1990issue C051-11
Constructing a nominal index price from earnings and a fitted yield
A constructed nominal price is four-quarter earnings divided by a fitted effective yield. The identity is derived on a quarterly earnings cycle, evaluated monthly, and judged by comparing implied earnings with later realized earnings.
- Nominal price is a constructed baseline: four-quarter earnings divided by a fitted effective yield, not the observed market print.
- The effective yield is the three-month bill rate raised to a linear combination fitted by linear least squares on a constant, the bill-minus-inflation spread, and the bill-minus-bond spread.
- The identity is derived on a quarterly earnings cycle and then evaluated monthly so the constructed path can be compared with the contemporaneous index.
- The construction is judged by comparing implied four-quarter-ahead earnings with later realized earnings, not by a trading rule.
A baseline price, not a market print
A constructed nominal price is defined as four-quarter earnings divided by a fitted effective yield. That nominal price is a baseline index level implied by those two inputs, not the observed market print.
The identity is derived on a quarterly earnings cycle and then evaluated monthly. The finer sampling interval lets the constructed path be compared with the contemporaneous index.
Fitting the effective yield
The effective yield is a regression-assembled interest factor used as the divisor in the nominal-price identity. It is formed from the three-month bill rate raised to a linear combination of a constant, the bill-minus-inflation spread, and the bill-minus-bond spread.
Linear least squares supplied the three coefficients: 0.91022 on the constant, 0.03083 on the bill-minus-inflation spread, and 0.04983 on the bill-minus-bond spread.
A yield exponent in the early sample
Before 1968 the fitted yield diverges from conventional bill and bond rates, so the construction applies a yield exponent. After that early sample the extra power later fluctuates around 1.
Implied earnings as the construction check
Solving the same identity for earnings produces implied earnings: a four-quarter-ahead total that can be compared with later realized earnings. One late-1980s episode showed an implied figure of 34 against later realized earnings of 23.75.
Editorial: that rearrangement is the out-of-sample test of the construction, not a signal for entering or exiting a market.
An exponential earnings trend
Average four-quarter-ahead earnings are represented by a least-squares exponential trend of 1.61485 times 1.06974 raised to a time index. The time index is a calendar coordinate equal to year plus quarter divided by four, minus 51.
Levels, changes, and a consistency check
In the examined history, the level of price shows little correlation with the level of earnings, while yearly price change aligns more closely with the yearly change in earnings four quarters after the price observation.
Yearly earnings growth rates of a large-capitalization industrial average and a broad market index are compared as a consistency check on whether one series was treated as representative of the other.
All readings on this track · 43 readings
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- 1990Constructing a nominal index value from forward earnings and fitted yield
- 1990Constructing a nominal index price from earnings and a fitted yield
- 1990Endpoint-pinned price paths are not forecasts
- 1990Constructing least-squares polynomial smoothers
- 1991Endpoint growth rates versus linear-regression consistency
- 1991Out-of-sample checks for linear growth fits
- 1991Trend as persistence, not a straight line
- 1991Quadratic trend, residual oscillator, and a secondary cycle calendar
- 1991Time-origin offset and residual-price divergence on a quadratic least-squares fit
- 1991A least-squares trendline from ordered prices
- 1992Constructing log-linear growth and reliability screens
- 1992Constructing log-linear growth-rate baselines
- 1992Next-session high, low, and close from rolling linear regression
- 1993Auditing an index price-earnings multiple with short-rate regression
- 1994Regression-seeded nested exponential price filter
- 1994Constructing the double exponential average from lag cancellation
- 1994Evaluating money supply as a linear leading-index baseline
- 1995Constructing least-squares trend channels
- 1995Linear baseline holdout checks for annual bill-rate forecasts
- 1995Projection bands from high and low regression slopes
- 1995Evaluating a least-squares end-point moving average on a known test series
- 1996Constructing an endpoint moving average from a least-squares line
- 1996Scoring equity path consistency with a k-ratio overlay
- 1996Evaluating month-end yield gaps for equity regimes
- 1996Constructing session-indexed standard error bands
- 1998Evaluating linear regression baselines for index valuation
- 1998R-squared as a two-state trend filter from a price-time fit
- 2000Second-order moving-average lag correction
- 2002Price regression line versus beta for index tracking
- 2003Regression slope with an r-squared trend confidence gate
- 2003Constructing finite-volume-element divergence with slope comparison
- 2004Building a daily score from regression, retracement, and volume
- 2004Constructing least-squares trendlines from ordered prices
- 2007Rectangle breakout targets beyond height
- 2007Confirming a price trend with regression slope and r-squared
- 2008A linear-regression angle assembled as one trend filter
- 2010A two-state swing machine from four running extremes
- 2016Score oil-complex tightness before divergence or regression
- 2017Nikkei-yen intermarket divergence as a regime case study
- 2017Constructing Calmar ratio and linear regression baselines
- 2019Pair-trade layer construction versus average-spread management
- 2020A convolution slope built from nested linear regression