The Correlation coefficient, also known as r, R, the arithmetic mean or Pearson's r is a measure of the strength and direction of a linear relationship that exists between two variables and is calculated as the covariance of the variables in a sample divided by the product of their standard deviations. The correlation coefficient is used to determine the market risk of a project.

(x1 - μ1)(x2 - μ2)/n

where x1 is the value of one variable,
x2 is the value of the other variable,
μ1 is the arithmetic mean of of x1,
μ2 is the arithmetic mean of of x2,
and n is the number of values being summed over (i.e. the size of the population or sample).

The correlation of x1 and x2 is:

(cov(x1,x2))/(σ1σ2)

the covariance of x1 and x2 /

the standard deviation of x1 x the standard deviation of x2

A risk-free asset has no systematic risk; therefore, it is the systematic risk that determines the price of investments. How does one determine the price of a stock in a portfolio?

•  Determine the risk-free rate.
•  Determine the expected return on the market.
• Estimate the beta of the security.
• The cost of capital is equal to the risk-free rate plus a premium.

Pricing however is risky since, projects have long economic lives that require multi-period analysis and measuring beta is difficult. (make use of betas from similar companies as an pre-calculation).

Whether a company defaults on risk or not depends on the company not being able to diversify its risk. If this happens if there is too much risk.

 Stock Expected Standard Correlation Return deviation with stock X X 10,00% 12,00% 1,00 Y1 14,00% 18,00% -1,00 Y2 14,00% 18,00% -0,25 Y3 14,00% 18,00% 0,25 Y4 14,00% 18,00% 1,00 Weights Portfolio's standard deviation Wx Wyi E(Rp ) Correl xy1 =-1.00 Correl xy2 =-0.25 Correl xy3=0.25 Correl xy4=1.00 0,00% 100,00% 14,00% 0,180 0,180 0,180 0,180 10,00% 90,00% 13,60% 0,150 0,159 0,165 0,174 20,00% 80,00% 13,20% 0,120 0,140 0,152 0,168 30,00% 70,00% 12,80% 0,090 0,122 0,139 0,162 40,00% 60,00% 12,40% 0,060 0,107 0,129 0,156 50,00% 50,00% 12,00% 0,030 0,095 0,120 0,150 60,00% 40,00% 11,60% 0,000 0,088 0,114 0,144 70,00% 30,00% 11,20% 0,030 0,088 0,111 0,138 80,00% 20,00% 10,80% 0,060 0,094 0,111 0,132 90,00% 10,00% 10,40% 0,090 0,105 0,114 0,126 100,00% 0,00% 10,00% 0,120 0,120 0,120 0,120 =((A15^2*\$C\$6^2)+(B15^2*\$C\$7^2)+(2*A15*B15*\$D\$7*\$C\$6*\$C\$7))^0,5 =((A15^2*\$C\$6^2)+(B15^2*\$C\$8^2)+(2*A15*B15*\$D\$8*\$C\$6*\$C\$8))^0,5