Chapter 3 Criteria For Optimal Investment Decsions

⾦融学答案12⾦融答案翻译12章CHAPTER 12CHOOSING AN INVESTMENT PORTFOLIOObjectivesTo understand the process of personal investing in theory and in practice.To build a quantitative model of the tradeoff between risk and reward.Outline12.1 The Process of Personal Portfolio Selection12.2 The Trade-off between Expected Return and Risk12.3 Efficient Diversification with Many Risky AssetsSummaryThere is no single portfolio selection strategy that is best for all people.Stage in the life cycle is an important determinant of the optimal composition of a person’s optimal portfolio of assets and liabilities.Time horizons are important in portfolio selection. We distinguish among three time horizons: the planning horizon, the decision horizon, and the tradinghorizon.In making portfolio selection decisions, people can in general achieve a higher expected rate of return only by exposing themselves to greater risk.One can sometimes reduce risk without lowering expected return by diversifying more completely either within a given asset class or across asset classes.The power of diversification to reduce the riskiness of an investor’s portfolio depends on the correlations among the assets that make up the portfolio. In practice, the vast majority of assets are positively correlated with each other because they are all affected by common economic factors. Consequently,one’s ability to reduce risk through diversification among risky assets without lowering expected return is limited.Although in principle people have thousands of assets to choose from, in practice they make their choices from a menu of a few final products offered by financial intermediaries such as bank accounts, stock and bond mutual funds, and real estate. In designing and producing the menu of assets to offer to their customers these intermediaries make use of the latest advances in financial technology.Solutions to Problems at End of Chapter1. Suppose that your 58-year-old father works for the Ruffy Stuffed Toy Company and has contributed regularly to his company-matched savings plan for the past 15 years. Ruffy contributes $0.50 for every $1.00 your father puts into the savings plan, up to the first 6% of his salary. Participants in the savings plan can allocate their contributions among four different investment choices: a fixed-income bond fund, a “blend” option that invests in large companies, small companies, and the fixed-income bond fund, a growth-income mutual fund whose investments do not include other toy companies, and a fund whose sole investment is stock in the Ruffy Stuffed Toy Company. Over Thanksgiving vacation, Dad realizes that you have been majoring in finance and decides to reap some early returns on that tuition money he’s been investing in your education. He shows you the most recent quarterly statement for his savings plan, and you see that 98% of its current value is in the fourth investment option, that of the Ruffy Company stock..a.Assume that your Dad is a typical risk-averse person who is consideringretirement in five years. When you ask him why he has made the allocation in this way, he responds that the company stock has continually performed quite well, except for a few declines that were caused by problems in a division that the company has long since sold off. In addition, he says, many of his friends at work have done the same. What advice would you giveyour dad about adjustments to his plan allocations? Why?b.If you consider the fact that your dad works for Ruffy in addition to his98% allocation to the Ruffy stock fund, does this make his situation more risky, less risky, or does it make no difference? Why?SOLUTION:a.Dad has exposed himself to risk by concentrating almost all of his plan moneyin the Ruffy Stock fund. This is analogous to taking 100% of the money afamily has put aside for investment and investing it in a single stock.⽗亲将⾃⼰完全置⾝于冒险中，通过将⼏乎所有的计划资⾦投资于Ruffy 存货基⾦。

