NEW YORK - Initial public offerings by real estate investment trusts faced a tough market on Wednesday as investors shied away from taking on risk in a volatile market.

Shares of Terreno Realty Corp began trading on the New York Stock Exchange 6.3 percent below their IPO price even after the size of the offering had been reduced twice. The shares opened at $18.75, and eased further in early trade.

Shares of Piedmont Office Realty Trust Inc began trading 1.7 percent above their IPO price on the NYSE after selling fewer shares than expected at a price below the anticipated range, although they were up about 4 percent in later trading.

Historically, shares have risen 10 to 12 percent in their debuts as companies look to reward investors for taking a risk on an unknown stock.

The Chicago Board Options Exchange Volatility Index, a measure of investor anxiety sometimes called the fear index, was at 26.65 at mid morning, indicating nervousness about market conditions.

A number over 25 indicates a volatile market in which it can be difficult to place IPOs, according to bankers.

The index fell from highs over 30 in the fall of 2009 to below 20 in mid-January. It is currently trending higher.

The index spiked over 67 during the height of the financial crisis in October 2008.

Terreno Realty plans to buy industrial real estate in six major U.S. coastal areas including Los Angeles, New York City and its headquarters city of San Francisco.

Piedmont specializes in high quality office buildings in major U.S. markets. It owns 73 properties and has said it would use proceeds from the IPO for general purposes and working capital including renewing leases and re-letting spaces, acquisition and development, and repaying debt.

(Reporting by Clare Baldwin in New York; Editing by Ted Kerr)