Risk Aversion: Deal or No Deal? Outline ¨ Risk Attitude and Expected Return ¨ Game: Deal or No Deal? Risk Attitude and Expected Return ¨ In each pair, please choose an asset out of the two options. ¨ A: Option 1: 50%: 100; 50%: 50 vs. Option 2: 100%: 60 ¨ B: Option 1: 50%: 100; 50%: 50 vs. Option 2: 100%: 70 ¨ C: Option 1: 50%: 100; 50%: 50 vs. Option 2: 100%: 75 ¨ D: Option 1: 50%: 100; 50%: 50 vs. Option 2: 100%: 80 ¨ E: Option 1: 50%: 100; 50%: 50 vs. Option 2: 100%: 90 Risk Attitude and Expected Return ¨ Expected value n Expected Value = ∑Pi ⋅ X i i=1 Risk Attitude and Expected Return ¨ Risk Aversion: a dislike of uncertainty 1. If your choice is (2,2,2,2,2), (1,2,2,2,2), (1,1,2,2,2), you are risk-averse. 2. If your choice is (1,1,1,1,1), (2,2,2,2,1) or (2,2,2,1,1), you are risk-loving. 3. If your choice is (1,1,1or2,2,2), you are risk-neutral. Indifferent Game: Deal or No Deal ¨ I am sure most of you have heard about the TV show – Deal or No Deal. If you haven’t, the youtube videos below give you an idea of how this game is played: ¨ Deal or No Deal (http://www.youtube.com/watch?v=hmZFHjQfx-o&feature=related) ¨ First 1 million winner (http://www.youtube.com/watch?v=gg7vtTCAkbY&feature=related) Game: Deal or No Deal ¨ We are going to play a simplified version of the game. ¨ First, I need two volunteers to play this game: 1 player and 1 banker. You will earn (or lose) credits. ¨ Player’s payoff = offer – 20 points Banker’s payoff = 50 points – offer Game: Deal or No Deal ¨ There are only 7 possible outcomes. (I choose 7 students sitting in the back of the classroom to play “models” who hold a piece of paper in their hands with the blank side facing the player) 1 5 10 20 50 75 100 Game: Deal or No Deal ¨ (Here is an example of how the game might go. I will use this example as an illustration) ¨ Suppose the first outcome drawn by the player is 20. The banker’s offer is 38. The player chooses “No Deal” ¨ Then, the player chooses another one, say 10. The banker’s offer is 30. The player chooses “No Deal.” ¨ The game continues… Game: Deal or No Deal ¨ How to be a savvy BANKER? You can estimate players’ degree of risk-aversion from his past choices. How? 1. After the first draw (20), the expected payoff became 40.2. The offer was 38. The fact that the player rejected this offer suggested that he was not very risk-averse. 2. So, after the second outcome was drawn (10), the expected payoff became 46.2. 3. If the banker’s goal is to deter the player from continuing, the banker should’ve given a better offer than 30. Why? We learned that the player was not very risk-averse from his first decision. Thus, the banker should have provided an offer much closer to the expected payoff, which is 46.2, so that the player would possibly have chosen to accept the offer. Game: Deal or No Deal ¨ Economists are interested in real-world games with large payoffs: 1. Deal or No Deal (Post et al., 2008, AER) 2. Card Sharks (Gertner, 1993, QJE) .