The pricing of any financial asset never exceeds three yardsticks: ① nominal growth rate (expected return / numerator), ② risk-free rate (cost of time / opportunity cost / denominator), ③ risk premium (probability). In a single sentence: “discount expected cash flows at the risk-free rate under a given probability”; switching asset classes merely changes the specific inputs into the numerator and denominator — the same pricing machine operates across equities, interest rates, and currencies.
The Framework As It Stands
This section is compiled from research draft notes: the original framework’s structure, terminology, and key formulations are preserved, with editorial bridges and supplementary factual notes; diagrams are drawn by the compiler following the original text’s structure.
Timestamp note: The course was recorded in January 2019. All rate levels, nominal GDP figures, exchange rate levels, and volatility readings cited in this section are judgments made at the time of the course (end-2018 / early 2019) or historical experience values; they do not represent the current state. Assessing current pricing requires current-period data.
I. Foundational Principles
Macro analysis ultimately serves asset pricing; its core objective is to identify arbitrage opportunities. Asset pricing = combining growth (numerator factor) with cost (denominator factor): high growth × low cost = high valuation; low growth × high cost = low valuation. The growth process corresponds to cyclical factors (Kuznets / Juglar / inventory), while cost corresponds more to structural issues and systemic risk.
The three yardsticks:
| Yardstick | Alias | Meaning |
|---|---|---|
| ① Nominal growth rate | Expected return / numerator | How much return an asset is expected to generate (real estate: rent; equities: dividends + earnings) |
| ② Risk-free rate | Cost of time / opportunity cost / denominator | The opportunity cost of holding any asset; expected return must exceed it |
| ③ Risk premium | Probability | The probability that the expected return actually materializes |
In a single sentence: discount expected cash flows at the risk-free rate under a given probability; no asset type’s pricing exceeds these three factors.
II. Equity Pricing = CAPM
- Numerator = corporate earnings: listed companies must earn over the long run, otherwise it is only a story; at the macro level, corporate earnings are determined by GDP (GDP ≈ the weighted sum of earnings growth rates across all sectors and companies).
- Second factor, risk-free rate = the opportunity cost of holding equities; in practice generally measured by the 10-year government bond yield.
- Third factor, risk premium: buying a large stable company carries different risk from buying a growth stock; higher risk demands higher return.
- Numerator = earnings; denominator (risk-free rate + risk premium) = valuation — this is the basic principle of CAPM.
Sensitivity and timing for the three equity-asset types:
| Type | Sensitivity | Conditions for Outperformance |
|---|---|---|
| Consumer | Loosely negatively correlated with GDP (cyclical when unpacked); liquor cross-year returns broadly track core CPI (historical experience as of end-2018) | Mid-to-downstream prices beat expectations, or economic uncertainty beats expectations and drives safe-haven demand |
| Cyclical | Volume highly correlated with business conditions; price follows PPI and upstream CRB raw-material prices | Economic growth or prices beat expectations (economy surprises to the upside / supply contraction pushes prices) |
| Innovation (small and mid-cap growth) | More sensitive to the denominator; a risk-premium-sensitive and rate-sensitive asset class | Overall interest rates declining, or risk appetite rising significantly / risk premium declining significantly |
III. Three Yardsticks for Interest Rate (Bond) Pricing
- ① Nominal GDP determines the cyclicality of rates (course at end-2018: nominal GDP approximately 11% → 9%+, corresponding to rates approximately 4.0 → 3.6).
- ② The China-U.S. spread determines the rate level (foreign investors hold approximately 50% of incremental government bonds, approximately 8% of stock; they do not accept a China-U.S. inversion — this is a constraint, not a determinant; at end-2018 U.S. Treasuries approximately 3.32 → 3.1, releasing spread pressure).
- ③ Risk premium constrains rate elasticity (generally observed via term spread and similar measures).
- Interest rate in essence = the return demanded for lending money to another party, comprising expected return on investment + inflation compensation + risk premium.
IV. Three Yardsticks for FX Pricing + RMB Range Stability
- ① Purchasing power parity determines the long-term foundation of exchange rates (the law of one price: the ratio of domestic to foreign currency needed to buy the same basket of goods); RMB (end-2018) approximately 1:6.x — no evident overvaluation in the medium-to-long term, no basis for depreciation.
- ② Interest rate parity (domestic-foreign spread) influences short-term FX moves (U.S. hikes + China does not hike — spread unfavorable for RMB).
- ③ Risk premium influences short-term FX moves (risk rises during economic adjustment, unfavorable for RMB).
