Expected Return unit of measurement?

[fofx]

Can anyone spot where I'm going wrong here? The only slightly confusing (but not incorrect) thing I have done, is when calculating Expected Return I convert 4% to 0.04. However when calculating Variance and Standard Deviation, I keep it as 4% to stop the numbers from getting too small.

[color=red]Expected Return for Company A[/color]
[b]Probability * Return[/b]
Very weak: 0.1 * -0.04 = -0.004
Weak: 0.2 * -0.01 = -0.002
Steady weak: 0.25 * 0 = 0
Steady strong: 0.2 * 0.01 = 0.002
Strong: 0.15 * 0.04 = 0.006
Very strong: 0.1 * 1 = 0.1

Sum: 0.102
[B]Expected Return 10.2%[/B]

[color=red]Expected Return for Company B[/color]
[b]Probability * Return[/b]
Very weak: 0.1 * -0.02 = -0.002
Weak: 0.2 * -0.015 = -0.003
Steady weak: 0.25 * -0.01 = -0.0025
Steady strong: 0.2 * 0.1 = 0.02
Strong: 0.15 * 0.4 = 0.06
Very strong: 0.1 * 0.45 = 0.045

Sum: 0.1175
[B]Expected Return 11.75%[/B]

Variance for Company A
I have kept everything as a percentage so the numbers don't get too small:

[b](Return - Expected Return)^2 * Probability[/b]
(-4 - 10.2)^2 * 0.1 = 20.164
(-1 - 10.2)^2 * 0.2 = 25.088
(0 - 10.2)^2 * 0.25 = 26.01
(1 - 10.2)^2 * 0.2 = 16.928
(4 - 10.2)^2 * 0.15 = 5.766
(100 - 10.2)^2 * 0.1 = 806.40400

Total: 20.164 + 25.088 + 26.01 + 16.928 + 5.766 + 806.40400
Total = 900.36
[B]Variance = 900.36[/B]
Standard Deviation = sqrt(900.36)
[B]Standard Deviation = 30.0059994%[/B]

Variance for Company B
I have kept everything as a percentage so the numbers don't get too small:

[b](Return - Expected Return)^2 * Probability[/b]
(-2 - 11.75)^2 * 0.1 = 18.90625
(-1.5 - 11.75)^2 * 0.2 = 35.1125
(-1 - 11.75)^2 * 0.25 = 40.640625
(10 - 11.75)^2 * 0.2 = 0.6125
(40 - 11.75)^2 * 0.15 = 119.709375
(45 - 11.75)^2 * 0.1 = 110.55625

Total: 18.90625 + 35.1125 + 40.640625 + 0.6125 + 119.709375 + 110.55625
Total = 325.5375
[B]Variance = 325.5375[/B]
Standard Deviation = sqrt(325.5375)
[B]Standard Deviation = 18.0426578%[/B]

[COLOR="Green"]CoVariance[/COLOR]

[COLOR="Red"]// Difference for Company A[/COLOR]
(-4 - 10.2) = (-14.2)
(-1 - 10.2) = (-11.2)
(0 - 10.2) = (-10.2)
(1 - 10.2) = (-9.2)
(4 - 10.2) = (-6.2)
(100 - 10.2) = (89.8)

[COLOR="Red"]// Difference for Company B[/COLOR]
(-2) - 11.75 = -13.75
(-1.5) - 11.75 = -13.25
(-1) - 11.75 = -12.75
10 - 11.75 = -1.75
40 - 11.75 = 28.25
45 - 11.75 = 33.25

[COLOR="Blue"]// Product of differences[/COLOR]
(-14.2)*(-13.75) = 195.25
(-11.2)*(-13.25) = 148.4
(-10.2)*(-12.75) = 130.05
(-9.2)*(-1.75) = 16.1
(-6.2)*(28.25) = -175.15
(89.8)*(33.25) = 2985.85

Sum: 195.25 + 148.4 + 130.05 + 16.1 + (-175.15) + 2985.85 = 3300.5

Average = 3300.5/6
Average = 550.083333
Covariance = 550.083333

[COLOR="DarkOrchid"]// Correlation[/COLOR]
550.083333 / (std_deviation_for_A * std_deviation_for_B)

550.083333 / (18.0426578 * 30.0059994) = 1.01606122

[COLOR="DarkOrchid"]// This number is still over 1 and should be between -1 and 1.
// Where am I going wrong?[/COLOR]

 

[Joey25]

You have to weight the products of differences by the probabilities, not the average.

e.g. 0.1*(-14.2)*(-13.75) for the first line

 

[fofx]

You have to weight the products of differences by the probabilities, not the average.

e.g. 0.1*(-14.2)*(-13.75) for the first line

Ty. I did this as follows:

[COLOR="Red"]// Product of difference[/COLOR]
(-14.2)*(-13.75) = 195.25
(-11.2)*(-13.25) = 148.4
(-10.2)*(-12.75) = 130.05
(-9.2)*(-1.75) = 16.1
(-6.2)*(28.25) = -175.15
(89.8)*(33.25) = 2985.85

[COLOR="red"]// Apply probability[/COLOR]
195.25*0.1 = 19.52500
148.4*0.2 = 29.68
130.05*0.25 = 32.5125
16.1*0.2 = 3.22
-175.15*0.15 = -26.2725
 2985.85*0.1= 298.58500

[COLOR="red"]// Sum to find covariance[/COLOR]
19.52500+29.68+32.5125+3.22+(-26.2725)+298.58500 = 357.25

[COLOR="red"]// Find Correlation[/COLOR]
357.25/ (18.0426578 * 30.0059994) = 0.659877969

A number between -1 and 1! Ty!

 

[scose-no-doubt]

:clap:

 

[fofx]

Special thanks to Joey25 and scose-no-doubt.