A number of quantitative finance textbooks mention something along the following lines, without further explanation:
A typical feature of implied volatility from stock index options is that it is higher than the historical/realized volatility of the index.
Here I assume that something like the VIX index or short-term ATM implied volatility is used as a measure of the overall level of implied volatility.
The above phenomenon seems to be referred to as the "volatility risk premium", defined on Wikipedia as
...a measure of the extra amount investors demand in order to hold a volatile security, above what can be computed based on expected returns.
Question 1: Can someone elaborate on this argument? Do seller of options overcharge because of the inherent volatility risk that cannot be hedged away? Is this related to the market price of volatility risk?
Also, this consistent overpricing of options can be taken advantage of, e.g. by taking a short position in an ATM straddle (sell ATM call and put), i.e. sell volatility. This seems to be a profitable strategy, see e.g. http://quantpedia.com/Screener/Details/20.
Question 2: Why don't simple strategies like these eliminate the fact that implied volatility is consistently higher than realized volatility?