(Refiles to clarify that the $70 billion in paragraph 15 refers to equity assets)

By Trevor Hunnicutt

NEW YORK, Oct 11 (Reuters) - The market's quick and hard-to-explain declines this week led some investors to point fingers at number-crunching fund strategies designed to control and balance risk.

The benchmark U.S. S&P 500 stock index marked its biggest one-day fall since February on Wednesday and added to losses the day after.

The order of events, rising bond yields followed by a stock market selloff, recalled a similar event in February and also placed the focus on mechanical investment strategies sensitive to volatility, including risk-parity funds.

WHAT ARE RISK-PARITY FUNDS?

Risk-parity funds refer to a set of rule-based investment strategies that combine stocks, bonds and other financial assets. They are a counterweight to traditional portfolio investment strategies where investors are split between equities and bonds but equities end up carrying more of the risk.

In most multi-asset portfolios, equities tend to determine an investors' return because their price moves up and down more than other assets.

The goal of risk parity is to build a "diversified" portfolio in which each group of assets contributes an equal amount of risk so that the return is not primarily determined by stocks. The formula is based on historical research on how each asset performs and relates to the other groups over time.

WHERE DO THEY COME FROM?

The strategy came into being in the 1990s but drew increased attention after the 2007-2009 global financial crisis refocused investor attention on risks in the stock market, and on hedge fund strategies to minimize those risks.

WHY DO THEY MATTER?

Risk-parity strategies are a poster boy for a whole set of investment strategies that are sensitivity to volatility and have a potential to trade after major moves in the market. Yet backers of such funds say they often trade against the trend in the market.

WHO ARE THE BIGGEST PLAYERS IN THE MARKET?

The strategy is most associated with Bridgewater Associates LP, the world's largest hedge fund, which launched its risk-parity All Weather Fund in 1996. Bridgewater's founder, Ray Dalio, and the company are well known for a unique culture of "radical truth and radical transparency" whereby intellectual conflict is encouraged to promote a meritocracy of ideas, avoiding traditional office politics. Other major investors in the space include AQR Capital Management LLC, whose founder Cliff Asness is also a well-known investor.

WHAT ARE THE ASSETS IN RISK-PARITY STRATEGIES?