Question

Assignment Chapters 5

1. If you invest $1,500 and you expect the following payoffs with correlating probability

$300.00 .3 $1500.00 .3 $1800.00. .3 $3500.00 .1

Calculate the the Expected value, Standard deviation, and Variance of each.

2. If you invest $1,500 and you expect the following payoffs with correlating probability

$600.00 .1 $1500.00 .5 $1800.00. .2 $2500.00 .2

Calculate the the Expected value, Standard deviation, and Variance of each. Which investment would you choose? Which one is riskier?

Answer 1

1. Let X be the payoff from investing $1500 in investment 1

The payoff table is

x	P(x)
300	0.3
1500	0.3
1800	0.3
3500	0.1

The expected value of X is

The expected value of is

The variance of X is

The standard deviation of X is

ans:

• The expected value is $1,430.00
• The variance is  854,100.00
• The standard deviation is $924.1753

2. Let Y be the payoff from investing $1500 in investment 2

The payoff table is

y	P(y)
600	0.1
1500	0.5
1800	0.2
2500	0.2

The expected value of Y is

The expected value of is

The variance of Y is

the standard deviation of Y is

ans:

• The expected value is $1,670.00
• The variance is   270,100.00  
• The standard deviation is $519.7115

The expected value pf payoff from investment 2 is higher than from 1.

ans: We will choose investment 2 as it has a higher expected value of payoff

The standard deviation of the payoff from investment 1 is higher than investment 2 and hence it is riskier.

ans: Investment 1 is riskier as it has a higher standard deviation of payoff.