What is the beta of the Hawkeyes Furniture store HF Standard

What is the beta of the Hawkeye\'s Furniture store (HF)?

Standard deviation of HF = 12. Correlatioin (rho) between HF and the S&P 500 = 0.8. Covariance between HF and the S&P 500 = 150.

Solution

correlation = covariance / SD_HF * SD_SP

0.8= 150/12*SD_SP

SD_sp= 150 / 0.8*12

SD_sp= 15.625

Thus beta of HF

Therefore beta = r * SD_HF/ SD_SP

   ₌ 0.8*12/15.625

=0.6144