Chapter 15 Trade-offs Involving Time and Risk. Outline. Modeling Time and Risk. The Time Value of Money. Time Preferences. Probability and Risk

Transcription

1 Involving Modeling The Value Part VII: Equilibrium in the Macroeconomy 23. Employment and Unemployment 15. Involving Web 1. Financial Decision Making 24. Credit Markets 25. The Monetary System 1 / 36

2 Involving Modeling The Value Chapter 15 Involving and / 36

3 Involving Modeling The Value 1 Modeling 2 The Value 3 4 Probability 5 3 / 36

4 Involving Modeling The Value Q:Do people exhibit a preference for immediate gratification? 4 / 36

5 Involving Modeling The Value Interest is the payment received for temporarily giving up the use of money. Economists have developed tools to calculate the present value of payments received at different points in the future. Economists have developed tools to calculate the value of risky payments. 5 / 36

6 Involving Modeling The Value 15.1 Modeling and Most decisions have costs and benefits that occur at different times. For example: going to college. exercising, dieting, and saving. We need to understand how to predict and value the delayed benefits. means that some of the costs and benefits are not fixed in advance. 6 / 36

7 Involving Modeling The Value When economists value rewards that will be experienced in the future, we multiply the reward by a positive factor that is less than 1 to capture that future reward are worth less than current reward. When a reward might not occur, economists incorporate this risk by multiplying the reward by the positive probability (again, less than 1) that the reward will occur. 7 / 36

8 Involving Modeling The Value 15.2 The Value of Money Financial markets enable people to transfer money through time. To move money into the future, depositors lend money to a bank now and then withdraw it, with interest, at a future date. Economists call such a change an inter-temporal transformation. 8 / 36

9 Involving Modeling The Value Future Value and the Compounding of Interest Principal: The amount of an original investment Interest:The payment received for temporarily giving up the use of money (or paid for the opportunity to temporarily use someone else s money) Future value: The sum of principal and interest Compound interest formula: Future value = principal (1 + r) T where r is the interest rate, T is the the number of period in the future. 9 / 36

10 Involving Modeling The Value Exhibit 15.1 Value of $1 Investment over the Next 50 Years Compound growth can be very powerful. 10 / 36

11 Involving Modeling The Value Rule of 70 According to the rule of 70, if some variable grows at a rate of r percent per year, then that variable doubles in approximately 70 years. r (1 + r/100) T = 2 T ln(1 + r/100) = ln 2 ln 2 T = ln(1 + r/100) r/100 = r 11 / 36

12 Involving Borrowing Versus Lending Modeling The Value Exhibit 15.2 The Mechanics of Lending and Borrowing 12 / 36

13 Involving Modeling The Value With a deposit, you receive (1 + r) T (Principal amount) when you withdraw the money, with interest, in T years. With a loan, you pay (1 + r) T (Loan amount) when you pay back the loan, with interest, in T years. Typical interest rates on loans tend to be higher than typical interest rates paid on deposit. 13 / 36

14 Involving Modeling The Value Present Value and Discounting Present value of a future payment is the amount of money that would need to be invested today to produce that future payment. Economists say that the present value is the discounted value of a future payment. Present Value Equation Present value = Payment T periods from now (1 + r) T The future payment is discounted to calculate the present value. 14 / 36

15 Involving Modeling The Value Is Invest $10,000 today to get $20,000 in 20 years a good deal? For a 5% interest rate, present value of $20,000 is 20, 000 = $7, 538 ( ) 20 The net present value is the present value of benefits minus present value of costs. The net present value is $7, 538 $10, 000 = $2, 462. Therefore, Invest $10,000 today to get $20,000 in 20 years is not a good deal. 15 / 36

16 Involving Modeling The Value Is Invest $10,000 today to get $10,000 in 10 years and $10,000 5 years later a good deal? The net present value is $10, 000 $10, $10, 000 (1.05) 10 (1.05) 15 = $6, $4, 810 $10, 000 = $949. Therefore, this is a good deal. 16 / 36

17 Involving 15.3 Modeling The Value Suppose you were asked to choose between a 60-minute massage in a year or 50-minute massage right now. Which one would you take? Most people prefer shorter, earlier massage. People want pleasurable events to occur sooner rather than latter. The Marshmallow Test: 17 / 36

18 Involving Modeling The Value Discounting Utils: Individual measures of utility or happiness Discount weight: Multiplies future utils to translate them into current utils Suppose that an hour-long massage generates 60 utils and the discount weight for one year from now is 1 2. In this example, the 60 future utils have a discount value of: ( ) 1 (60 utils in a year) = 30 current utils / 36

19 Involving Modeling The Value What about starting a diet? Should you start a diet today or wait until tomorrow? Starting today: Benefit is become healthier more quickly. Cost is giving up food you enjoy earlier. Starting tomorrow: Benefit is you get to eat what you want for another day. Cost is delaying becoming healthier. Problem: The benefit of starting today is in the future, while its cost is immediate. The benefit of starting tomorrow is immediate, while the cost is in the future Result: Diets that always start tomorrow. 19 / 36

20 Involving Modeling The Value Discount weights enable us to compare delayed utils and immediate utils, helping us identifying the preferred option. The greater your discount weight in other words, more highly you weight things that happen in the future the more your current decisions are driven by the future consequences of those decisions. 20 / 36

21 Involving Modeling The Value Preference Reversals Suppose that you discount in the following special way. You place full weight on the present and half weight on all future days. Weight: 1 Today Tomorrow The Day After Tomorrow All of the future days are roughly alike. It is today that is special. This type of preference pattern is called present bias. 21 / 36

