The Rooster Doesn't Make the Dawn: What Ukrainian Data Say About the NBU's Real Reach

 I. Why this post exists now

    I wrote this because I got tired. Tired of hearing the same unexamined premise in academic seminars and business conversations alike — that the National Bank of Ukraine is the institution doing the job: setting the rate, taming inflation, drawing the government yield curve by decree. It gets repeated as settled fact, and almost no one stops to test it against the data. The push to actually run that test came from Aswath Damodaran’s 2024 post, “Fed up with Fed Talk? Fact-checking Central Banking Fairy Tales!”, which makes the case for the United States: the Fed is far more a follower of markets than a setter of them — a rooster whose crowing the yard mistakes for the cause of sunrise.

    Damodaran ran it on the US. Ukraine is not the US — and here the dependency is less obvious, because our financial system is thinner and bank-centric rather than market-centric, and because since 2015 the NBU has operated under a far more rigorous, externally disciplined inflation-targeting regime. Those two features make the regulator look more powerful than its American counterpart, which is exactly why the myth is stickier here. But the fundamentals are always the same: a policy rate is a reaction to inflation and growth before it is a cause of anything, and the further you move from the overnight corridor, the less the central bank is setting and the more the market is.

II. The three myths in one sentence

    Ukrainian public discussion typically rolls three claims into one sentence: that by raising the key policy rate the NBU has administratively (1) set the rate of inflation, (2) set the yield on government bonds, and (3) set the cost of corporate bank credit. For journalism this is convenient. For practice it is dangerous — because it glues three different transmission mechanisms into a single administrative act. The paper tests each of them separately on Ukrainian data, and each of them fails.

III. Reading the policy rate as a reaction, not a decision

    If the central bank reacts to macro conditions rather than setting them, then the rate itself ought to be explainable from the simplest pair of those conditions: lagged inflation and lagged real growth. Damodaran’s intrinsically-implied risk-free rate is the arithmetic sum of those two; for our purposes a linear regression is more honest than the sum.

The empirical core of the paper is a two-variable regression of the quarterly average policy rate on lagged year-over-year CPI and lagged real GDP growth, calibrated separately on four institutional windows:

• 2002–2025, the long history: R² = 0.54. Useful as background but it mixes institutionally incompatible regimes — pre-Maidan and post-Maidan, peace and war.
• 2015–2025, the post-Maidan period: R² = 0.58. The NBU is operating under tighter external discipline from this point.
• 2015–2021, the cleanest peacetime approximation: R² = 0.62. Pre-war post-Maidan window.
• 2022–2025, wartime: R² = 0.73. The narrower we draw the window, the more disciplined the rate-setting looks.

    Picture 1. Actual NBU policy rate versus the implied value of the lagged CPI + GDP model. The fit tightens as the window narrows from the long history to wartime

    The climb in R² is the central reading. It is not consistent with an arbitrary administrative rate; it is consistent with a regulator that reacts more tightly the more dominant inflation becomes in the macro environment. Wartime also doubles the loading on lagged CPI: the coefficient moves from 0.33 in the peacetime window to 0.57 in wartime — each printed percentage point of inflation translates into roughly 0.57 p.p. of policy rate next quarter. That doubling is itself an argument against the administrative reading. If the rate were set arbitrarily, its sensitivity to inflation wouldn’t have to double in exactly the regime where inflation became the dominant macro stressor.

    A richer meeting-level reaction function (94 NBU rate decisions, February 2015 to March 2026) adding 12-month household inflation expectations, one-month hryvnia depreciation, and a war-regime dummy lifts R² to 0.74. The two heaviest coefficients are household expectations (β = 0.65, p < 0.001) and the war dummy (≈4.8 p.p., p < 0.001). Same reading: the policy rate looks like a reaction function, not a decision variable.

    The honest limit. A pseudo out-of-sample test inside each window confirms that the model does not beat the naive “rate stays unchanged” rule on the level of next quarter’s rate. Naive persistence is a hard benchmark on quarterly data — most variants of the Taylor rule on developed economies lose to it too. But on the direction of the next move — up, down, or hold — the model classifies correctly about twice as often as naive persistence in every window, including the wartime one. That is real structural information about where the rate is going; it just is not an instrument for forecasting the level.

