How to calculate the risk free rate of return on Securities

The other posters who are familiar with CAP-M are correct. The proxy for the risk free rate of return are US Treasuries. You can find the rates of return for Treasuries on either yahoo finance or google finance.
You may also notice that betas tend to differ slightly - it depends on whether they're historical, forward looking, based on consensus, etc.
You can also find the rate of return on the market (use the S&P Index) at either google finance or yahoo finance.

Here's part of an article on the Capital Asset Pricing Model from Investopedia.com:

Here is the formula:

rj = rf + b(rm-rf)
where:
rj= expected return on asset j
rf= ten year US Treasury rate (the "risk free" rate)
b= beta
rm=market return


CAPM's starting point is the risk-free rate - typically a 10-year government bond yield. To this is added a premium that equity investors demand to compensate them for the extra risk they accept. This equity market premium consists of the expected return from the market as a whole less the risk-free rate of return. The equity risk premium is multiplied by a coefficient that Sharpe called "beta".

Beta
According to CAPM, beta is the only relevant measure of a stock's risk. It measures a stock's relative volatility - that is, it shows how much the price of a particular stock jumps up and down compared with how much the stock market as a whole jumps up and down. If a share price moves exactly in line with the market, then the stock's beta is 1. A stock with a beta of 1.5 would rise by 15% if the market rose by 10%, and fall by 15% if the market fell by 10%. (For further reading, see Beta: Gauging Price Fluctuations and Beta: Know The Risk.)

Beta is found by statistical analysis of individual, daily share price returns, in comparison with the market's daily returns over precisely the same period. In their classic 1972 study titled "The Capital Asset Pricing Model: Some Empirical Tests", financial economists Fischer Black, Michael C. Jensen and Myron Scholes confirmed a linear relationship between the financial returns of stock portfolios and their betas. They studied the price movements of the stocks on the New York Stock Exchange between 1931 and 1965.

How to calculate market return using historical data For Portfolio Management

The link is broken for some reason (could be me or maybe it's on your side)... however, I don't need it to help you.

CAPM:

Stock Return = Beta (Rm - Rf) + Rf
Where Rf = Risk Free rate and Rm = Market return

"Market return" should be the geometric average return from inception (the earliest date) to today. If you're looking for market return of 1984, then you take the price of the market on December 31, divide by the price on 1 January and then subtract one. The Risk Free rate is the long-term sovereign rate (should be given to you).

Market risk is the standard deviation of the market (on a daily basis). This is the sum of the square differences from the mean divided by the number of days (minus one).