Question5 Suppose a stock that was originally bought at [math]45. Investor believes that next period, stock could go to [math]50 with equal chances. According to Prospect Theory, the agent is going to: Sell the stock The prediction depends on the extent to which the agent is assumed to distort the probabilities Hold on to it ResetMaximum marks: 1 Flag question undefined单项选择题
A
Sell the stock
B
The prediction depends on the extent to which the agent is assumed to distort the probabilities
C
Hold on to it

Question

Question5 Suppose a stock that was originally bought at [math]45. Investor believes that next period, stock could go to [math]50 with equal chances. According to Prospect Theory, the agent is going to: Sell the stock The prediction depends on the extent to which the agent is assumed to distort the probabilities Hold on to it ResetMaximum marks: 1 Flag question undefined单项选择题

A

Sell the stock

B

The prediction depends on the extent to which the agent is assumed to distort the probabilities

C

Hold on to it

BlackTom AI · Accepted Answer

Prospect theory’s two key ingredients are a reference-dependent value function v(·) that is concave for gains, convex for losses and steeper for losses (loss aversion λ>1), and a probability weighting function that transforms objective probabilities into decision weights w(·). These determine whether the investor prefers to sell now (realize a reference outcome) or keep the risky prospect.

Step-by-step reasoning and algebra:
1. Set the reference point at the current (purchase) price, so a sale now yields zero gain: v(0)=0.
2. Suppose the next period outcomes are +5 (to 50) with objective probability 0.5 and −5 (to 40) with probability 0.5. Prospect value of holding = decision weight on gain × value of gain + decision weight on loss × value of loss:
   U_hold = w^+(0.5)·v(+5) + w^-(0.5)·v(−5).
3. Use loss aversion parameter λ so v(−5) = −λ v(+5). Let v(+5)=g>0. Then:
   U_hold = w^+(0.5)·g − w^-(0.5)·λ g = g [w^+(0.5) − λ w^-(0.5)].
4. Selling immediately yields U_sell = v(0) = 0. The investor prefers to hold if U_hold > 0, i.e. if w^+(0.5) > λ w^-(0.5); prefers to sell if the inequality reverses; is indifferent when equality holds.

Why the answer depends on probability distortion:
- If the weighting function makes the gain relatively overweighted (w^+ large) compared with the loss weight times λ, holding is preferred.
- If loss weight times λ dominates, selling (realizing zero) is preferred.
- Thus the decision is not categorically “sell” or “hold” but hinges on the extent and asymmetry of probability weighting and the degree of loss aversion.

Why the other choices are incorrect:
- “Sell the stock” is only correct in the parameter region where λ·w^-(0.5) > w^+(0.5).
- “Hold on to it” is only correct where w^+(0.5) > λ·w^-(0.5).
Because prospect-theory predictions change with the weighting/loss-aversion parameters, the correct statement is that the prediction depends on how the agent distorts probabilities.