Has the real interest rate been unusually low?

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.

Were lower market-beta portfolios good crash hedges?

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.)

Source: Levi-Welch, 2017.

Is the CAPM a reasonable approximation?

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.

Are Info Cascades relevant with many actions?

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.

Are referees reliable in academic paper assessments?

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.)

Source: Welch, RFS 2014.

Over the last x years, what would you have earned?

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%.

Source: Levi-Welch, JFQA 2016.

How has left-tail disaster risk evolved?

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.

Source: Welch, FAJ 2016.

What would left-tail disaster insurance (have) cost?

Protection against sharp drops in the stock market has different prices at different times. It costs around 0.2%/year as of 2018.

Source: Welch, FAJ 2016.

Could lagged dividend-price ratios predict stock returns?

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.)

Source: Goyal-Welch, RFS 2008.

Are portfolio reversals&momentum proxies of stock reversals&momentum?

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.

Source: Patel-Welch, RAPS 2016.

Have returns of portfolios of S&P500-changers changed over the decades?

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.

Source: Patel-Welch, RAPS 2016.

Did firms target specific leverage ratios?

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.

Source: Welch, JPE 2004 and CFR 2013.

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