LONDON -- Shares that are relatively unaffected by extreme market moves are what market statisticians call "low beta" shares. Here are the 10 FTSE 100 shares with the lowest beta.

CompanyPrice (pence)BetaP/EYield %Market Cap (Million Pounds)
Severn Trent (LSE:SVT) 1,614 0.22 17.8 5.0 3,855
Reckitt Benckiser 4,654 0.30 17.3 3.0 33,399
National Grid 729 0.32 13.4 5.8 26,718
Randgold Resources (LSE:RRS) 4,208 0.32 17.1 0.8 3,879
Wm. Morrison Supermarkets 260 0.33 10.0 4.9 6,046
United Utilities (LSE:UU) 649 0.33 15.2 5.5 4,425
AstraZeneca (LSE:AZN) 3,112 0.35 9.1 5.8 38,959
SSE 1,489 0.39 12.7 5.9 14,359
Imperial Tobacco 2,295 0.41 10.9 5.1 22,343
RSA Insurance (LSE:RSA) 119 0.41 9.6 5.7 4,491

My thoughts on five of these are as follows.

Randgold Resources
Resources companies like Randgold are always a play on the changing market value of the underlying resource.

The price of gold has fallen 21% in the past 12 months. In that time, shares in Randgold are down 28%.

The way a stock's beta is calculated means that Randgold looks a steadier investment than it really is. While the shares have not previously exaggerated the movements of the wider market, they have still been a wild ride. In the past five years, the shares have traded as low as 1,580 pence in 2008, rising to 7,775 pence in November 2012.

Investors must decide where precious-metals prices are likely to go before taking a position in a share like Randgold.

RSA Insurance
Ten years ago, RSA was one of the most volatile shares in the FTSE 100. At that time, its business was hugely geared to the fortunes of the stock markets.

Today, RSA is a very different proposition. In the past 12 months, shares in RSA have traded in the range of 105 pence to 136 pence. In that time, the FTSE 100 has moved from a low of 5,450 to a high of 6,840.

Analysts are today forecasting that earnings per share for the company will hit 12.4 pence for 2013, rising to 12.9 pence next year. At today's price, that's a 2013 P/E of 9.6, falling to 9.2 times for the year after.

I expect RSA shares to offer a prospective yield for 2013 of 5.2%.

AstraZeneca
In the past month, shares in pharmaceutical giant AstraZeneca are down 10.7%. They haven't been this cheap since March.

AstraZeneca has long been criticized for the apparent lack of new drugs being developed by the company. There are signs that AstraZeneca is taking steps to address this. In the past month, AstraZeneca has announced the acquisition of two smaller companies, Omthera Pharmaceuticals and Pearl Therapeutics, for a total price that could rise to $1.5 billion.

Brokers expect that AstraZeneca will make $5.26 of EPS this year and pay a dividend to shareholders of $2.80 per share. At today's price, that puts AstraZeneca shares on a forward P/E of 9.1, with the prospect of a 5.8% yield for the year.

United Utilities
Shares in United Utilities' sector are frequently referred to as "defensives." Whatever is going on in the world, United's customers will always require its water and sewerage services. This means that the company's share price is largely immune from the events that affect most FTSE 100 companies. The result is a low-beta share that can be relied on to avoid the wildest market movements.

Therefore, I am shocked to see that the shares have lost 17% of their value in the past month. Of that drop, 3.5% came from when the shares went ex-dividend on June 19.

According to current forecasts, United shares are trading at a 2014 P/E of 15.2, with a prospective yield of 5.5%.

Severn Trent
Shares in Severn Trent rose sharply in May, when the water utility received a takeover offer from a consortium of investors. Sares spiked upwards to almost 2,100 pence. This offer was rejected and withdrawn in June. The shares are now at a level lower than they were before talks began.

According to the consensus broker forecasts, Severn Trent is today trading at 17.8 times estimates for 2014. Although that may sound expensive, Severn Trent's sales and profits are extremely reliable, given the regulated, monopolistic nature of its business.

A dividend of 80.4 pence is forecast for the year, putting the shares on a yield of 5%, rising to 5.3% next year.

Owning a portfolio of low-beta shares is perfect for investors that want to sleep at night without worrying about sudden bear market moves. For more solid shares, check out the latest free Motley Fool report from our team of analysts: "5 Shares to Retire On" is the Motley Fool's latest free analysis for private investors looking for long-term opportunities. Just click here to get your free copy today.

David O'Hara and The Motley Fool have no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.