- RMB range stability: 2007–2018, 11 years; annual move generally within 7%, appreciation and depreciation alternating (2007: +6.5%; 2008: +6.4%; 2015: −6.1%; 2016: −6.8%; 2017: +5.8%; 2018: depreciation).
One Pricing Machine = Discount Expected Cash Flows at the Risk-Free Rate Under a Given Probability
Numerator: Nominal Growth Rate / Expected Return
Denominator: Risk-Free Rate (Opportunity Cost) + Risk Premium (Probability)
│
├─ Equities: Numerator = Earnings (determined by GDP) / Denominator = 10-yr Treasury + Risk Premium = CAPM
│ └ Consumer (negative correlation / cyclical when unpacked) / Cyclical (volume~sentiment · price per PPI/CRB) / Innovation (sensitive to denominator)
│ └ Timing: Cyclical=growth/price beats expectations · Consumer=downstream price beats/risk-off · Innovation=rates fall/risk appetite rises
├─ Interest Rates: Nominal GDP determines cyclicality / China-U.S. spread determines level / Risk premium constrains elasticity
│ └ Intuition: Expected return on investment + inflation compensation + risk premium
└─ FX: PPP determines long-term / Interest rate parity determines short-term / Risk premium
└ RMB: Range-bound stability · annual move ≤7% · appreciation and depreciation alternate (2007–2018, 11 years)Compiler’s Perspective
Coordinates: Category = Cognitive Algorithms / axis_h = Fa / axis_v = What It Is / soul_anchor = No 100% Certainty · Trust in Purity · Heaven’s Reckoning Outweighs Man’s
Connecting the Level
This framework collapses all asset pricing into the same machine, but the machine has one structure that is routinely misused: among the three yardsticks, ① (numerator / nominal growth rate) and ② (denominator / risk-free rate) can be quantified to a point estimate using models, while ③ (risk premium) is inherently “no 100% certainty” — it is a function of probability, not a fixed number. Those who already know CAPM before using this framework tend to treat the discounted value as the endpoint; the output is actually a range of values under a particular probability assumption. Collapsing it to a point estimate quietly assigns ③ a value of zero, and the practitioner is left unprepared when the market’s risk premium shifts suddenly.
Consumer equities being loosely negatively correlated with GDP contains a hidden condition. The course at the time (historical experience as of end-2018) showed that cross-year returns on liquor-type assets broadly track core CPI, not GDP — meaning the numerator proxy for consumer equities is CPI, with a different lag structure from cyclicals. Using “consumer equities = defensive = hold when the economy is weak” as a simple rule will result in numerator-and-denominator compression in tandem when CPI declines alongside an economic slowdown, rather than protection from defensiveness.
Innovation equities (small and mid-cap growth) are the only one of the three equity types whose primary sensitivity axis is the denominator (risk-free rate + risk premium). This produces an asymmetric signal: during an easing cycle, even before the numerator (earnings / GDP) has improved, innovation equities already have the conditions for revaluation; conversely, during a rate-rising cycle, innovation equities face pressure first even if macro growth is solid. No equivalent “denominator-dominant, numerator-secondary” inverse structure exists in consumer or cyclical equities — this is a signal endogenous to the three-yardstick framework and cannot be read directly from the standard CAPM formulation.
On the RMB exchange rate, the 11-year (2007–2018) range stability — “annual move generally ≤7%, appreciation and depreciation alternating” — is the historical constraint boundary of the risk premium (third yardstick) under a specific policy framework. Extrapolating “purchasing power parity shows no depreciation basis at 1:6.x end-2018” directly to the present is a classic timestamp error; the current answer requires running all three yardsticks with current-period data.
See Also
- The Nature of Macro Research and the Sense of Position — the endpoint of positional output is exactly the input end of the three yardsticks: the position within the economic cycle determines the phase for the numerator (earnings / GDP); the rate level determines the phase for the denominator
- Finding High Probability Through Empirical Regularities: Six Case Studies in Practice — the six cases provide specific empirical calibration points for the risk premium (third yardstick) in historical experience, supplementing the probability layer of the three-yardstick framework
- Three Modes of Macro Research Thinking and the Primacy of Empirical Regularity — empirical regularity takes precedence over logic; this is the epistemological premise for building numerator expectations without “constructing logic first and then finding data”
- The Three-Step Macro Diagnosis: Empirical Regularity, Logic, Data, Pricing — the final step of the three-step diagnosis, “mapping to asset prices,” calls on this article’s three yardsticks as the pricing-side interface; the two articles together constitute the complete end-to-end chain
Sources
- Compiler’s draft z-0093 · collected 2026-07