Abstract
In this chapter, we explore two applications of regression modeling: the question of regression-weighting of GNP forecasts and the issue of estimating models associated with security totals returns. We examine the forecasting of GNP by major econometric firms and the modeling of security returns as a function of well-known investment variables and strategies. We illustrate regression analysis and problems with highly correlated independent variables. We will refer to the correlation among independent variables as multicollinearity.
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Notes
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Granger (1989) additionally pointed out that if the optimum value for k is 0.3, one may still obtain poor combined forecast if k takes two values only, being 0 on 60% of occasions and 1.0 on the remaining 40%.
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This research was supported in part by the National Science Foundation under Grant IST 8600788. We thank George Jaszi of the BEA and Donald Straszheim of Wharton, who graciously provided the forecasts from their respective econometric models. The authors are indebted to Professors S. Sharma and W.L. James for providing access to their LRR procedure as described in Sharma and James (1981). The original data for this analysis is not available from either John Guerard or Bob Clemen.
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Savita Subramanian (2011), “US Quantitative Primer,” Bank of America Merrill Lynch, May.
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There are many approaches to security valuation and the creation of expected returns. The first approaches to security analysis and stock selection involved the use of valuation techniques using reported earnings and other financial data. Graham and Dodd (1934) recommended that stocks be purchased on the basis of the price-earnings (P/E) ratio and Basu (1977) reported evidence supporting the low P/E model. James (Jim) Miller, Chief Investment Officer, CIO, of Continental Bank commissioned the project with Drexel, Burnham, Lambert, in 1989. Miller and Guerard (1991) presented a stock selection model at The Berkeley Program in Finance that used earnings, book value, cash flow, sales, relative variables, and earnings per share forecast revisions. Miller and Guerard experimented with a price momentum variable, the Columbine Alpha, described in Brush (2001). Jack Brush’s Columbine Alpha “pushed out” the eight-factor EP, BP, CP, SP, and relative variables’ Efficient Frontier. Guerard delivered paper sat Columbine Equity Research conferences in 1989 and 1994. See Guerard (1990).
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Guerard (2006) reestimated the GPRD model using PACAP data at The Wharton School from Wharton Research Data Services (WRDS). The WRDS/PACAP data is as close to the GPRD data as was possible in academia. The average cross-sectional quarterly WLRR model F-statistic in the GPRD analysis was 16 during the 1974–1990 period whereas the corresponding F-statistic reported in the Guerard (2006) was 11 for the post-publication, 1993–2001 period. Both sets of models were highly statistically significant and could be effectively used as stock selection models.
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Haugen and Baker (2010) extended their 1996 study in a recent volume to honor Harry Markowitz. Haugen and Baker estimated their model using weighted least squares. In a given month they estimated the payoffs to a variety of firm and stock characteristics using a weighted least squares multiple regression in each month in the period 1963 through 2007. Haugen and Baker found the most significant factors were; residual Return is last month’s residual stock return unexplained by the market.
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Cash Flow-to-Price is the 12-month trailing cash flow-per-share divided by the current price.
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Earnings-to-Price is the 12-month trailing earnings-per-share divided by the current price.
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Return on Assets is the 12-month trailing total income divided by the most recently reported total assets.
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Residual Risk is the trailing variance of residual stock return unexplained by market return.
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12-month Return is the total return for the stock over the trailing 12 months.
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Return on Equity is the 12-month trailing eps divided by the most recently reported book equity.
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Volatility is the 24-month trailing volatility of total stock return.
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Book-to-Price is the most recently reported book value of equity divided by the current market price.
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Profit Margin is 12-month trailing earnings before interest divided by 12-month trailing sales.
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3-month Return is the total return for the stock over the trailing 3 months.
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Sales-to-Price is 12-month trailing sales-per-share divided by the market price.
The four measures of cheapness are found in the USER model: cash-to-price, earnings-to-price, book-to-price, and sales-to-price, all have significant positive payoffs. Haugen and Baker (2010) found statistically significant results for the four fundamental factors as did the previously studies we reviewed. The Haugen and Baker (2010) analysis and results are consistent with the Bloch et al. (1993) model.
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Guerard, J.B. (2013). Regression Analysis and Multicollinearity: Two Case Studies. In: Introduction to Financial Forecasting in Investment Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5239-3_4
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