IV. Where the signal actually passes — and where it doesn’t

    If the rate itself reads as reactive, the natural follow-up is how far its signal then propagates into market prices. The answer in Ukrainian data is “not nearly as far as the public discussion assumes.” The signal is tightest at the very short end of the money market and loosens steadily as we move outward.

    Picture 2. The hierarchy of direct rate-setting: how far the policy-rate signal reaches across UONIA, government-bond tenors, bank rates and consumer inflation.

    a.  UONIA — the overnight interbank rate. Operationally tied to the policy-rate corridor. Descriptive R² ≈ 0.96 between UONIA and the policy rate over 2020–2026; after the October 2023 corridor redesign it is closer to one. UONIA is the closest thing in the system to “the NBU sets this.” It is also the only thing the NBU literally sets, and it is not a price anyone outside the interbank market actually trades.

    b.  Domestic government bonds, by tenor. Pre-war the short end (<1 year) loads on the policy rate at β = 0.77 with R² = 0.89; the 1–3 year bucket at β = 0.53, R² = 0.81; the 3–5 year bucket at β = 0.31, R² = 0.53. The further out the curve, the less the policy rate explains, and the more the price is doing its own work — pricing inflation, liquidity, and fiscal risk. Post-24.02.2022 the short-end coupling collapses outright (β = 0.09, R² = 0.04): the NBU raised the rate to 25 % in June 2022 and government-bond yields did not follow immediately. The NBU’s own communication at the time acknowledged it was waiting for government-bond and deposit rates to reprice, which is the tell — administrators don’t wait for the price they set.

    Picture 3. NBU policy rate versus government-bond yields and spreads by tenor. The short end tracks the rate; the long end carries its own inflation, liquidity and fiscal premia.

    c.  Commercial bank lending and deposit rates. Pre-war these are the cleanest transmission story in the system: β = 0.57 for non-financial corporate credit, β = 0.62 for deposits, both with R² > 0.88, both with a one-month lag. Post-war the betas fall to ≈0.30 and R² to ≈0.66–0.68. Even in the tightest peacetime regime the pass-through is partial — credit risk, liquidity, bank competition, and a wartime premium all write the final corporate borrowing rate on top of the policy-rate signal.

    The combined reading: the NBU directly sets the corridor and indirectly anchors the very short end of the curve. Outside that narrow zone its signal arrives partially and with a lag — and increasingly so as the instrument lengthens or the regime breaks.

V. Inflation: the market does most of the work

    The third myth is the centrepiece — the claim that the central bank sets inflation. We test it in two steps.

    Step one: estimate a market-only CPI equation with lagged producer-price inflation, three-month hryvnia depreciation, and 12-month household expectations. The model explains 64.2 % of the variation in year-over-year CPI over August 2014 – March 2026, before any monetary variable enters. Household expectations carry most of the load (β ≈ 1.92); lagged PPI contributes the rest.

    Step two: add the 12-month-lagged policy rate to the same specification. R² rises from 64.2 % to 68.3 %, and the rate enters with a negative, statistically significant coefficient (β ≈ –0.47). On a robustness check with core CPI as the dependent variable, the rate coefficient remains negative and significant (β ≈ –0.41), with R² = 0.65.

    Picture 4. Actual CPI versus the market-only model and the model with the lagged policy rate added. The monetary variable adds a thin lagged layer on top of a market-driven base.

    That four-point lift is real, but it is small relative to the market layer that was already there before any monetary variable arrived. Inflation in Ukraine is born from the market first and gets a thin lagged disinflationary topcoat from the policy rate later. That is not “the NBU set the rate of inflation.” That is the NBU dampening, with a lag, an inflation print whose level was determined elsewhere.

VI. The cross-regime lesson

    The pattern across the three myths converges on one reading. The NBU’s signal is tightest where the rule is literally administrative — the corridor and the overnight interbank market — and loosens systematically as we move outward into prices that other players also write. By the time we reach consumer inflation, the policy-rate contribution is a thin lag on top of a market-driven layer that already explains most of the variation. The wartime window is the partial exception: in a crisis the NBU can move proactively, as it did in June 2022, but that proactive step does not translate automatically into government-bond yields, bank rates, or consumer prices either — the long tail of transmission stays partial and lagged even when the headline policy move is decisive.

