bài giảng kinh tế vi mô tiếng anh ch17 uncertainty

1 Chapter 17 Uncertainty Main topics 1. degree of risk 2. decision making under uncertainty 3. avoiding risk 4. investing under uncertainty Degree of risk • probability: number, 4, between 0 and 1 that indicates likelihood a particular outcome occur • frequency: estimate of probability, 4 = n/N, where n is number of times a particular outcome occurred during N number of times event occurred • if we don’t have frequency, may use subjective probability – informed guess Probability distribution • relates probability of occurrence to each possible outcome • first of two following examples is less certain Probability, % 20 10 40 Days of rain per month 01234 10% 20% 10% 30 (a) Less Certain 20% 40% Figure 17.1 Probability Distribution Probability, % 20 10 40 Days of rain per month 01234 30% 40% 30% Probability distribution 30 (b) More Certain Expected value example • 2 possible outcomes: rains, does not rain • probabilities are ½ for each outcome • promoter’s profit is • $15 with no rain • -$5 with rain • promoter’s expected value (“average”) EV = [Pr(no rain)GValue(no rain)]+[Pr(rain)GValue (rain)] = [ ½ G $15] + [ ½ G (-$5)] = $5 2 Variance and standard deviation • variance: measure of risk • variance = [Pr(no rain) G (Value(no rain - EV) 2 ] + [Pr(rain) G (Value (rain) – EV) 2 ] = [½ G ($15 - $5) 2 ] + [½ G (-$5 - $5) 2 ] = [½ G ($10) 2 ] + [½ G (-$10) 2 ] = $100 • standard deviation = square root of variance Decision making under uncertainty • a rational person might maximize expected utility: probability-weighted average of utility from each possible outcome • promoter’s expected utility from an indoor concert is EU = [Pr(no rain) G U(Value(no rain))] + [Pr(rain) G U(Value(rain))] = [½ G U($15)] + [½ G U(-$5)] • promoter’s utility increases with wealth Fair bet • wager with an expected value of zero • flip a coin for a dollar: [½ G (1)] + [½ G (-1)] = 0 Attitudes toward risk • someone who is risk averse is unwilling to make a fair bet • someone who is risk neutral is indifferent about making a fair bet • someone who is risk preferring wants to make a fair bet Risk aversion • most people are risk averse: dislike risk • their utility function is concave to wealth axis: utility rises with wealth but at a diminishing rate • they choose the less risky choice if both choices have the same expected value • they choose a riskier option only if its expected value is sufficiently higher than a riskless one • risk premium: amount that a risk-averse person would pay to avoid taking a risk 3 Figure 17.2 Risk Aversion Utility, U Wealth, $10 26 40 64 70 a b d e U (W ealth) U ($70) = 140 0.1U ($10) + 0.9U ($70) = 133 U ($26) = 105 U ($40) = 120 U($10) = 70 0 Risk premium 0.5U ($10) + 0.5U($70) = c f Risk averse decision • Irma’s initial wealth is $40 • her choice • she can do nothing: U($40) = 120 • she may buy a risky Ming vase Expected value of Ming Vase • worth $10 or $70 with equal probabilities • expected value (point d): $40 = [½ G $10] + [½ G $70] • expected utility (point b): 105 = [½ G U($10)] + [½ G U($70)] Irma’s risk premium • amount Irma would pay to avoid this risk • certain utility from wealth of $26 is U($26) = 105 • Irma is indifferent between • having the vase • having $26 with certainty • thus, Irma’s risk premium is $14 = $40 - $26 to avoid bearing risk from buying the vase Figure 17.3a Risk Neutrality Utility, U Wealth, $10 40 70 a b U (Wealth) (a) Risk-Neutral Individual U ($70) = 140 U ($10) = 70 0 U ($40) = 105 0.5U($70) = 0.5U ($10) + c Risk-neutral person’s decision • risk-neutral person chooses option with highest expected value, because maximizing expected value maximizes utility • utility is linear in wealth 105 = [½ G U($10)] + [½ G U($70)] = [½ G 70] + [½ G 140] • expected utility = utility with certain wealth of $40 (point b) 4 Figure 17.3b Risk Preference Utility, U Wealth, $10 40 58 70 a b d e c U (Wealth) (b) Risk-Preferring Individual U ($70) = 140 U ($40) = 82 U ($10) = 70 0 0.5U ($70) = 105 0.5U ($10) + Risk-preferring person’s decision • utility rises with wealth • expected utility from buying vase, 105 at b, is higher than her certain utility if she does not vase, 82 at d • a risk-preferring person is willing to pay for the right to make a fair bet (negative risk premium) • Irma’s expected utility from buying vase is same as utility from a certain wealth of $58, so she’d pay $18 for right to “gamble” Risky jobs • some occupations have more hazards than do others • in 1995, deaths per 100,000 workers was • 5 across all industries • 20 for agriculture (35 in crop production) • 25 for mining Risk of workplace homicides per 100,000 workers 1.3Fire fighter 1.5Butcher-meatcutter 2.3Bartender 5.9Gas station worker 6.1Police, detective 10.7Sheriff-bailiff 22.7Taxicab driver RateOccupation Risky jobs have small premium • Kip Viscusi found workers received a risk