The correlation coefficient for a series of returns on two investments is equal to 0.80. Their covariance of returns is 0.06974 . Which of the following are possible variances for the returns on the two investments? A) 0.04 and 0.19. B) 0.02 and 0.44. C) 0.08 and 0.37.
correlation * std1 * std2 = cov take sqrt(0.04)*sqrt(0.19) * 0.8 -> gives you 0.06974
but how did you get to a conclusion that std1=.04 and std2=.19,Kindly explain
they gave you variances. in the answer choices which is stddev^2. it was a plug and chug problem… they gave you covariance, correlation and choices for the variances.
Correlation is simply given as: Cov/S.D Therefore, the SD of the returns of the 2 investments is: Cov/Correlation Coeff. which is 0.06974/0.8 = 0.08718. The Variance of both investments becomes: 0.08718^2 = 0.00760. Multiplying the variances given in option A gives 0.00760, that is 0.04*0.19.