博迪投资学第10版英⽂教材课后答案（6）CAPITAL ALLOCATION TO RISKY ASSETSCHAPTER 6: RISK AVERSION ANDCAPITAL ALLOCATION TO RISKY ASSETS PROBLEM SETS1. (e)2. (b) A higher borrowing rate is a consequence of the risk of the borrowers’ default.In perfect markets with no additional cost of default, this increment would equal the value of the borrower’s option to default, and the Sharpe measure, with appropriate treatment of the default option, would be the same. However, in reality there are costs to default so that this part of the increment lowers the Sharpe ratio. Also,notice that answer (c) is not correct because doubling the expected return with afixed risk-free rate will more than double the risk premium and the Sharpe ratio. 3. Assuming no change in risk tolerance, that is, an unchanged risk aversioncoefficient (A), then higher perceived volatility increases the denominator of theequation for the optimal investment in the risky portfolio (Equation 6.7). Theproportion invested in the risky portfolio will therefore decrease.4. a. The expected cash flow is: (0.5 × $70,000) + (0.5 × 200,000) = $135,000With a risk premium of 8% over the risk-free rate of 6%, the required rate ofreturn is 14%. Therefore, the present value of the portfolio is:$135,000/1.14 = $118,421b. If the portfolio is purchased for $118,421, and provides an expected cashinflow of $135,000, then the expected rate of return [E(r)] is as follows:$118,421 × [1 + E(r)] = $135,000Therefore, E(r) =14%. The portfolio price is set to equate the expected rate ofreturn with the required rate of return.c. If the risk premium over T-bills is now 12%, then the required return is:6% + 12% = 18%The present value of the portfolio is now:$135,000/1.18 = $114,4076-1CAPITAL ALLOCATION TO RISKY ASSETSd. For a given expected cash flow, portfolios that command greater riskpremia must sell at lower prices. The extra discount from expected valueis a penalty for risk.5.When we specify utility by U =E(r) – 0.5A σ2, the utility level for T-bills is: 0.07The utility level for the risky portfolio is:U = 0.12 – 0.5 × A × (0.18)2 = 0.12 – 0.0162 × AIn order for the risky portfolio to be preferred to bills, the following must hold:0.12 – 0.0162A > 0.07 ? A < 0.05/0.0162 = 3.09A must be less than 3.09 for the risky portfolio to be preferred to bills.6. Points on the curve are derived by solving for E(r) in the following equation:U = 0.05 = E(r) – 0.5A σ2 = E(r) – 1.5σ2The values of E(r), given the values of σ2, are therefore:σσ 2E(r)0.00 0.0000 0.050000.05 0.0025 0.053750.10 0.0100 0.065000.15 0.0225 0.083750.20 0.0400 0.110000.25 0.0625 0.14375The bold line in the graph on the next page (labeled Q6, for Question 6) depicts the indifference curve.7. Repeating the analysis in Problem 6, utility is now:U = E(r) – 0.5Aσ2 = E(r) – 2.0σ2 = 0.05The equal-utility combinations of expected return and standard deviation arepresented in the table below. The indifference curve is the upward sloping line in the graph on the next page, labeled Q7 (for Question 7).