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Time and Uncertainty - chapter 11

11.1. Timing Matters

  • Money is worth more in the present than in the future because it can be immediately spent or invested in productive opportunities
  • The interest rate is the cost of borrowing money for a certain unit of time
    • It is usually expressed as a percentage per time period
  • The interest rate is the amount needed to compensate the lender for the opportunity cost of loaning out money
    • The amount of money the lender could have earned investing in something else if he or she weren’t lending it

11.2. Compounding

  • Compounding: the process of accumulation that results from the additional interest paid on previously earned interest
  • With compound interest, the amount of interest earned increases each period, since interest payments earned in the past themselves accumulate interest in future periods
  • Future value = Present value x (1 + r)^n

11.3. Present Value

  • present value: how much a certain amount of money that will be obtained in the future is worth today
    • Present value = (Future value) / (1 + r)^n
    • Translating cost or benefits that occur at different times into their present values gives you a common unit of value, allowing you to compare apples to apples

11.4. Expected Value

  • Risk: exists when the costs or benefits of an event or choice are uncertain
    • The possibility that things won’t turn out as you expect
  • expected value: the average of each possible outcome of a future event, weighted by its probability of occurring
    • Allows us to account for risk when comparing options

11.5. Propensity for Risk

  • People have varying degrees of willingness to take on risk
    • Risk-averse: having a low willingness to take on situations with risk
    • Risk-seeking: having a high willingness to take on situations with risk
  • People are generally risk-averse in the limited sense that when two choices have the same expected value, they will prefer the less-risky one
  • People generally would prefer to gain a smaller amount than to risk losing everything
  • The loss of utility caused by losing a large sum is greater than the benefit of gaining the same amount

11.6. The Market for Insurance

  • The tendency to choose the less risky option is explained by the concept of diminishing marginal utility
    • The loss of utility caused by losing a large sum is greater than the benefit of gaining the same amount
  • Insurance is a common strategy for managing risk
  • An insurance policy lets people pay to reduce uncertainty in some aspect of their lives
    • Such products usually involve paying a regular fee (premium) in return for an agreement that someone else will cover any unpredictable costs that arise
  • Insurance doesn’t reduce the risk of something bad happening
    • It guarantees that the cost of the event to the insured person will be low
  • Risk aversion makes a market for insurance profitable
  • People are willing to pay to shield themselves from the cost of bad things happening, above and beyond the actual expected cost of those things

11.7. Pooling and Diversifying Risk

  • risk pooling: organizing people into a group to collectively absorb the risk faced by each individual
    • Doesn’t decrease the risk that a bad event will occur, it only reduces the cost to a particular individual in the event that it does occur
  • Diversification: the process by which risks are shared across many different assets or people, reducing the impact of any particular risk on any one individual
    • The cost of failure for any one investment is not so great, and the chance of many different investments all failing together is small, so the risk of losing a large amount is reduced
    • Like pooling, diversification doesn’t change the likelihood that a bad event will occur, it only reduces the cost associated with a single event

11.8. Problems with Insurance

  • Adverse selection: a state that occurs when buyers and sellers have different information about the quality of a good or the riskiness of a situation; results in failure to complete transactions that would have been possible if both sides had the same information
    • If insurance companies were able to accurately identify risky clients, adverse selection would not be a problem, insurers would charge more for higher-risk clients
    • But clients often know much more about their relevant risk factors than the insurance company does
  • moral hazard: the tendency for people to behave in a riskier way or to renege on contracts when they do not face the full consequences of their actions