22 Involving Modeling The Value Suppose that you are considering whether or not to eat a ice cream. Assume that the ice cream offers immediate pleasures of 6 utils and delayed cost (e.g. reduced health of fitness) of 8 utils. You are happy to eat the ice cream today because the immediate benefit (6 utils) exceeds the discounted value of the delayed cost ( = 4). Suppose, however, that the ice cream store is unexpectedly closed today. Your friend asks you if you d like to come back tomorrow. What is your answer? From today s perspective, the value of eating ice cream tomorrow is: ( 1 2) 6 ( 1 2) 8 = 1. (Why?) You decide not to eat ice cream tomorrow. 22 / 36

23 Involving Modeling The Value You decided that you wanted to eat ice cream today. You also decided that you do not want to eat ice cream tomorrow. Once the sun rises tomorrow morning, it will once again be like today and you ll once again want to eat ice cream. This preference pattern is an example of a preference reversal. If you are always planning to stop eating ice cream tomorrow, when will your diet actually begin? 23 / 36

24 Involving Modeling The Value Q: Do people exhibit a preference for immediate gratification? 24 / 36

25 Involving Modeling The Value You have been approached by a market tester taking orders for free snacks. The list of options: apple, banana, potato chips, Mars bar, Snickers bar, or borrelnoten. Order the snack you want today and the market tester will return in a week to bring you whatever you choose. One week later, the market tester returns and tells you that you can choose whatever you want from the original list regardless what you previously ordered. Would you pick the same snack that you chose a week ago? 25 / 36

26 Involving Modeling The Value When Dutch workers were asked to order a snack one week in advance, 74% asked for a healthy snack: bananas or apples. When the researchers came back one week later, only 30% of the workers chose fruit for immediate consumption. One average, subjects exhibited a preference reversal. Ask ahead of time they ordered something healthy. But when the moment of truth arrived, many subjects switched their priorities and went for the salty snack of the candy. Other kinds of preference reversals. On Sunday night, students decide to get to the library early on Monday morning. Would-be exercisers pay for gym memberships with good intentions. 26 / 36

27 Chapter 15 Involving Modeling The Value 15.4 exists when outcomes are not known with certainty in advance. If something is risky, then it is said to have a component that is random. 27 / 36

28 Involving Modeling The Value Roulette Wheels and Probabilities In an American casino, a roulette wheel has 38 equal-sized pockets. There is a 1-in-38 chance that the ball will land in any particular pocket. For simplicity, imagine a hypothetical roulette wheel with 100 pockets, labeled from 1 to 100. What is the chance that you will win if the bet on the number 79? The answer is or 1%. A probability is the frequency with which something occurs. The probability that one of the N numbers comes up is just N / 36

29 Involving Modeling The Value Independence and the Gambler s Fallacy The outcome of one spin of the roulette wheel will not help you predict the outcome of the next spin. When two random outcomes are independent, knowing about one outcome does not help you predict the other outcome. Suppose that 64 comes up 3 times in a row, what is the probability that 64 will come up on the next spin? The likelihood of winning on the next spin for betting on 64 is always 1 in 100. No more, no less. 29 / 36

30 Involving Modeling The Value Some gamblers believe in streaks: if they got lucky on the last spin, they mistakenly believe that they have a higher chance of winning on the next spin. This is called the hot hand fallacy. Other gamblers believe that the wheel somehow tends to avoid repeats. This is called the gambler s fallacy. Remember that roulette wheels don t have memory. What happened on the last spin has no bearing on the next spin. 30 / 36

31 Involving Modeling The Value Expected Value Expected value is the sum of all possible outcomes or values, each weighted by its probability of occurring. What is the expected value of the following bet: If the ball ends up on the number 64 you win $100. If the ball ends up on the number 15 you lose $200. If the ball ends up on any other number, nothing happens. The answer is ($100) ( $200) + ($0) = $ / 36

32 Involving Modeling The Value Is Gambling Worthwhile? For the 100-pocket roulette wheel, if the wheel spins on any number from 1 through 47, you win x dollars. If the wheel spins on any number from 48 through 100, you lose x dollars. What is the expected winning playing this game (with bet x)? Expected Winning= ($x) ( $x)=-6% of $x. One average, you will lose 6 percent of the amount you bet. 32 / 36

33 Involving Modeling The Value Extended Warranties You buy a $300 TV with a 1-year warranty included. Should you buy an extended warranty for years 2 and 3 for another $75? There are two components involved: risk and present value. : assume that the probability of breakdown is 10% per year. Present value: if TV breaks in year 2, could replace it for $250 without a warranty, in year 3, could replace for $ / 36

34 Involving Modeling The Value Suppose the interest rate is 10%. The net present value of buying the extended warranty is $250 ( ) $200 ( ) 3 $75 = $ $15.03 $75 = $39.31 Extended warranties are a bad deal for most customers unless they are psychologically highly averse to the prospect of a broken TV and the financial cost of replacing it. 34 / 36

35 Involving Modeling The Value 15.5 Loss aversion is the idea that people psychologically weight a loss more heavily than they psychologically weight a gain. Researchers usually find that losses are weighted twice as heavily as gains. This degree of loss aversion implies that a person would be indifferent between 1. $0 for sure 2. $200 gain if heads or $100 loss if tails. With loss aversion, the psychological value of this coin toss is ($200) ( $100) = $0 35 / 36

36 Involving Modeling The Value Daniel Kahneman and Amos Tversky first showed that loss aversion is a common behavior. Their work led to a Nobel Prize that was awarded to Kanneman. Tversky died at a young age and the Nobel is not given posthumously. Three categories of risk preferences. Consider a person choosing between two investments with the same expected rate of return but one investment has a fixed return and the other investment has a risky return. averse people prefer the investment with fixed return. People are risk averse in most situations. seeking people prefer the investment with risky return. neutral people are indifferent. 36 / 36