σσ 2E(r)0.00 0.0000 0.05000.05 0.0025 0.05500.10 0.0100 0.07000.15 0.0225 0.09506-2CAPITAL ALLOCATION TO RISKY ASSETS0.20 0.0400 0.13000.25 0.0625 0.1750The indifference curve in Problem 7 differs from that in Problem 6 in slope.When A increases from 3 to 4, the increased risk aversion results in a greaterslope for the indifference curve since more expected return is needed in order to8. The coefficient of risk aversion for a risk neutral investor is zero. Therefore, thecorresponding utility is equal to the portfolio’s expected return. The corresponding indifference curve in the expected return-standard deviation plane is a horizontal line, labeled Q8 in the graph above (see Problem 6).9. A risk lover, rather than penalizing portfolio utility to account for risk, derivesgreater utility as variance increases. This amounts to a negative coefficient of risk aversion. The corresponding indifference curve is downward sloping in the graph above (see Problem 6), and is labeled Q9.6-3CAPITAL ALLOCATION TO RISKY ASSETS6-410. The portfolio expected return and variance are computed as follows:(1) W Bills (2) r Bills (3) W Index (4) r Index r Portfolio (1)×(2)+(3)×(4) σPortfolio(3) × 20% σ 2 Portfolio0.0 5% 1.0 13.0% 13.0% = 0.130 20% = 0.20 0.0400 0.2 5% 0.8 13.0% 11.4% = 0.114 16% = 0.16 0.0256 0.4 5% 0.6 13.0% 9.8% = 0.098 12% = 0.12 0.0144 0.6 5% 0.4 13.0% 8.2% = 0.082 8% = 0.08 0.0064 0.8 5% 0.2 13.0% 6.6% = 0.066 4% = 0.04 0.0016 1.05%0.013.0%5.0% = 0.0500% = 0.00 0.000011. Computing utility from U = E(r) – 0.5 × A σ2 = E(r) – σ2, we arrive at the valuesin the column labeled U(A = 2) in the following table:W Bills W Index r Portfolio σPortfolio σ2Portfolio U(A = 2)U(A = 3) 0.0 1.0 0.130 0.20 0.0400 0.0900 .0700 0.2 0.8 0.114 0.16 0.0256 0.0884 .0756 0.4 0.6 0.098 0.12 0.0144 0.0836 .0764 0.6 0.4 0.082 0.08 0.0064 0.0756 .0724 0.8 0.2 0.066 0.04 0.0016 0.0644 .0636 1.00.00.0500.00 0.00000.0500 .0500The column labeled U(A = 2) implies that investors with A = 2 prefer a portfolio that is invested 100% in the market index to any of the other portfolios in the table.12. The column labeled U(A = 3) in the table above is computed from:U = E(r) – 0.5A σ2 = E(r) – 1.5σ2The more risk averse investors prefer the portfolio that is invested 40% in the market, rather than the 100% market weight preferred by investors with A = 2.13. Expected return = (0.7 × 18%) + (0.3 × 8%) = 15%Standard deviation = 0.7 × 28% = 19.6%14. Investment proportions: 30.0% in T-bills 0.7 × 25% = 17.5% in Stock A 0.7 × 32% = 22.4% in Stock B 0.7 × 43% = 30.1% in Stock CCAPITAL ALLOCATION TO RISKY ASSETS6-515. Your reward-to-volatility ratio: .18.080.3571.28S -== Client's reward-to-volatility ratio: .15.080.3571.196S -== 16.17. a.E(r C ) = r f + y × [E(r P ) – r f ] = 8 + y × (18 - 8) If the expected return for the portfolio is 16%, then:16% = 8% + 10% × y ?.16.080.8.10y -== Therefore, in order to have a portfolio with expected rate of return equal to 16%, the client must invest 80% of total funds in the risky portfolio and 20% in T-bills.CAPITAL ALLOCATION TO RISKY ASSETS6-6b.Client’s investment proportions: 20.0% in T-bills0.8 × 25% = 20.0% in Stock A 0.8 × 32% = 25.6% in Stock B 0.8 × 43% = 34.4% in Stock Cc.σC = 0.8 × σP = 0.8 × 28% = 22.4%18. a.σC = y × 28%If your client prefers a standard deviation of at most 18%, then:y = 18/28 = 0.6429 = 64.29% invested in the risky portfoliob. ().08.1.08(0.6429.1)14.429%C E r y =+?=+?=19. a.y*0.36440.27440.100.283.50.080.18A σr )E(r 22Pf P ==?-=-=Therefor e, the client’s optimal proportions are: 36.44% invested in the risky portfolio and 63.56% invested in T-bills.b. E(r C ) = 8 + 10 × y* = 8 + (0.3644 × 10) = 11.644% σC = 0.3644 × 28 = 10.203%20. a.If the period 1926 - 2009 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(r M ) ? r f = 7.93%, σM = 20.81% (we use the standard deviation of the risk premium from Table 6.7). Then y * is given by:M f 22ME(r )r 0.0793y*0.4578A σ40.2081-===? That is, 45.78% of the portfolio should be allocated to equity and 54.22%should be allocated to T-bills.b.If the period 1968 - 1988 is assumed to be representative