Academic economics research questions and answers can range from the mundane, simple, and obvious; to the subtle, complex, and sophisticated. Some first-order questions fall into the former category—for example, why do people herd, what is the real interest rate, what drives corporate leverage ratios? Other first-order questions fall into the latter category—for example, how can Bayesians persuade (Gentzkow) or can one recover expected returns from options (e.g., Ross)? My own research tends to fall into the former category; and, ideally, my research answers will seem obvious ex-post.


publishing

Curriculum Vitae (CV)

Links to my Published Papers +

SSRN →

Links to my Working Papers


historical asset class performance


Source: Levi-Welch, JFQA 2017.

  • Over the last 50 years, the realized equity premium consisted of about 4-5% term premium and 2% risk premium: Stocks outperformed T-Bills by about 6-7%/yr, and T-Bonds by about 1.5%/yr. Of course, stocks are more like long-term assets—well, even longer-term than 20 year bonds.

    Incidentally, the prevailing term spread has not changed much over the last few decades. In 2017, it still stands around 2.5-3%/yr.

  • What about the equity premium puzzle? Mehra-Prescott was written in 1985 and looked back until 1926. Their sample happened to have had the largest geometric risk premium (about 4-6%/yr) and the smallest term premium (about 1-2%), for an equity premium of about 7-8%/yr. They thought they had a risk-premium puzzle.

    I believe we have no reason to discard data since 1985. Instead, we should update with it. M-P is obsolete, because their phenomenon seems to have disappeared since at least 3-5 decades ago. The principal puzzle over the last 3-5 decades is the large term premium.

  • Not shown, pushing backwards into the 19th Century, again brings the risk premium back down to about 2%/yr. The most unusual aspect of the MP sample was not the performance of stocks, which just continued as before, but the low term-spread. I consider the puzzle to be primarily the term premium, not the risk premium.

disaster tail risk

The following are estimates derived from S&P 500 index options. Source: Welch, FAJ 2016.


The graph above shows the time-series of at-the-money volatility, plus the extra below-the-money volatility. Note how the 1987 crash and the 1998 mini-crash showed jumps in crash risk, while the 2008-10 crisis showed modest and smooth increases. Most of the volatility is ordinary at-the-money volatility.

... and its maximum possible impact on the equity premium

The graph below shows the upper bound to the possible magnitude of disaster risk, given that it could be insured in real time against with far-below-the-money puts. As of 2017, less than 0.5% equity premium per year can be attributed (in real time!) to disaster fear.


data etc

Please refer to my "professional" URL.

Most interesting there are (a) the time-varying tail-risk series; and (b) the goyal-welch (csv) files.

I have also the fred-csv.info gateway to FRED (Federal Reserve Economic Data) data, which returns csv files in 'yyyymmdd,series' format (and can be called from the command line). I find this far more convenient than dealing with APIs, GUIs, etc.