VII. What I’d say now

    The conclusion I keep coming back to is deliberately less complimentary than the one that dominates the Ukrainian public discussion. The NBU is best read as an administrative, constrained, reactive institution. Its signal is tightest at the very short end of the money market and in wartime hryvnia repricing; outside those zones its impact on the broader structure of rates and on inflation is partial, lagged, and widely overstated. The policy-rate decision is not the cause of the macro picture; it is a structurally disciplined response to the macro picture, executed under tighter external discipline since 2015 and especially since 2022.

    Damodaran’s bird is the right metaphor — the rooster whose crowing the yard credits with the sunrise it merely accompanies. The practical implication for Ukrainian economic communication, in wartime and toward post-war reconstruction, is that we should stop building narratives of macro-stability on an overstated NBU power over prices. The market sets the rate; the regulator’s task is to be disciplined enough not to obstruct it.

Shell, Eleven Months Later: A Retrospective Check on the June 2025 Valuation

    I. Why this post exists

    In my previous post on Shell I valued the company at 13 June 2025, ran four methods in parallel, and ended with a Kennedy refrain handing the decision over to the reader. The post stopped at a buy-decision built on a 55.9 % probability of underpricing in the base run, with the explicit thesis that the next leg up would come from fundamentals rather than from a higher Brent print. It did not commit to anything beyond that. The honest thing to do – eleven and a half months later – is to come back and check.

The window is unusually clean. On 2 March 2026 a major geopolitical incident around the Strait of Hormuz spliced the observation period into two regimes – a quiet, fundamentals-driven stretch from 13 June 2025 to 27 February 2026, and a shock-driven stretch from 2 March 2026 through (so far) 26 May 2026 – twelve weeks long enough that the shock half is now meaningfully bigger than a single news cycle. That accidental split is the kind of natural experiment a valuation methodology rarely gets in clean form: a calm regime to test the fundamental layer of the model, a shock regime to test the option layer.

    II. What was on the table at 13 June 2025

    A quick recap, for readers who didn’t see the June post.

    At the valuation date Shell traded at $36.25 per share on the article basis. I applied four methods in parallel, each yielding a per-share number on a consistent share count:

    • Fundamentals normalisation – baseline (cycle-median revenue × 8 % operating margin): $26.50. The 8 % was the 2010–2024 cycle-median operating margin; the revenue side was the cycle-median top line over the same window. On its own logic, Shell looked overpriced.

    • Fundamentals normalisation – conservative (cycle-median revenue × 10 % operating margin): $42.16. I called the higher margin conservative precisely because the company was already earning above 11 % and management had given no sign of reversal. On its own logic, underpriced.

    • Oil-price normalisation: $41.68 at the spot of $73, $44.09 at the cycle-median $75.85, with a middle of $42.89. Underpriced.

    • Monte Carlo with correlated Brent and operating-margin draws (100 000 trials): median $40.50; 5th–95th percentile range $25.50–$64.30; 55.9 % of the mass above market. Underpriced on median.

    Four anchors, not one. The fundamentals baseline at $26.50 was deliberately the cheap stress test – it asks what Shell would be worth if its sustainable operating margin reverted from the 11–14 % range it had been printing back to the 2010–2024 cycle-median 8 %, i.e. if recent above-cycle profitability were treated as a temporary tailwind rather than a sustainable level. The other three methods clustered between $40 and $44. I bought at $36.25 with the explicit thesis that the next leg up would come from fundamentals – sustained margin above the cycle median, the buyback, the rising payout ratio – rather than from a higher Brent print.

    III. The window, the regimes, the gap that closed

    Between 13 June 2025 and 26 May 2026 the share price rose 18.3 % on the consistent article basis, from $36.25 to $42.88. Brent ran the opposite way through the calm half of that window – from $76.00 on the valuation date down to $71.32 on the eve of the shock, or –6.2 % and then broke regime on 2 March. The first half of the window is the cleaner test: the re-rating happened despite weak oil, not because of it.

