Buying Below Fair Value

I

The price you pay decides the return you get

Part I and Part II focused on variance, Kelly sizing, and asset class personalities. We treated returns as if they were a property of the asset itself. They are not. Returns are a property of the price you paid. The same asset bought at two different prices produces two completely different geometric outcomes — and the gap is wider than most investors realise.

Three frameworks all describe the same phenomenon from different angles:

Margin of safety (Benjamin Graham)

If you buy an asset at a discount to its fair value, two things happen at once. Your potential upside expands — because you have a larger gap to close as price reverts toward value. And your downside contracts — because the discount itself absorbs future bad news. Margin of safety is not just defensive. It is the most powerful return amplifier in investing.

Mean reversion

Two separate empirical facts get bundled here: (1) post-crash bounce — the 1–3 years after a drawdown deliver above-trend returns (this is the dataset in Section III), and (2) long-run reversal — over 5–10 year windows, starting CAPE explains a large share of forward return variance (Fama-French 1988). They are distinct mechanisms; conflating them is how investors talk themselves into selling expensive assets too early. The bigger the dislocation, the bigger the rebound bias — but the timeframe matters.

Valuation timing

Each asset class has metrics that historically signal whether prices are stretched or compressed. The CAPE ratio for stocks. The MVRV Z-score for Bitcoin. Price-to-rent for real estate. Real TIPS yield for Treasuries. Real interest rates for gold. Futures-curve shape for commodities. None of these are timing tools at 1–3 year horizons — Asness and AQR have shown the 1-year correlation between CAPE and forward return is near zero. The signal only sharpens past 7–10 years (3–5 for the more cyclical assets). Treat valuation as a multi-year bet about geometry, not a next-quarter forecast.

This article puts numbers behind all of them. Let’s start with the most studied case: the S&P 500.

II

S&P 500 — CAPE and the next decade

Robert Shiller’s CAPE ratio (Cyclically Adjusted Price-to-Earnings) divides the S&P 500’s price by its 10-year average inflation-adjusted earnings. The 10-year smoothing strips out recession noise and reveals the underlying valuation level. The historical median is approximately 16. Anything above 25 has historically been “expensive.” Below 15, “cheap.”

The relationship between starting CAPE and the next 10 years of annualized returns is one of the most robust findings in financial economics. It is not a perfect predictor — but the correlation is strong enough that ignoring it requires active disagreement.

The mechanism: starting yield (1/CAPE) plus earnings growth must equal forward return. If you pay 35× cyclical earnings, the yield is 2.9% and there is little room for multiple expansion to bail you out — the algebra forces low returns over a decade. Crucially, this same algebra says almost nothing about the next 12 months: in any single year, sentiment and rate moves dominate fundamentals by 5–10×. Valuation is signal at 7–10y horizons and noise below 3y.

The pattern is unmistakable. When the CAPE was below 10 (deep value), forward 10-year real returns averaged roughly 11–13% annually. When the CAPE was above 30 (extreme expensive), forward 10-year real returns averaged 0–3%, with several windows turning negative. The current CAPE sits around 36 — historically, this implies forward 10-year real returns of around 0–3%.

A worked example: $10,000 over 10 years

Imagine two investors. Both invest $10,000 in the S&P 500. Investor A buys when the CAPE is in its cheapest quintile (below ~13). Investor B buys when the CAPE is in its most expensive quintile (above ~25). What did the next decade actually deliver, on average, across all such historical windows?

Same asset. Same currency. Same 10-year holding period. The ending wealth differs by nearly 3×. The only variable was the price paid at the start.

This is not a stock-picking story — it is the broad index. The “boring” S&P 500 produces dramatically different outcomes depending on whether you bought it at a discount or a premium to its long-run earnings power.

III

Mean reversion — buying after the crash

A simpler form of “below fair value” is buying after a market crash. You don’t need a valuation model — the price tells you the asset has dislocated from its trend. The question is whether forward returns from those moments justify the courage required.

The historical answer is yes, dramatically. Here are the four largest S&P 500 drawdowns of the modern era and what the next 5 years delivered to investors who bought near the bottom:

The average S&P 500 return across all 10-year windows is roughly 10% nominal. The 5 years following major bottoms delivered 17% on average — a 70% improvement over the unconditional baseline. That is the mean reversion premium expressed in dollars.