of future expected performance, then we use the following data tocompute the fraction allocated to equity: A = 4, E(r M ) ? r f = 3.44%, σM = 16.71% and y* is given by:CAPITAL ALLOCATION TO RISKY ASSETS6-7M f 22M E(r )r 0.0344y*0.3080A σ40.1671-===? Therefore, 30.80% of the complete portfolio should be allocated to equity and69.20% should be allocated to T-bills.c.In part (b), the market risk premium is expected to be lower than in part (a) and market risk is higher. Therefore, the reward-to-volatility ratio is expected to be lower in part (b), which explains the greater proportion invested in T-bills.21. a. E(r C ) = 8% = 5% + y × (11% – 5%) ? .08.050.5.11.05y -==-b. σC = y × σP = 0.50 × 15% = 7.5%c.The first client is more risk averse, allowing a smaller standard deviation.22. Johnson requests the portfolio standard deviation to equal one half the marketportfolio standard deviation. The market portfolio 20%M σ=which implies 10%P σ=. The intercept of the CML equals 0.05f r =and the slope of the CML equals the Sharpe ratio for the market portfolio (35%). Therefore using the CML:()()0.050.350.100.0858.5%M fP f P ME r r E r r σσ-=+=+?==23. Data: r f = 5%, E(r M ) = 13%, σM = 25%, and B f r = 9%The CML and indifference curves are as follows:CAPITAL ALLOCATION TO RISKY ASSETS6-824. For y to be less than 1.0 (that the investor is a lender), risk aversion (A) must be large enough such that:1A σr )E(r y 2M f M <-=1.280.250.050.13A 2=-> For y to be greater than 1 (the investor is a borrower), A must be small enough: 1A σr )E(r y 2M f M >-=0.640.250.090.13A 2=-< For values of risk aversion within this range, the client will neither borrow nor lend, but will hold a portfolio comprised only of the optimal risky portfolio:y = 1 for 0.64 ≤ A ≤ 1.2825. a.The graph for Problem 23 has to be redrawn here, with: E(r P ) = 11% and σP = 15% CAPITAL ALLOCATION TO RISKY ASSETS6-9E(r)σ913251115b.For a lending position: 2.670.150.050.11A 2=->For a borrowing position: 0.890.150.090.11A 2=-<Therefore, y = 1 for 0.89 ≤ A ≤ 2.6726. The maximum feasible fee, denoted f, depends on the reward-to-variability ratio.For y < 1, the lending rate, 5%, is viewed as the relevant risk-free rate, and we solve for f as follows: .11.05.13.05.15.25f ---= ? .15.08.06.012 1.2%.25f ?=-== For y > 1, the borrowing rate, 9%, is the relevant risk-free rate. Then we notice that,even without a fee, the active fund is inferior to the passive fund because:`More risk tolerant investors (who are more inclined to borrow) will not be clients ofCAPITAL ALLOCATION TO RISKY ASSETS6-10the fund. We find that f is negative: that is, you would need to pay investors to choose your active fund. These investors desire higher risk-higher return complete portfolios and thus are in the borrowing range of the relevant CAL. In this range, the reward-to-variability ratio of the index (the passive fund) is better than that of the managed fund..13.08-28. a.With 70% of his money invested in my fund’s portfolio, the client’s expected return is 15% per year and standard deviation is 19.6% per year. If he shifts that money to the passive portfolio (which has an expected return of 13% and standard deviation of 25%), his overall expected return becomes: E(r C ) = r f + 0.7 × [E(r M ) ? r f ] = .08 + [0.7 × (.13 – .08)] = .115 = 11.5% The standard deviation of the complete portfolio using the passive portfolio would be:σC = 0.7 × σM = 0.7 × 25% = 17.5%Therefore, the shift entails a decrease in mean from 15% to 11.5% and adecrease in standard deviation from 19.6% to 17.5%. Since both mean return and standard deviation decrease, it is not yet clear whether the move isCAPITAL ALLOCATION TO RISKY ASSETS6-11beneficial. The