| Cut-and-Paste R Code | R² Predicting Future Betas† |
wins.rel <- function( r, rmin, rmax ) {
rlo <- pmin(rmin,rmax); rhi <- pmax(rmin,rmax)
ifelse( r<rlo, rlo, ifelse(r>rhi, rhi, r) )
}
wbsw <- function( ri, rm, delta=3.0, rho=2.0 ) {
wri <- wins.rel( ri, (1-delta)*rm, (1+delta)*rm )
beta <- function(...) coef(lm(...))[2]
bsw <- beta( wri ~ rm )
wbsw <- beta( wri ~ rm, w=exp(-rho*(length(ri):1)/252) )
}
|
| 1-Year Ahead | Predict OLS | Effort |
| OLS (Base R²) | 40% | easy 1-Pass |
| Vasicek 1973 | +4% | medium 2-Pass |
| Dimson 1979 | –10% | easy 1-Pass |
| Martin-Simin 2003 | +3% | difficult |
| Frazzini-Pedersen 2014 | –10% | medium 1-Pass |
| bsw 2019 | +5% | easy 1-Pass |
| wbsw 2019 | +6% | easy 1-Pass |
| 1-Month Ahead | Predict Self | Other |
| Vasicek 1973 | 50% | 52% |
| bsw 2019 | 57% | 51% |
|
| † The R²'s of the estimated betas with the true (unknown) betas would be approx the square-root of these R²'s. |
| | |
Source:
Welch, 2019. The two novel estimators are bsw ("beta slope-winsorized") and wbsw ("weighted beta slope-winsorized"). They are no worse than those in Vasicek (1973) and Martin-Simin (2003). Yet, the key advantage of bsw and wbsw is that they are super-easy to use: (1) you apply a simple prior to winsorize the daily firm-specific input returns first, and (2) you then run a standard least-squares regressions. The empirical performance ordering of these estimators is robust. It appears in nearly all partitions and all subsamples.
Incidentally, never use industry betas or monthly stock returns for forecasting individual stock betas. Their performance is terrible.
20-Year Treasuries have been offering just typical real (i.e., after-inflation) rates of return to taxed retail investors (i.e., after-tax on nominal interest paid), even over the last 8 years. (Not shown: The inference is similar for 1-year T-Bills.)
Source: Feenberg-Tepper-Welch, 2018.
The ex-ante OLS market-beta was a good measure of hedging against ex-post market crashes. (Not shown: the ex-ante plain OLS beta completely dominates the ex-ante asymmetric market betas.)
The CAPM is not even close to a reasonable approximation. It does not fail in the nuance; it fails in the basics.
Source: Welch (Corporate Finance textbook), 2017.
Even for good signal accuracy (p=0.6 on signals H or L), the expected (asymptotic) distance from the best action with 10 equally spaced possible action choices is still >10%.
Source: Bikhchandani-Hirshleifer-Tamuz-Welch, 2018.
LHS: This is the typical referee-reported assessment variations, given papers' true agreeable characteristics. RHS: Variations influence reported referee recommendation (and editorial decisions)? (Not shown: It is almost as important to draw a referee who is generally generous as it is to write a good paper.)
Estimated over the last 50 years (1967-2017), the equity risk premium was about 1-2% above long-term Treasuries. The term premium was twice as large, about 3-4%.
There was a modest increase in left-tail disaster risk after 2008, but nothing like the two sharp increases in 1987 and 1998. Most ex-ante risk was generic and not left-tail specific.
Protection against sharp drops in the stock market has different prices at different times. It costs around 0.2%/year as of 2018.
It was never really possible to predict equity premia with lagged dividend-price ratios. (This figure was updated to 2016.) For data and programs, go to the
goyal-welch webpage. (Not shown: No other variables seem to have predicted out of sample, either.)
Individual stocks can show reversal/momentum when their portfolios do not, and vice-versa. A sensible test should not convolute a theory of one with data evidence on the other. Unfortunately, dominated tests are common in the literature.
LHS: Portfolios of stocks added to the S&P500 did not revert (within 6 months) in the 1980s, but fully reverted in the 2000s. RHS: Portfolios of stocks removed from the S&P500 had tremendous post-removal performance from 1985 to 2008.
Corporations did not systematically seek to undo (counter) value effects on their leverage ratios. Ergo, managers did not seem to (aggressively) target stable leverage ratios.
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