Exam 8: Confirmation and Overconfidence

An overconfident individual may perceive an asset to be less risky than it really is because they under-estimate the variance of the return on the asset, but correctly estimate the mean of the return.

I believe that there is an $80 \%$ chance that I will get the promotion. The day before my supervisor tells me that he has "valuable" information about the chance that I get promoted. He tells me that there is an $80 \%$ chance that I will get the promotion. What type of forecast is this to me?

Overconfidence in one's own knowledge is a type of self-serving bias.

An individual who displays a confirmation bias in the type of information they seek is said to display "hypothesis-based filtering."

Which of the following statements is an example of optimistic overconfidence?

Under the hypothesis filtering model, my beliefs about the state will always be further from the "truth" than if I did not exhibit a confirmation bias.

Confirmation bias is counter to the idea of conservatism.

Suppose an asset has a risky return given by $x \sim N\left(\mu, \sigma^{2}\right)$ . Gus believes the return on the asset is given by $\hat{x} \sim N\left(\mu, \hat{\sigma}^{2}\right)$ , where $\hat{\sigma}>\sigma$ . Lulu believes the return on the asset is given by $x \sim N\left(\mu, \sigma^{2}\right)$ . Gus and Lulu have the same risk averse preferences. Which of the following is true?

The confirmation bias concerns the type of information an individual seeks and the way an individual interprets that information.

I believe that there is an $80 \%$ chance that I will get the promotion. The day before my supervisor tells me that he has "valuable" information about the chance that I get promoted. He tells me that there is an $80 \%$ chance that I will get the promotion. My supervisor's forecast was valuable because it contained new information.

An individual is said to be overconfident if

One stylized fact about overconfidence is that people tend to be more overconfident when facing easy questions and under-confident when facing difficult questions.

Suppose an asset has a risky return given by $x \sim N\left(\mu, \sigma^{2}\right)$ . Yi-Yi believes the return on the asset is given by $\hat{x} \sim N\left(\hat{\mu}, \sigma^{2}\right)$ , where $\hat{\mu}>\mu$ . Kyle believes the return on the asset is given by $x \sim N\left(\mu, \sigma^{2}\right)$ . Kyle and Yi-Yi have the same risk averse preferences. Which of the following is true?

There are four cards on the table each labeled with one of the following words: swan, white, black, bat. On one side of a card is a color on the other side is an animal. Consider the following statement: if there is a swan on any one side of the card, then there is white written on the other side. a. Which card provides confirmatory information? b. Which card provides disconfirmatory information?

I believe there is a $60 \%$ chance that toilet paper is going on sale tomorrow for $\$ .75$ per roll and a $40 \%$ chance that it will not and cost $\$ 2$ per roll. Unfortunately, I have to place an order today. I have $\$ 10$ to spend on toilet paper. a. Given my beliefs, how many rolls do I order? b. If I receive insider information from the store that toilet paper will definitely be on sale, how many rolls do I order? (Suppose you can order fractions of a roll.) c. If I receive insider information from the story that toilet paper will definitely not be on sale, how many rolls do I order?

Self-serving biases always cause individuals to make sub-optimal decisions.

Sally is asked 10 questions and is told to give her answer in intervals such that $15 \%$ of the time the correct answer fell above the interval and $15 \%$ of the time the answer fell below the interval. The experimenter concludes that Sally is overconfident. For how many questions did the true answer fall within Sally's given intervals?

Consider the statement "if it is a swan, then it is white." The contra-positive of this statement is "if white, then it is a swan."

There are four cards on the table each labeled with one of the following words: swan, white, black, bat. On one side of a card is a color on the other side is an animal. Consider the following statement: if there is a swan on any one side of the card, then there is white written on the other side. Which card would an individual with a confirmation bias turn over?

Sally is asked 10 questions and is told to give her answer in intervals such that $5 \%$ of the time the correct answer fell above the interval and $5 \%$ of the time the answer fell below the interval. The experimenter concludes that Sally is calibrated. For how many questions did the true answer fall within Sally's given intervals?