The market does not reward you for holding through a crash. It rewards you for buying during one.

The catch — and there is always a catch — is that nobody rings a bell at the bottom. By the time the dust settles, prices have already moved. The investor who waits for “confirmation” typically misses the steepest part of the recovery. The mean reversion premium accrues to those willing to act when the news flow is still terrible.

This is also where Part I’s Kelly framework returns. After a 50% crash, your edge has objectively improved (lower starting price, higher forward expected return), and your psychological ruin tolerance arguably matters more than your financial one. Kelly says: in the wake of dislocation, size up — carefully, but without flinching.

IV

Bitcoin — three completed cycles since 2013

Bitcoin has a much shorter history than equities, but a more dramatic one. Its volatility makes valuation timing both more painful and more rewarding. The on-chain metric most closely tracked is the MVRV Z-score, which compares Bitcoin’s market value to its “realized value” (the average price at which all coins last moved). When the Z-score is deeply negative, holders are sitting on losses and prices are historically cheap. When it is extremely high, prices are euphoric.

Bitcoin’s history since 2013 contains three completed cycles (the 2010–2011 micro-cycle pre-dates reliable on-chain data and is excluded). Each cycle bottomed when MVRV Z-score crossed below 0 and stayed there for 3+ months — the canonical accumulation zone in Bitcoin on-chain literature. Here’s what buying $10,000 at each of those bottoms produced over the next 3 years:

Note the trajectory: +6,400% (2015) → +1,400% (2018) → +490% (2022). The cheap-entry premium is decaying as the asset matures and the natural buyer base broadens. Do not extrapolate the historical average forward — the next cycle’s bottom may deliver a fraction of what 2015 did.

Now compare those to investors who bought near cycle tops:

The same asset. Buying within roughly the same overall era. Outcomes differing by more than 25×on average. With Bitcoin, the entry point isn’t a small adjustment to your return — it is essentially the entire return.

The discipline this demands is brutal. Cycle bottoms occur precisely when sentiment is most negative, headlines proclaim Bitcoin “dead” for the Nth time, and most early holders have already capitulated. Cycle tops occur when adoption stories dominate the news, your friends are texting you about Bitcoin, and “this time is different” feels obviously true. Empirically, MVRV Z-score below 0 has historically marked the upper bound of accumulation zones; the average forward 3-year return from those moments has been ~27× the average from MVRV Z>5. Sentiment and signal happen to coincide — but the trade is the metric, not the mood.

V

Real estate — price-to-rent and price-to-income

Real estate’s “fair value” is harder to pin down because it has two cash flow streams (rental income and appreciation) and is highly local. But two ratios travel well across markets. Price-to-rent compares purchase price to annual rent — the inverse of gross rental yield. Price-to-income compares median home price to median household income. Both have historical norms, and both signal stretched conditions when they spike.

Major real estate dislocations are rarer than equity ones — a property cycle takes 15–20 years rather than 5–7. But the same logic applies. The 2008–2011 housing crash in the US drove price-to-income ratios from ~4.7× back down to ~3.3× in many metros. Investors who bought at the bottom captured both the price recovery and roughly 6–8% rental yields on dramatically reduced cost basis.

The 2011 buyer’s outcome was over 2× the 2006 buyer’s, on the same neighborhoods, the same building stock, the same rental market. Real estate’s slower cycles can lull investors into thinking entry timing doesn’t matter — but the math says it matters as much as in equities, just on a longer clock.

Real estate has one additional wrinkle the others lack: leverage. A 20% down payment turns an 8% unleveraged return into something closer to 25–30% return on equity in a normal market. In a depressed market with a 6%+ rental yield, leveraged returns at the bottom can exceed even Bitcoin’s mean-reversion premium — with far less variance. This is why patient, well-capitalized real estate investors disproportionately become wealthy from one or two well-timed cycles.

VI

Bonds, gold, and commodities — valuation in the defensive set

The metrics so far — CAPE, MVRV, price-to-rent — are equity-like. The defensive assets from Part II have their own valuation languages. They’re less famous, but the math is the same: every asset class has a starting condition that explains a large share of forward returns over a 5–10y window.

