A stock will have a loss of 11.5% in a bad economy, a return of 11.3% in a normal economy, and a return of 31% in a hot economy. There is a 29% probability of a bad economy, a 32% probability of a normal economy and a 39% probability of a hot economy. What is the variance of the stock's returns

Variance = 0.030096 or 3.0096% rounded off to 3.01%

Explanation:

To calculate the variance of the stock's returns, we first need to calculate the expected return on the stock. The expected return on the stock can be calculated by multiplying the stock return in each scenario by the probability of that scenario and taking a sum of the answers for each scenario.

Expected return of stock rE=  pA * rA  +  pB * rB  + ... + pN * rN

Where,

Expected return of stock rE = 0.29 * -0.115  +  0.32 * 0.113  +  0.39 * 0.31

Expected return of stock rE = 0.12371 or 12.371%

Variance = ∑ p * (r - rE)²

Variance = 0.29 * (-0.115 - 0.12371)^2  +  0.32 * (0.113 - 0.12371)^2  +  

0.39 * (0.31 - 0.12371)^2

Variance = 0.030096 or 3.0096% rounded off to 3.01%

cognitive overload: having a lot on your mind impairs decision-making and tends to result in the simplest, but not necessarily best, option being selected.

empathy gaps: overlooking how you might feel in a different situation can result in unnecessary purchases, such as overbuying when shopping for food on an empty stomach.

optimism and overconfidence: wearing rose-tinted glasses and having unrealistic expectations about the future can affect money management and leave you unprepared for a change in circumstance.

instant gratification: seeking instant gratification drives impulsive spending and can undermine long-term planning and savings.

harmful habits: automatic or mindless behaviour can amplify a poor financial decision as it becomes a recurring event.

social norms: we are heavily influenced by the actions of others; while this can be in certain circumstances, it also contributes to the pressure to keep up with the joneses through conspicuous consumption.