Question

Ana has reference-dependent preferences over money. Let her utility over money cmoney be given by: U = v(cmoney − rmoney) where v(x) = ( x if x ≥ 0, 2x if x < 0.

Let Ana start with no income, and a reference point of zero money. Every day, Ana has the option to invest in stocks. The stock price changes over the course of the day such that with 50% chance, Ana earns $100 and with 50% chance, Ana loses $60.

(a) Suppose Ana plans on checking her stock portfolio at the end of each day. She will experience gain/loss utility depending on whether the stock went up or down. What is her expected utility if she invests? What is her expected utility if she does not invest? Will Ana invest in stocks?

(b) Suppose Ana plans on checking her stock portfolio every two days instead. At the end of two days, what are the possible money outcomes that Ana can end up with? What is the likelihood of each?

(c) If she checks her stock portfolio every two days, what is her expected utility if she invests? What is her expected utility if she does not invest? Will Ana invest in stocks?

(d) Explain why financial advisors give advice saying to check stock balance every once in a while.

(e) Now suppose Ana starts with -$40, and a reference point of zero money. Ana plans to checks her stock portfolio at the end of that day. What is her expected utility if she invests? What is her expected utility if she does not invest? Will Ana invest in stocks?

(f) Explain the intuition as to why your answer here differs from part (a).

Answer 1

Elu (expected ulty) since V(x) = X for x 4x100 + = o x 2.x (-60) & v(a) = 2x for xxo I Here 100 so. - 60co SO - 60 3 -10 there's no money. (2) if doesn't invest = since initially utility = 0 No, And will not invest in stocke. E(K) = 2 2 x 1 xlov xico + + x1, xfbo) x400) 2 2 2 100 X(-60) + + L x x (-60) (-60) gain in dayt + loss in day 2] it can be explained = gain in both + (first day loss gain in second] + [lost on both days = -1500 + 2500 - 15oot goo = 400 possible outcomes Expected wtility as cateulated in above part = 4004 Yes, she'll invest in stocks. one the more number days takes to invest , lesser will be the probability of making losses (though the amount she'll lose will increase but there's a fair chance of earning). Porat is you'll also lose the probability of making money (more sum of money). so it's better to check your stock once in a while so that you can adjust your investments in accordance with the respactive probabilities.