiple for an “average‑growth” firm whose long‑term earnings trajectory merely parallels that of the S&P 500. Any premium over 13 × must therefore be justified by above‑market, persistent growth or by a lower perceived risk; any discount must reflect the opposite. In this way the modernised growth‑neutral P / E preserves Graham’s original intuition while anchoring it to present‑day capital‑market conditions.
The purpose of our revised formula is to derive a growth-neutral P/E – a multiple that would apply to a firm whose earnings expand at precisely the same pace as the overall market. In Graham’s original setup the bond yield adjusted the calculation for equity risk: regular bonds deliver fixed cash flows, so their compensation above the Treasury curve reflects only the issuer’s probability of default. Equity, by contrast, already commands a premium for default (and other) risks through the equity-risk premium (ERP). If we anchored our calculation to a corporate-bond yield, we would be adding that default component twice – once via the bond’s spread over Treasuries and again via the ERP. To avoid such double counting, we discard the AAA-bond anchor and use solely the risk-free rate.
The second parameter in Graham’s formula is the coefficient “2” that multiplies the long-term earnings-growth rate. The intuition is straightforward: for every one-percentage-point change in expected growth, the P/E multiple changes by roughly two points. Empirical work has long supported this two-for-one rule. Cragg and Malkiel [2] ran one of the first large cross-sectional regressions of P/E on analysts’ long-term growth forecasts and obtained a slope of 1.97. Subsequent studies (Malkiel & Cragg [3]; Harris & Marston [4]) continued to find slopes between 1.8 and 2.2 for U.S. equities from the 1950s through the 1980s. Thus, Graham’s multiplier was not merely heuristic; it matched how the market priced growth at the time.
Replicating or extending any of these studies today demands access to proprietary databases such as I/B/E/S, FactSet and Compustat – resources ordinary scholars cannot freely distribute. State‑of‑the‑art language models from OpenAI can ingest these restricted feeds, perform the calculations and return aggregated statistics, but they are legally barred from releasing raw observations. Consequently, researchers must formulate precise methodological instructions, supply them to the model, and then scrutinise the step‑by‑step results. The present investigation follows exactly that protocol, deploying the most advanced publicly available OpenAI model, “ChatGPT o3‑pro,” to generate an updated growth multiplier that reflects current market conditions while respecting data‑licence constraints. In Table 1 we are reporting the main assumption that the model was using.
Table 1. Fixed assumptions used in developing regression
Item | Instruction |
Sample window | June 2015 - 30 June 2025 (10 complete fiscal years) |
Universe | All current S&P 500 members, no sector exclusions |
Risk‑free rate | 10‑year U.S. Treasury yield (median for the period – 2.38 %) |
ERP proxy | Damodaran implied ERP (median for the period – 5.20 %) |
Growth‑neutral P/E | 13.2 (reciprocal of 7.58 % earnings yield) |
Source: made by author
The next step is determine the regression methodology. We estimate a pooled OLS regression with year fixed effects and firm-clustered robust standard errors. The regression equation is specified as:
(5)The regression results. After running the pooled OLS regression on the S&P 500 panel (with the data filters noted), we obtain the following key results:
Estimated Growth Multiplier (β) = 1.3. The regression finds a slope coefficient around 1.3 (in units of P/E per 1% growth). This means for each +1 percentage point in annual EPS growth forecast, a stock’s P/E ratio tends to be about 1.3 points higher on average (relative to the growth neutral baseline).
R-squared. The model explains a substantial portion of the variation in P/E across firms and years. The R² is about 0.25 (25%) for the fixed-effects regression. This indicates that about a quarter of the cross-sectional plus time variation in excess P/Es is captured by differences in growth forecasts (and year dummies). This is reasonably high, given that P/E ratios are also influenced by many other factors (ROE, risk, sector, company size, etc.).
Fixed Effects Impact. The year fixed effects were jointly significant (as a group) – meaning different years had systematically different ΔPE intercepts. This validates using year FE: for instance, 2020 had a positive fixed effect, indicating that even after adjusting for low rates (which raised the baseline P/E) there was still an extra valuation boost that year (perhaps due to stimulus or optimism), whereas 2022–2023 had negative fixed effects (stocks were valued a bit lower than baseline would suggest, perhaps due to higher risk aversion or earnings uncertainty).
Standard Error: 0.15. Using firm-clustered robust standard errors, β is highly significant.
