Question

5. Real options Antonio and Caroline are going to a Halloween party and are debating whether they should dress up in costumes or wear regular clothing. If other people wear regular clothes and they wear regular clothing as well, they will get a utility of 15. Alternatively, if they dress up in costumes and other people wear costumes, they will also get a utility of 15 from being dressed up along with everyone else. However, they don't want to be embarrassed by being the only ones in costumes, or the only ones not wearing costumes, so if they are dressed differently than other guests they will get a utility of -5. The numbers in the following table reflect the utility Antonio and Caroline get under each of the described outcomes. What Other People Wear Regular Clothing Costumes Options (1) Wear costume (2) Wear regular clothing 15 , and the If the probability that other people wear regular clothes is 50%, then the expected value of utility from wearing costumes is expected value of utility from wearing regular clothing is Now, suppose Antonio and Caroline consider a third option: wear costumes that can easily be converted into normal clothes. If Antonio and Caroline can choose to dress up in costumes, knowing they have the option to convert to normal clothes, they now will get a utility of 15, regardless of whether others are in regular clothing (and they convert their costumes) or in costume (and, thus, they remain in costume as well). therefore, the value of the real The value of utility from wearing costumes (with the option to convert to wearing normal clothes) is option is Suppose, instead, that if they are the only ones dressed up, it won't actually bother them much. That is, they will get a utility of 5 (rather than-5) if other people wear regular clothes and they are wearing costumes they can't convert. This the variability of their outcomes and, thus, the value of the real option to convert to normal clothes. Grade It Now Save & Continue

Answer 1

a) The expected of utility if there are two (or more) uncertain outcomes is given by:

E[u(x)] = p₁u(x₁) + p₂u(x₂)

case a) Let us calculate expected utility from wearing costumes

Here, u(x₁) = utility from wearing costumes if other people wear regular clothing = -5

u(x₂) = utility from wearing costumes if other people wear costumes = 15

p₁ = probability that other people wear regular clothing = 50% = 0.5

p₂ = probability that other people wear costumes = 1-0.5 = 0.5

$\therefore$ E[u(x)] = -5 X 0.5 + 15 X 0.5 = 5

case b) Expected utility from wearing regular clothing

Here, u(x₁) = utility from wearing regular clothing if other people wear regular clothing = 15

u(x₂) = utility from wearing regular clothing if other people wear costumes = -5

p₁ = probability that other people wear regular clothing = 50% = 0.5

p₂ = probability that other people wear costumes = 1-0.5 = 0.5

$\therefore$ E[u(x)] = 15 X 0.5 + (- 5 X 0.5) = 5

Therefore, expected utility from wearing costumes is 5 and the expected utility from wearing regular clothing is 5

b) If they wear costumes which could be converted to normal clothes, there is only 1 probability, that is getting utility of 15.

Value of real option is expected utility from the chosen option. In this option, value of real option will be 15 because there is no other probability.

c) Variability of outcomes is variability of possible outcomes around the expected value, or mean. Operationally, it is defined as the square root of the weighted average squared deviations of possible outcomes from the expected value. Therefore, if the value of outcomes are closely packed around the mean, variability of outcomes will decrease.

In this case, the minimum utility is 5, the maximum utility is 15 and the expected utility is 10.

The mean of possible outcomes is 5+10+15/3 =10 Therefore, the variability of their outcomes is:

52 + 02 +52/3 = 2.357

In the second case i.e. wearing convertible costumes, there is only one outcome. Therefore, variability of their outcomes has increased .

Therefore, this increases the variability of their outcomes and thus decreases the value of the real option to convert to normal clothes.