premium (extra annual earnings) for job hazards of $400 on average in 1969 • amount was relatively low because annual risks incurred by workers were relatively small • in a moderately risky job, • danger of dying was about 1 in 10,000 • risk of a nonfatal injury was about 1 in 100 Value of life • given these probabilities, estimated average job-hazard premium implies that workers placed a value on their lives of about $1 million • and an implicit value on nonfatal injuries of $10,000 5 Gambling Why would a risk-averse person gamble where the bet is unfair? • enjoys the game • makes a mistake: can’t calculate odds correctly • has Friedman-Savage utility Application Gambling Utility, U WealthW 1 W 2 W 3 W 4 W 5 a b b* d * c d e U (Wealth) Avoiding risk • just say no: don’t participate in optional risky activities • obtain information •diversify • risk pooling • diversification can eliminate risk if two events are perfectly negatively correlated Perfectly negatively correlated • 2 firms compete for government contract • each has an equal chance of winning • events are perfectly negatively correlated: one firm must win and the other must lose • winner will be worth $40 • loser will be worth $10 If buy 1 share of each for $40 • value of stock shares after contract is awarded is $50 with certainty • totally diversified: no variance; no risk If buy 2 shares of 1 firm for $40 • after contract is awarded, they’re worth $80 or $20 • expected value: $50 = (½ ´ $80) + (½ ´ $20) • variance: $900 = [½ ´ ($80 - $50) 2 ] + [½ ´ ($20 - $50) 2 ] • no diversification (same result if buy two stocks that are perfectly positively correlated) 6 If stocks values are uncorrelated • each firm has 50% chance of a government contract • whether a firm gets a contract doesn’t affect whether other wins one • expected value $50 = (¼ ´ $80) + (½ ´ $50) + (¼ ´ $20) • variance $450 = [¼ ´ ($80 - $50) 2 ] + [½ ´ ($50 - $50) 2 ] + [¼ ´ ($20 - $50) 2 ] • buying both results in some diversification Mutual funds • provide some diversification • Standard & Poor’s Composite Index of 500 Stocks (S&P 500) • Wilshire 5000 Index Portfolio (actually 7,200 stocks) S&P 500 Funds • you can get close to rate of return on S&P 500 by buying a stock fund that tries to duplicate that index • deviation is due to management fees (which are low) • 1996: • S&P 500 rose by 7.45% • Vanguard Index 500’s return was 7.37% • similar funds’ returns ranged between 7.19 and 7.27% International risks • if you invest in only U.S. stocks and bonds, you bear systematic risk associated with shifts in the U.S. economy • holding foreign funds helps diversify: U.S. returns are not perfectly correlated with foreign ones • however, foreign investments may actually increase your risk Exchange rate risk • a foreign investment may increase risk because of fluctuations in the exchange rate: how many dollars you must trade to obtain a unit of another country's currency • once, a Latin America fund lost 17% of its value in a month due to exchange rate shifts Default • lesser-developed countries may have high risks of default: failure of a borrower to repay money owed • U.S. investors were concerned about threat of default in Latin America in 1990s • only held Latin American bond funds that paid a large premium over safer U.S. Treasury bonds • at the peak of Latin American debt in March 1995, risk premium averaged 19 percentage points • as threat of default eased over the next year, the differential fell to about 6 percentage points 7 $10,000 certificates of deposit • in 1995, investing in whichever country had the highest rate of return on its CDs produced the largest return • but that does not happen if rate of change in exchange rates is negative enough (as almost happened to the British CD) Returns on $10,000 1 Year CD $9,165-10.251.05Japanese yen $9,617-7.753.63German mark $10,5250.005.25U.S. $ $10,533-0.646.00British pound $11,2194.627.00 New Zealand $ $11,6185.3210.00Italian lira Final Value % Change in $ Return rate Diversification traps • investors less diversified than they think if the returns on their investments tend to move together • suppose you decide to invest in a bond fund and in a stock fund to obtain a diversified portfolio • during expansions, stock prices rise and bond values fall • during contractions, the opposite happens Trap • trap: some stock funds hold disproportionate share of stocks in financial institutions and utilities • Stratton Monthly Dividend fund had 29% of its portfolio in financial stocks and 71% in utilities • Weitz Value fund had 56% in financial institutions and 14% in utilities • you are less diversified if you pair bond fund with stock fund that concentrates on financial institutions and utilities - so the price of the funds are positively correlated - than if you use other types of stock funds 3 common measures of risk • standard deviation • Morningstar measure of risk