Hi!!
Let me start defining the variables:
E(RA) = expected return on Stock A
E(RB) = expected return on Stock B
STDA = standard deviation of stock A
STDB = standard deviation of stock B
VarA = variance of stock A
VarB = variance of stock B
Cor(RA,RB) = correlation between RA and RB
Cov(RA,RB) = covariance between RA and RB
- Part a).
Since it is not stated we can consider the same probability for each
possible state of the economy, that is 1/3, then:
E(RA) = (1/3)*(0.063) + (1/3)*(0.105) + (1/3)*(0.156) =
= 0.1080 =
= 10.80%
So the expected return on Stock A is 10.80%.
E(RB) = (1/3)*(-0.037) + (1/3)*(0.064) + (1/3)*(0.253) =
= 0.0933 =
= 9.33%
The expected return on Stock B is 9.33%.
- Part b).
For definition and formulas of variance and standard deviation see
"Standard Deviation and Variance: Common Measures of Variability"
http://davidmlane.com/hyperstat/A16252.html
VarA = (1/3)*(0.063 - 0.108)^2 + (1/3)*(0.105 - 0.108)^2 +
+ (1/3)*(0.156 - 0.108)^2 =
= 0.001446
STDA = sqrt(0.001446) =
= 0.0380 =
= 3.80%
The standard deviation of returns of Stock A is 3.80%.
VarB = (1/3)*(-0.037 - 0.0933)^2 + (1/3)*(0.064 - 0.0933)^2 +
+ (1/3)*(0.253 - 0.0933)^2 =
= 0.014447
STDB = sqrt(0.014447) =
= 0.1202 =
= 12.02%
The standard deviation of returns of Stock B is 12.02%.
- Part c).
For formulas and definitions see "Covariance and correlation"
http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=mga.section.2685
or
"Statistical Review with formula of, and rules for the mean, variance,
covariance, correlation coefficient":
http://www.kaspercpa.com/statisticalreview.htm
Cov(RA,RB) = (1/3)*(0.063 - 0.108)*(-0.037 - 0.0933) +
+ (1/3)*(0.105 - 0.108)*(0.064 - 0.0933) +
+ (1/3)*(0.156 - 0.108)*(0.253 - 0.0933) =
= 0.004539
The covariance between the returns of the two stocks is 0.004539.
Cor(RA,RB) = Cov(RA,RB) / (STDA * STDB)
= 0.004539 / (0.0380 * 0.1202) =
= 0.9937
The correlation between the returns of the two stocks is 0.9937.
Search strategy:
variance formula
covariance correlation formula
I hope this helps you. Feel free to request foe a clarification if you need it.
Regards,
livioflores-ga |