Question

the correlation coefficient between a security and the market portfolio is 0.7 the standard deviation of the security is 39% while the market porftolio has a standard deviation of 15% the beta of the security is closest to:

Answer 1

The beta of the security, given a correlation coefficient with the market portfolio of 0.7 and standard deviations of 39% for the security and 15% for the market, is closest to 1.82.

Step-by-step explanation:

The question asks to calculate the beta of a security given its correlation coefficient with the market portfolio, its own standard deviation, and the standard deviation of the market portfolio. The standard formula to calculate beta (β) is:

Beta (β) = Correlation(security, market) × (Standard Deviation of the security / Standard Deviation of the market)

Using the given figures:

• Correlation coefficient = 0.7
• Standard deviation of the security = 39%
• Standard deviation of the market portfolio = 15%

Plugging these values into the formula gives us:

Beta (β) = 0.7 × (0.39 / 0.15) = 0.7 × 2.6 = 1.82

Therefore, the beta of the security is closest to 1.82.