1990issue C051-2
Constructing a nominal index value from forward earnings and fitted yield
A nominal value is built by dividing four-quarter-ahead earnings by an effective yield. Least-squares fits supply the smooth earnings path and the bill-rate scaler, so a later check can separate that baseline from the leftover expectation residual.
- A nominal value is a reference price formed by dividing yearly four-quarter-ahead earnings by an effective yield.
- In the construction sample, concurrent index price and earnings showed little correlation, while the yearly change in price tracked the yearly change in those forward earnings.
- A least-squares earnings average and a linearly scaled bill-rate effective yield, with a yield exponent before 1968, form the explicit baseline.
- The gap between traded price and that constructed level is read as an expectation residual, not as the nominal value itself.
Start with the nominal value
A nominal value is a constructed reference price formed by dividing a chosen earnings input by an effective yield. In this construction the earnings input is four-quarter-ahead earnings: yearly earnings dated one year after the price observation. A nominal price level can be constructed by dividing those yearly earnings by an effective yield.
In the construction sample, concurrent index price and earnings showed little correlation, while the yearly change in price tracked the yearly change in those four-quarter-ahead earnings.
Fit four-quarter-ahead earnings
When a smooth earnings path is required, four-quarter-ahead earnings were summarized by a least-squares earnings average: an exponential trend fitted to those forward earnings from 1963 onward and used in place of raw earnings. The least-squares exponential average used yearly multiplier 1.06974 and time index T equal to calendar year plus quarter divided by four, minus 51. Adding one year to that time index raises the fitted earnings average by 6.974 percent.
Scale the bill rate into an effective yield
Effective yield is a three-month bill-rate baseline scaled by linear least-squares adjustments for the bill-minus-inflation and bill-minus-long-bond spreads. In the construction, that scaler is a linear least-squares function of those two spreads, with intercept 0.91022 and slope coefficients 0.03083 and 0.04983.
Reconcile the rate with a yield exponent
The yield exponent is a power applied to effective yield so the implied rate from average earnings over price can be reconciled with later-period bill rates. Before 1968 the yield implied by average earnings over price diverged from the bill rate, so the construction applied a yield exponent equal to the log of average-earnings-over-price divided by the log of yield. After 1968 that exponent fluctuated around 1.0. Before 1968 it was approximated as 0.01684 times year plus quarter over four, minus 0.161988.
Read the leftover gap as an expectation residual
The constructed level is treated as a consensus nominal value. The gap between observed price and that level is read as an expectation residual: the market's implied view of future earnings rather than the nominal itself.
TradersWeek editorial: keep that residual distinct from the nominal value. The least-squares earnings-and-yield baseline is the part of the path the scaffold can explain. The leftover gap is what a later out-of-sample check would inspect separately.
All readings on this track · 43 readings
- 1990Constructing dollar baselines from rates, inflation, and residuals
- 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