Picture 1. Brent and Shell rebased to 13 Jun 2025 = 100. The dashed line marks 2 Mar 2026 – the Hormuz shock. Brent series ends 18 May 2026 (FRED 5-business-day publication lag).

    Splitting the window at the day before the Hormuz shock sharpens the point. In the pre-shock regime, from 13 June 2025 to 27 February 2026, Shell rose 15.1 % on basis – almost the entire long-run gap to the methods that had said underpriced closed in nine months on a falling Brent. The share price crossed the Monte Carlo median ($40.50) on 25 February 2026, the lower edge of the oil-price normalisation band ($41.68) on 27 February 2026 – literally the eve of the shock – and the conservative fundamental ($42.16) and the oil-price middle ($42.89) on 6 and 11 March 2026 respectively. None of those crossings coincided with Brent above $75. The market re-rated Shell to its intrinsic-value range on the strength of fundamentals, before there was any extra geopolitical premium to allocate.

Picture 2. Monte Carlo distribution of Shell’s intrinsic value (100 000 draws, log-normal calibrated to the June 2025 paper). Markers show where the realised price sat at three reference dates: the valuation date, the eve of the shock, and today.

    Then came 2 March 2026. Brent indexed to the valuation date jumped from 94 to a peak of 182 – close to a doubling off the week before. Shell on the same index moved from 115 to a post-shock peak of 130 on 7 April 2026, then drifted back to 118 by 26 May as Brent receded from its peak. That is a striking asymmetry: an almost doubling in spot Brent delivered, at peak, fifteen index points on top of a share that had already re-rated by fifteen – and most of that incremental fifteen has since unwound while Brent is still trading around 155. The interpretation is straightforward once we sit with the model. The bulk of Shell’s value sits in already-producing assets whose discounted cash flows are not very sensitive to a one-quarter spike in spot Brent. The option layer on undeveloped reserves – Whale, Bonga North, Manatee, the rest – is the only piece of the valuation that should react to a regime change in oil-price volatility, and it did, but in measured size, and only for as long as the volatility regime itself looked changed.

Picture 3. Shell daily close (article basis) against the three near-money valuation anchors – Monte Carlo median, conservative fundamental, oil-price middle – with the Hormuz shock dashed in. The stress-test anchor (Fundamentals 8 % at $26.50) sits below the plotted range.

IV. Reading out each method against eleven months of price tape

    Picture 4 below plots the mean absolute deviation of the realised price from each method’s central anchor, separately for the two regimes. The ranking is informative because it inverts.

Picture 4. Mean absolute deviation of realised price from each method’s central anchor – pre-shock regime (green) versus post-shock regime (orange). Computed from daily Shell article-basis prices, 13 Jun 2025 – 26 May 2026.

    a. Pre-shock regime (the fundamental period). Monte Carlo wins (MAD 9.4 %). The conservative fundamental at 10 % margin is a close second (12.9 %). The oil-price normalisation comes third (14.4 %). The fundamentals baseline at 8 % is last by a wide margin (38.6 %) – which confirms what was already obvious in June: an 8 % anchor is artificially low for a company already earning above 11 %.

    b. Post-shock regime (the geopolitical period). The ranking flips. Oil-price normalisation is now the most accurate (MAD 4.2 %) – intuitively correct, because that method is the one explicitly tied to where oil prices sit. The conservative fundamental holds up unexpectedly well (5.4 %), because the margin anchor turned out to be the right long-run anchor regardless of regime. Monte Carlo is third (9.5 %), barely worse than its pre-shock score; the reason it loses any accuracy at all is that the empirical 2005 – mid-2025 Brent distribution simply did not contain prints above $130, so the realised path strayed outside the bulk of the simulated distribution. The fundamentals baseline at 8 % is again last and by a much wider margin (67.4 %), because the share price kept walking away from a value anchor that was wrong to begin with.

