Terms in this set (27)

Which of the investment plans in the previous example carries more risk?

To decide which plan carries more risk, we need to look at their variances. Let's begin by calculating the variance separately for each investment plan.

Option A:
x | P(X=x)
-$2000 | 0.2
-$575 | 0.1
$950 | 0.3
$1000 | 0.3
$4000 | 0.1

x P(X=x) | x^2 P(X=x)
-2000 0.2 = -400 | (-2000)^2 0.2=800,000
-575 0.1 = -57.5 | (-575)^2 0.1 = 33,062.5
905 0.3 = 285 | (950)^2 0.3 = 270,750
1000 0.3 = 300 | (1000)^2 0.3 = 300,000
4000 0.1 = 400 | (4000)^2 0.1 =1,600,000
=527.5 =3,003,812.5

Variance:
standard deviation sign^2 = sum sign [ xi^2 * P(X=xi) ] - Mu^2

=3,003,812.5 - (527.5)^2
=3,003,812.5 - 278,256.25
=2,725,556.25

Standard deviation:
standard deviation sign = square root of "sum sign [ xi^2 * P(X=x) ] - Mu^2"

= square root of 2,725,556.25
=$1650.93

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Option B:
x | P(X=x)
-$1000 | 0.1
-$690 | 0.2
-$100 | 0.2
$1500 | 0.3
$3000 | 0.2

x P(X=x) | x^2 P(X=x)
-1000 0.1 = -100 | (-1000)^2 0.1 =100,000
-690 0.2 = -138 | (-690)^2 0.2 = 95,220
-100 0.2 = -20 | (-100)^2 0.2 = 2000
1500 0.3 = 450 | (1500)^2 0.3 = 675,000
3000 0.2 = 600 | (3000)^2 0.2 =1,800,000
= 792 =2,672,220

Variance:
standard deviation sign^2 = sum sign [ xi^2 * P(X=xi) ] - Mu^2

=2,672,220 - (792)^2
=2,044,956

Standard deviation:
standard deviation sign = square root of "sum sign [ xi^2 * P(X=x) ] - Mu^2"

=square root of 2,044,956
=$1430.02

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Comparing the standard deviations, since Option A has a standard deviation of $1650.93, and option B has a standard deviation of $1430.02, we can see that not only does Option B have a higher expected value, but its profits vary slightly less than Option A. Therefore, we can conclude that Option B carries a lower amount of risk than Option A.
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