Question1.14 According to prospect theory, investors are:Select one alternative: Risk seekers with regard to losses and risk averse with regard to gains. Risk neutral with regard to gains and risk seekers with regard to losses. Risk neutral with regard to gains and risk averse with regard to losses. None of the options is correct. Risk seekers with regards to gains and risk averse with regard to losses. ResetMaximum marks: 2.5 Flag question undefined

Question

BlackTom AI · Accepted Answer

Prospect theory models a value function that is concave for gains and convex for losses and steeper for losses than for gains. This shape implies diminishing sensitivity and loss aversion: investors become risk averse when considering gains (concavity) and risk seeking when facing losses (convexity).

Relevant knowledge points:
- Reference dependence: outcomes evaluated relative to a reference point (not final wealth).
- Diminishing sensitivity: marginal value decreases with magnitude (concave for gains, convex for losses).
- Loss aversion: losses hurt more than equal-sized gains (value function is steeper for losses).

Step-by-step reasoning with a simple numerical illustration:
1. Use a typical prospect-theory value function: v(x) = x^0.5 for gains, v(x) = −λ(−x)^0.5 for losses, with λ > 1 (loss aversion). Let λ = 1.5.
2. Gains example: Choose between a sure gain of $50 and a 50% chance to gain $100 (otherwise $0).
   - Expected value of gamble = 0.5*100 = $50 (same as sure gain).
   - Prospect utility of sure gain: v(50) = 50^0.5 = 7.07.
   - Prospect utility of gamble: 0.5*v(100) + 0.5*v(0) = 0.5*10 + 0 = 5.0.
   - Since 7.07 > 5.0, investor prefers the sure gain → risk averse for gains.
3. Losses example: Choose between a sure loss of $50 and a 50% chance to lose $100 (otherwise $0).
   - Prospect utility of sure loss: v(−50) = −1.5*(50^0.5) = −1.5*7.07 = −10.61.
   - Prospect utility of gamble: 0.5*v(−100) + 0.5*v(0) = 0.5*(−1.5*10) + 0 = −7.5.
   - Since −7.5 > −10.61, investor prefers the gamble → risk seeking for losses.

Why the correct answer is correct:
- The concave value for gains yields risk aversion; the convex value for losses yields risk seeking. Empirical experiments (Kahneman and Tversky) support this pattern.

Why the other options are incorrect:
- “Risk neutral with regard to gains” (options 2 and 3) contradicts observed concavity for gains.
- “Risk averse with regard to losses” (option 3 and 5 reversed) contradicts the convex loss region.
- “Risk seekers with regards to gains” (option 5) is the opposite of prospect-theory predictions.
- “None of the options” is wrong because the first option matches prospect theory.

Conclusion: Investors are risk seekers with regard to losses and risk averse with regard to gains, which matches the provided correct answer.

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