The price of call options has fallen to record lows, which has created extraordinary opportunities for nimble bulls to take advantage of potential gains with limited risk.

The options market's mirror image of a stock -- call options that expire in one month and have strike prices equal to the stock price -- is at the lowest level since 2002 for the average Standard & Poor's 500 index stock.

The implied volatility of one-month, at-the-money S&P 500 stocks is 18.6% while that of at-the-money, three-month calls is 22.2%, near the 1990 low of 19%. The low volatility is an anomaly because three-month calls expire after the November general election and a rash of market-moving economic data, according to a study released early Wednesday by John Marshall, a Goldman Sachs derivatives strategist, and Robert D. Boroujerdi, the co-head of the firm's equity research.

Many investors buy call options when implied volatility -- essentially the options market's view of a stock's future -- is unusually low. The Goldman Sachs study suggests investors can earn returns of 155% to 726% buying three-month calls on top-rated stocks if those stock prices move halfway to analysts' price targets.

Consider Boeing (ticker: BA). With the stock at $73.27, compared to the bank's 12-month price target of $94, investors can a buy November $80 call for 44 cents, just 0.6% of the price of the underlying stock. If Boeing's stock rises to $83.64, investors would realize a 726% return on the money spent to buy the call.

Halliburton (HAL) also offers potentially strong returns for investors who buy the November $38 call when the stock is at $35.16. If the stock hits $42.58 -- the six-month price target is $50 -- investors could realize a 452% return on the 83 cents spent to buy the call.

Other opportunities exist in other companies assigned Goldman Sachs' top Conviction List investing rating, including Cisco Systems (CSCO), VMware (VMW), AmerisourceBergen (ABC), Simon Property Group (SPG), Pfizer (PFE), Activision Blizzard (ATVI), Precision Castparts (PCP) and Prudential Financial (PRU).

The potential for triple-digit returns in relatively short periods has obvious broad appeal. But the market often defies the clinical rationality of financial models that predict stocks should trade at a certain price over a certain stretch of time if a company's future is anything like its past.

The real world is filled with uncertainty and risk. Stock prices could sharply decline, for example, if the Federal Reserve and European Central Bank disappoint many investors who now expect them to yet again intervene in the financial markets in the next few weeks.

But that also is why equity investors often prefer to replace stocks that trade near 52-week highs with options, especially when option prices are depressed, as they are now. That way they only risk the small price paid for the option rather than the potential loss on a high-priced stock.

While it would seem natural that stock and option prices would rise in tandem, they can disconnect when equity prices rise steadily without investors actively buying defensive put options as a hedge. The absence of fear -- or the existence of complacency toward the rally -- mechanically lowers options' implied volatility.

Computer models that price options begin to assume the future will be like the recent past. So historical volatility becomes unusually low, which in turn tamps down implied volatility -- the key factor in determining options premiums.

We have referred to the unusually low implied volatility levels as an historical anomaly in the options market. We have recommended investors buy bullish calls on the Select Sector Financial SPDR exchange-traded fund (XLF) (see Striking Price, "Bulls Buy Calls on Financials," Aug. 18), and we have advised hedging portfolios to preserve strong year-to-date gains amid uncertainty on the economic policy and political fronts (see "Protect -- or Profit -- From Market-Moving Events," Aug. 21).

Goldman's recommendation to replace stocks with cheaply priced options is consistent with these ideas that exploit low volatility in order to further investors' goal of reducing risk and maximizing gains. It is a rare opportunity that may not last if volatility reverts to its norms.

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Comments: steve.sears@barrons.com, http://twitter.com/sm_sears

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Steven Sears is the author of The Indomitable Investor: Why a Few Succeed in the Stock Market When Everyone Else Fails.

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