There are several assets that are frequently labelled a safe haven such as gold, U.S. and German government bonds, currencies such as the Swiss franc and the U.S. dollar and, more recently, Bitcoin. This paper proposes a safe haven index to benchmark safe haven assets and identify some stylized facts. The analysis shows that (i) safe haven assets are risky (in general and in crises) despite their "safe" label, (ii) the crisis-specific riskiness is a necessary condition to function as a strong safe haven, and (iii) safe haven asset risk can be diversified. An analysis of the COVID-19 shock in March 2020 reveals that the safe haven index briefly fell with the market contrasting previous crises over the last 40 years.