    The cross-regime lesson is the central takeaway of this retrospective. No single method dominates in both states of the world. Monte Carlo is the right tool when the market is weighing fundamentals; oil-price normalisation is the right tool when the market is reacting to a price shock; the conservative fundamental is a useful sanity check across both; and the baseline at the cycle-median margin is mostly a stress test that tells us what Shell would be worth if everything we knew about its recent operating performance were wrong. The right output is the range the four methods jointly span, not any one anchor on its own.

    V. The option layer, an area to keep exploring

    In the June post I priced Shell’s undeveloped reserves as a portfolio of European call options on oil, using Black-Scholes with q = 1/n to penalise time-to-expiry. That layer added a non-trivial premium to the producing-asset DCF. A few fellow financiers reasonably asked whether the option layer was doing real work or just decorating the model with mathematics.

    Let me be precise about what the option-pricing model actually tells us. Black-Scholes is unambiguous on direction: higher realised volatility raises the value of a long-dated call, and lower volatility releases that premium back. Between 2 March and roughly the second week of April 2026 Brent’s realised volatility jumped sharply, then started normalising; over the same window Shell traced a path from $42 to a peak around $47 article basis on 7 April and back toward $43 by 26 May. The option layer must have contributed something to that round trip – the model leaves no room to claim otherwise. What I am not ready to tell you is how much. Disentangling the option-layer contribution from the producing-asset DCF response inside a single shock episode is its own piece of work; I treat it as an open area for further exploration, not a question I have answered here.

    VI. The Graham line, eleven months late

    Benjamin Graham’s observation about the market being a voting machine in the short run and a weighing machine in the long run gets quoted often enough that it has nearly worn itself out. The Shell window is a rare clean example of what he meant. In the nine months before the shock there was no news on oil that should have re-rated Shell by 15 % – Brent went down over that period. What changed was that the market progressively recognised what the four methods had already weighed in June: that Shell’s sustainable operating margin was closer to 14 % than to 8 %, that the buyback was real, that the reinvestment rate was settling at a level consistent with a mature commodity producer returning more cash than it deployed. The market weighed. Then geopolitics arrived and the market voted – briefly, on volatility – in a direction broadly consistent with what an option-pricing layer would predict, before giving most of the incremental premium back as volatility eased. The producing-asset DCF carried the underlying value through both halves.

    VII. And so, dear friends, you just have to carry on

    The cleanest evidence sits in the calm half of the window, not the loud half. By 27 February 2026, the eve of the Hormuz shock, Shell had already crossed the Monte Carlo median ($40.50), touched the lower edge of the oil-price normalisation band ($41.68), and was within striking distance of the conservative fundamental ($42.16) and the oil-price middle ($42.89). On a falling Brent. The market closed the gap between $36.25 and the band the four methods jointly defined while spot oil drifted from $76 to $71. That is the part of the test the Iran shock did not run for me: it had already finished, in my favour, before the first headline out of Hormuz.

    One footnote on hindsight. The post-shock numbers benefit from it; the pre-shock crossings do not – they happened in the calm regime, with Brent working against the trade, and they happened to all three near-money anchors before 2 March.

    Every time I sit down with a valuation I come back to professor Damodaran’s reminder: it is all about fundamentals. And this is another example of professor’s wisdom.

Mind the Multiplier: Calibrating Growth Multiples to Unlock Mispriced Equities

Constructing a robust, fully fledged DCF model is labour‑intensive: it demands a deep grasp of the business, its industry, legal jurisdictions, strategic outlook, and countless other inputs to achieve a reasonably precise estimate of intrinsic value. Because analytical time is scarce, investors must pick their battles—deciding which companies merit that level of scrutiny. What is needed first, therefore, is a quick‑and‑dirty multiplier that can flag the firms most likely to be undervalued and worth the heavier DCF treatment.

This article revisits Benjamin Graham’s intrinsic‑value rule, adapting it to the post‑crisis investment landscape. It replaces the original fixed constants with dynamic anchors linked to prevailing bond yields and market equity‑risk premia, then recalibrates the growth multiplier through contemporary cross‑section data. The resulting formula keeps Graham’s hallmark simplicity, yet reflects today’s low‑rate environment, wider dispersion of corporate growth paths and faster information cycles.

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