Expected Value Exercise 8
1. Consider a
lottery with three possible outcomes:
● $125 will be received with probability 0.2
● $100 will be received with probability 0.3
● $50 will be received with probability 0.5
a. What is the
expected value of the lottery?
b. What is the
variance of the outcomes?
c. What would a
risk-neutral person pay to play the lottery?
a. E(x)= 0.2(125) + 0.3(100) + 0.5 (50)
ReplyDelete25+30+25
=80
b. variance = 0.2[(125-80)square] + 0.3[(100-80)square] + 0.25 [(50-80)square]
=405 + 120 +450
=975
c. we have to find the standard deviation to know how big is the risk. take a root from variance 31.22. yes, he would. because there's a risk neutral indifferent between uncertain and certain payoffs with the same expected value.
3 possible outcomes from a lottery
ReplyDelete- 0.2 will received $125
- 0.3 will received $100
- 0.5 will received $50
a. Expected Value : (1st Pr)(1stprize) + (2nd Pr)(2ndprize)+(3rdPr)(3rdprize)
EV : (0.2)($125) + (0.3)($100) + (0.5)($50) = 25 + 30 + 25 = $80
so, it means from the probability of the lottery returns $80
b. the Variance or S2 (S square)
S2 : (0.2) ($125-80)2 + (0.3) ($100-80)2 + (0.5) ($50-80)2 = $975
the variance describing how far the numbers lie from the expected value which is $975
c. a risk-neutral person would buy the lottery, and naturally would pay the $80 because risk-neutral is being indiffirent(ignore) between certain and uncertain so no need to calculate the risk.
a. EV= (125x0.2)+(100x0.3)+(50x0.5)= 80
ReplyDeleteb. variance= 0.2(125-80)2+0.3(100-80)2+0.5(50-80)2=975
c. as we know that a risk neutral person is indifferent between certain income and uncertain income, so this person doesnt care about their income which related to their risk.
a. E(v)= 0.2(125)+0.3(100)+0.5(50)
ReplyDelete=$80
b. V= 0.2(125-80)2+0.3(100-80)2+0.5(50-80)2
=$975
c. a risk neutral person would pay the $80 as the expected value
a. E(v)= (0.2)(125)+(0.3)(100)+(0.5)(50)
ReplyDelete= 25 + 30 + 25
= 80
b. V = (0.2)(125-80)(2) + (0.3)(100-80)(2)+(0.5)(50-80)(2)
= 975
c. the risk neutral person is indifferent between certain income and an uncertain income. so this person will pay the lottery $80 as the result of expected value
ANSWER:
ReplyDeletea.
The expected value, EV, of the lottery is equal to the sum of the returns weighted by their probabilities:
EV = (0.2)($125) (0.3)($100) (0.5)($50) = $80.
b.
The variance is the sum of the squared deviations from the mean, $80, weighted by their probabilities:
Variance = (0.2)(125 80)2 (0.3)(100 80)2 (0.5)(50 80)2 = $975.
c.
A risk-neutral person would pay the expected value of the lottery: $80.