Treasury bonds — real yield is the metric

For Treasuries, “fair value” is anchored to two things: the real yield (nominal yield minus expected inflation) and the term premium. When real yields are negative — as they were in 2020–21 — you are guaranteed to lose purchasing power even if you hold to maturity. When real yields are above 2%, history says a conservative 60/40 portfolio delivers 5–7% real over the next decade. The 10-year US TIPS yield is the cleanest readout: above 2% is structurally cheap, below 0 is structurally rich.

Investors who bought 10Y Treasuries in late 2018 (real yield ~1%) locked in moderate forward returns. Investors who bought in mid-2020 (real yield ~−1%) suffered the −25% drawdown of 2022. Investors who bought in late 2023 (real yield ~2.3%) captured the post-rate-cut rally. Same asset, three different starting yields, three completely different decade-forward outcomes. The discipline: ignore nominal yields; price Treasuries off real yields, and accept that “TINA for bonds” is the bond equivalent of buying CAPE 36 stocks.

Gold — real interest rates and central-bank flows

Gold has no cash flow, so it has no “earnings yield.” The closest valuation anchor is the negative of real interest rates: gold rallies when real rates fall (the opportunity cost of holding a non-yielding asset shrinks) and falls when real rates rise. The historical bands: when real 10Y yields are below 0, gold tends to deliver 8–15% annualized real over the next 3–5 years. When real yields are above 2%, gold tends to deliver ~0% real or worse.

A second signal — central-bank gold buying — has historically marked durable bottoms. The 2015–18 accumulation phase by emerging-market central banks preceded gold’s 2019–25 run. Both signals lined up in 2018 and again in late 2022; both diverged in 2011–13 (when central banks bought but real yields were rising), and gold underperformed despite the institutional bid. When the two signals agree, the historical hit rate on a 3-year horizon has been substantially higher than for either alone.

Commodities — contango, backwardation, and the cycle

Broad commodity indices have two valuation signals. The first is the futures curve: when the curve is in backwardation (front months priced above back months), holders earn a positive roll yield; when in contango, they bleed. Persistent backwardation in energy and grains has historically marked supply-tight regimes that deliver multi-year above-trend returns. The second is the long-cycle marginal-cost anchor — when prices fall below the marginal producer’s breakeven (~$40/bbl for oil, ~$1,000/oz for gold, historically), supply destruction sets in and prices recover. The 2020 oil collapse to negative prices was the most extreme version of this: investors who bought USO or GSCI within 90 days of the bottom captured the +120% rally over the following 18 months.

The catch with commodities: their long-run real return is closer to zero than equities’. Mean reversion works on cycles but doesn’t compound across them. A diversifying allocation captured at the bottom of a contango regime and exited at the top of backwardation can produce equity-beating multi-year returns, but holding through a full cycle returns roughly inflation. Valuation discipline matters more here than in any other asset class — which is also why most retail investors lose money in commodities: they buy after the rally and sell after the drawdown.

VII

The pattern across asset classes

Across very different asset classes, time periods, and metrics, the same pattern holds: entry valuation is one of the largest determinants of long-run returns. Here’s the gap between buying cheap and buying expensive, expressed as the multiple by which the cheap-entry investor’s forward wealth exceeded the expensive-entry investor’s, on each asset’s natural horizon:

Thresholds at a glance

One table to operationalize all seven asset classes (T-bills excluded — they have no valuation timing dimension by construction). Use these as starting bands, not hard rules — the value-trap caveat below applies everywhere.

The ratios scale with volatility. Treasury bonds’ ~1.6× advantage is real but compressed — bonds are the lowest-variance asset that has a valuation timing signal. Real estate’s ~2.3× is meaningful but moderate. The S&P 500 and gold both deliver ~3×. Commodities and NASDAQ ~4–4.5×. Bitcoin’s ~25× is extreme. This is not a coincidence — high-variance assets have wider valuation swings, which means more opportunity to buy meaningfully below fair value and more risk of buying meaningfully above it.

From Part I we know that variance is generally an enemy of compounding. Margin of safety flips that relationship. The same volatility that destroys returns when you buy at the top creates outsized opportunities when you buy at the bottom. Variance becomes useful when paired with discipline about entry price.

Volatility without valuation discipline is just risk. Volatility with valuation discipline is opportunity.

VIII

The trap — and why most investors don't capture this

If buying below fair value is so obviously superior, why don’t more people do it? Three reasons, all behavioural rather than mathematical.