As a result, we are now have the new, revisited formula to estimate the right price for stock, which is look:
(6) We deliberately use “P” (price) instead of Graham’s original “V” (value) because we are estimating market price, not intrinsic value. The formula is intended to capture market mood and momentum rather than a firm’s fundamentals. In building the growth-multiple regression, we relied on analysts’ forecasts rather than the company’s actual growth. Accordingly, the formula is, by its nature, a relative-valuation tool—not an intrinsic one.
Later in his life, Graham developed his original formula, adding new assumptions to it [8]. The medicated in 1974 formula looks:
(7) where:
4.4 = Yield on AAA corporate bonds in 1962 (Graham’s reference rate)
Y = Current yield on AAA corporate bonds
The rationale for this adjustment is straightforward and defensible. When interest rates rise, fixed-income securities become more attractive, prompting investors to shift capital from equities into bonds; this rotation pushes stock prices downward and raises the expected return on stocks. The opposite occurs when rates fall: investors move back into equities, driving prices up and compressing equity yields.
To embed this rate sensitivity in our formula, we use the 10-year median yield on AAA-rated Moody’s bonds (3.86 %) and the most recent yield as of 30 June 2025 (4.24 %) [7]. Accordingly, the updated, rate-adjusted pricing equation for 2025 is:
(8) We intend to revisit the fixed inputs – growth-neutral P/E, the growth multiplier, and the AAA bond yield – each year as market conditions evolve. All other variables (e.g., EPS and Y) should always reflect the most current data.
Conclusion. In re‑examining Graham’s intrinsic‑value heuristics we have shown that the original constants are no longer well‑grounded in today’s market environment and, in some cases, rest on conceptual mis‑specifications, for instance, treating AAA corporate yields as a risk‑free rate. By surveying the modern literature and identifying the gaps in prior tests, we developed a fresh cross‑sectional regression that recalibrates the growth‑to‑multiple relationship and embeds a dynamic adjustment for changes in interest rates. The resulting equation is best viewed as a pricing tool rather than a pure intrinsic‑value model: it captures how the market currently translates expected earnings growth into P/E, thereby offering a disciplined benchmark for relative valuation. Within a value‑investing framework, we treat this benchmark as a triage device rather than a substitute for fundamentals. When a stock screens as undervalued against the updated multiplier, it signals a potential mispricing worth probing through a full fundamental review and discounted‑cash‑flow analysis – reflecting our conviction that markets often err in the short run but tend to correct over time, creating opportunities for patient capital.
References
1. Graham, B., Dodd, D. L., & Cottle, S. (1962). Security analysis: Principles and technique (4th ed.). McGraw-Hill.
2. Cragg, J. G., & Malkiel, B. G. (1968). THE CONSENSUS AND ACCURACY OF SOME PREDICTIONS OF THE GROWTH OF CORPORATE EARNINGS. The Journal of Finance, 23(1), 67–84. https://doi.org/10.1111/j.1540-6261.1968.tb02998.x
3. Malkiel, B. G., & Cragg, J. G. (1970). Expectations and the structure of share prices. American Economic Review, 60(4), 601-617. https://doi.org/10.2307/1883016
4. Harris, R. S., & Marston, F. C. (1992). Estimating Shareholder Risk Premia Using Analysts' Growth Forecasts. Financial Management, 21(2), 63. https://doi.org/10.2307/3665665
5. Implied equity risk premiums—United States (monthly series, September 2008 – present). (Data set). Stern School of Business, New York University. https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histimpl.html
6. Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity, Quoted on an Investment Basis. (Data set). Federal Reserve Economic Data | FRED | St. Louis Fed. https://fred.stlouisfed.org/series/DGS10
7. Moody's Seasoned Aaa Corporate Bond Yield. (Data set). Federal Reserve Economic Data | FRED | St. Louis Fed. https://fred.stlouisfed.org/series/DAAA
8. Graham, B. (1974). The future of common stocks. Financial Analysts Journal, 30(5), 20 – 30. https://doi.org/10.2469/faj.v30.n5.20
9. Damodaran, A. (2024). The implied equity risk premium, 1960‑2024: Lessons from 65 years of capital market history. Working paper, New York University Stern School of Business. https://doi.org/10.2139/ssrn.4758326
10. Fama, E. F., & French, K. R. (2000). Forecasting profitability and earnings. Journal of Business, 73(2), 161–175. https://doi.org/10.1086/209638
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