of loss •beta Morningstar, Inc. • Chicago funds rating company • looks at a fund's monthly returns and determines how many times it has failed to match the results of risk-free investments like Treasury bills • then compares that figure to those of similar funds and sets the risk at 1 for the average • higher the number indicates riskier fund 8 Beta (+) • shows whether a fund's return moves with that of the market as a whole • beta = 1 means fund's return moves with S&P 500 • beta = 1.5 means, • if S&P goes up 10%, fund rose 15% • if S&P went down 10%, it fell 15% Reasonableness of beta • beta is a reasonable way to assess risk of stocks • can be misleading for non-stock investments • example • price of gold and foreign funds do not move closely with the U. S. stock market, so they have very low betas • such investments tend to be very risky in terms of standard deviations Vanguard 500 fund • weighted average of the S&P 500 stocks • standard deviation for 3 years • Vanguard 500 was 8.1 • highest observed was on Lexington Strategic investment, 49.3 • lowest was on T. Rowe Price Spectrum Income fund, 3.8 3-year Morningstar measure • Vanguard 500 was 0.7 • Lexington Strategic Investments was 3.8 • Merger fund was 0.2 3-year beta • Vanguard 500 is 1.0 • Smith Barney Special Equities B fund was 1.6 • Merger fund was 0.1 Insurance • risk-averse people will pay money – risk premium – to avoid risk • world-wide insurance premiums in 1998: $2.2 trillion 9 House insurance • Scott is risk averse • wants to insure his $80 (thousand) house • 25% chance of fire next year • if fire occurs, house worth $40 With no insurance • expected value of house is $70 = (¼ ´ $40) + (¾ ´ $80) • variance $300 = [¼ ´ ($40 - $70) 2 ] + [¾ ´ ($80 - $70) 2 ] With insurance • suppose insurance company offers fair insurance • lets Scott trade $1 if no fire for $3 if fire • insurance is fair bet because expected value is $0 = (¼ ´ [-$3]) + (¾ ´ $1) • Scott fully insurances: eliminates all risk • pays $10 if no fire • receives $30 if fire • net wealth in both states of nature is $70 Commercial insurance • is not fair • available only for diversifiable risks Investing under uncertainty • monopoly’s owner has an uncertain payoff this year • if risk neutral, owner maximizes expected value of return • otherwise, owner maximizes his or her expected utility • summarize analysis in decision tree Figure 17.04 Investment Decision Tree with Risk Aversion Low demand High demand $200 80% 20% –$100 $0 EV = $140 EV = $140 Invest (a) Risk-Neutral Owner Do not invest Low demand High demand U($200) = 40 80% 20% U (– $100) = 0 U($0) = 35 EU =35 EU = 32 Invest (b) Risk-Averse Owner Do not invest 10 Investing under uncertainty and discounting • problem is more complicated if future returns are uncertain • need to calculate expected utility (or value) and then discount Figure 17.5 Investment Decision Tree with Uncertainty and Discounting Low demand High demand R = $125 C = $25 80% 20% R = $50 $0 ENVP = $75 EV = $110 EPV = $100 Invest This year Next year Do not invest Investing with advertising • future demand is uncertain • advertising affects demand • suppose risk neutral owner Figure 17.6 Investment Decision Tree with Advertising EV = $10 Invest Do not invest Low demand High demand $100 80% 20% – $100 Low demand High demand $100 40% 60% – $100 EV = $10 $0 EV = $60 EV = –$20 Advertise – $50 Do not advertise 1. Degree of risk • probability: likelihood that a particular state of nature occurs • expected value: probability-weighted average of the values in each state of nature •variance • commonly used measure of risk • weighted average of the squared difference of the value in each state of nature and the expected value 2. Decision making under uncertainty • most people are risk averse • people choose the option that provides the highest expected utility • expected utility is the probability-weighted average of the utility from the outcomes in the various states of nature [...]... optional risks • take actions that lower probabilities of bad events or reduce harms from those events • collect information before acting • diversify • insure 4.Investing under uncertainty • • • • • investment depends on uncertainty of payoff attitudes toward risk expected return interest rate cost of altering the likelihood of a good outcome 11 . 1 Chapter 17 Uncertainty Main topics 1. degree of risk 2. decision making under uncertainty 3. avoiding risk 4. investing under uncertainty Degree of risk • probability:. (-$5 - $5) 2 ] = [½ G ($10) 2 ] + [½ G (-$10) 2 ] = $100 • standard deviation = square root of variance Decision making under uncertainty • a rational person might maximize expected utility: probability-weighted. certain utility from wealth of $26 is U($26) = 105 • Irma is indifferent between • having the vase • having $26 with certainty • thus, Irma’s risk premium is $14 = $40 - $26 to avoid bearing