The bottom never feels like a bottom.By definition, prices reach extreme cheapness only when sentiment is universally bearish. Buying at that moment requires acting against the consensus of every news source, every friend, and your own pattern-recognition instincts. The investor who “waits for confirmation” almost always misses the entry. The same is true at tops — the period when buying is most dangerous is exactly when it feels most justified.

The wait is longer than people expect.Valuation extremes can persist for years before resolving. The S&P 500’s CAPE has been above 25 for most of the last decade. Bitcoin spent 2018–2020 in extended undervaluation. Patient capital is rare precisely because patience is psychologically expensive when the rest of the market appears to be making money without you.

The “fair value” anchor moves. Every cycle produces new arguments for why the old metrics no longer apply — new monetary regimes, new technologies, structural shifts in earnings. Sometimes these arguments are right. More often they are post-hoc justifications for paying high prices. Distinguishing real regime changes from rationalizations is the hardest judgment in investing, and there is no formula for it.

The value trap — cheap-and-stays-cheap.The fourth trap is the one the dataset hides. Japan’s TOPIX traded below its 1989 high for 34 years; UK and European equities have spent most of the last 15 years cheap on CAPE without delivering the historical 11–13% return premium. The empirical edge described above is conditional on the dataset surviving — and the most stretched single market in history (Japan, CAPE 90+ in 1989) is the dataset most often quietly excluded. Cheap on CAPE is a necessary but not sufficient condition; structural decline can keep an asset cheap for decades. The same trap applies to commodities (the 2014–20 secular decline made “cheap” oil cheaper for six years) and to bonds in a sustained inflation regime.

None of this invalidates the data. It explains why the data persists. If buying below fair value were easy, the premium would arbitrage away. The premium exists precisely because executing on it is uncomfortable.

IX

Frequently asked questions

What CAPE ratio is considered overvalued for the S&P 500?

The historical median CAPE is approximately 16. Anything above 25 has historically been “expensive” — forward 10-year real returns from those entry points averaged 0–3% annually. Below 15 is “cheap,” with forward returns averaging 11–13%.

How much do entry valuation differences affect 10-year returns?

For the S&P 500, a $10,000 investment compounded over 10 years becomes roughly $29,700 when bought in the cheapest CAPE quintile versus $10,500 when bought in the most expensive — a ~3× spread on the same index, currency, and holding period. For Bitcoin the spread is over 25×.

Does valuation work as a short-term timing tool?

No. Asness and AQR have shown that the 1-year correlation between CAPE and forward return is near zero. Valuation is signal at 7–10 year horizons (3–5 for cyclical assets like gold and commodities) and noise below 3 years — in any single year, sentiment and rate moves dominate fundamentals by 5–10×.

What is the MVRV Z-score and when is Bitcoin cheap?

The MVRV Z-score compares Bitcoin’s market value to its realized value (the average price at which all coins last moved). Historically, Z < 0 has marked accumulation zones and Z > 5 has marked distribution zones. Each completed cycle bottomed when MVRV Z crossed below 0 and stayed there for 3+ months.

How do TIPS yields signal Treasury bond value?

The 10-year US TIPS yield reads off the real yield available on a Treasury — nominal yield minus expected inflation. Historically, buying 10Y Treasuries when TIPS yields exceeded 2% has delivered 5–7% real returns over the following decade. Buying when TIPS yields were negative (2020–21) locked in guaranteed real losses and exposed bondholders to the −25% drawdown of 2022 when rates normalized. Real yield, not nominal yield, is the discipline.

When is gold considered cheap?

Gold has no cash flow, so the cleanest valuation anchor is the inverse of real interest rates: gold tends to deliver 8–15% annualized real over the next 3–5 years when real 10-year yields are negative, and roughly 0% real when they exceed 2%. A confirming signal — central-bank net buying — has historically marked durable bottoms (2015–18, late 2022). When both align, historical hit rates jump materially.

How do you tell if commodities are cheap?

Two signals: (1) the futures curve — persistent backwardation flags supply-tight regimes that deliver positive roll yield; deep contango is the opposite, and (2) the marginal-cost anchor — when spot prices fall below the marginal producer’s breakeven (~$40/bbl oil, ~$1,000/oz gold historically), supply destruction eventually triggers a cycle reversal. Neither signal is a precise timer; together they bracket the cyclical lows.