disadvantage of the shift is that, if the client is willing to accept a mean return on his total portfolio of 11.5%, he can achieve it with a lower standard deviation using my fund rather than the passive portfolio. To achieve a target mean of 11.5%, we first write the mean of the complete portfolio as a function of the proportion invested in my fund (y ):E(r C ) = .08 + y × (.18 ? .08) = .08 + .10 × yOur target is: E(r C ) = 11.5%. Therefore, the proportion that must be invested in my fund is determined as follows:.115 = .08 + .10 × y ? .115.080.35.10y -== The standard deviation of this portfolio would be:σC = y × 28% = 0.35 × 28% = 9.8%Thus, by using my portfolio, the same 11.5% expected return can be achieved with a standard deviation of only 9.8% as opposed to the standard deviation of 17.5% using the passive portfolio.b.The fee would reduce the reward-to-volatility ratio, i.e., the slope of the CAL. The client will be indifferent between my fund and the passive portfolio if the slope of the after-fee CAL and the CML are equal. Let f denote the fee:Slope of CAL with fee .18.08.10.28.28f f---==Slope of CML (which requires no fee).13.080.20.25-== Setting these slopes equal we have:.100.200.044 4.4%.28ff -=?==per year29. a.The formula for the optimal proportion to invest in the passive portfolio is:2MfM A σr )E(r y*-=Substitute the following: E(r M ) = 13%; r f = 8%; σM = 25%; A = 3.5:20.130.08y*0.2286=22.86% in the passive portfolio 3.50.25-==?CAPITAL ALLOCATION TO RISKY ASSETS6-12b.The answer here is the same as the answer to Problem 28(b). The fee that you can charge a client is the same regardless of the asset allocation mix of the client’s portfolio. You can charge a fee that will equate the reward-to-volatility ratio of your portfolio to that of your competition.CFA PROBLEMS1. Utility for each investment = E(r) – 0.5 × 4 × σ2We choose the investment with the highest utility value, Investment 3. Investment ExpectedreturnE(r)Standarddeviationσ Utility U 1 0.12 0.30 -0.0600 2 0.15 0.50 -0.3500 3 0.21 0.16 0.1588 4 0.240.210.15182. When investors are risk neutral, then A = 0; the investment with the highest utility is Investment 4 because it has the highest expected return.3. (b)4. Indifference curve 25. Point E6. (0.6 × $50,000) + [0.4 × (-$30,000)] - $5,000 = $13,0007. (b)CAPITAL ALLOCATION TO RISKY ASSETS6-138. Expected return for equity fund = T-bill rate + risk premium = 6% + 10% = 16% Expected rate of return of the clien t’s portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Expected return of the client’s portfolio = 0.12 × $100,000 = $12,000 (which implies expected total wealth at the end of the period = $112,000) Standard deviation of client’s overall portfolio = 0.6 × 14% = 8.4% 9.Reward-to-volatility ratio =.100.71.14=CHAPTER 6: APPENDIX1. By year end, the $50,000 investment will grow to: $50,000 × 1.06 = $53,000Without insurance , the probability distribution of end-of-year wealth is:Probability Wealth No fire 0.999 $253,000 Fire0.001$ 53,000For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(253,000)] + [0.001 × ln(53,000)] = 12.439582 The certainty equivalent is:W CE = e 12.439582 = $252,604.85With fire insurance , at a cost of $P, the investment in the risk-free asset is:$(50,000 – P)Year-end wealth will be certain (since you are fully insured) and equal to:[$(50,000 – P) × 1.06] + $200,000 Solve for P in the following equation:[$(50,000 – P) × 1.06] + $200,000 = $252,604.85 ? P = $372.78This is the most you are willing to pay for insurance. Note that the expected loss is “only” $200, so you are willing to pay a substantial risk premium over the expected value of losses. The primary reason is that the value of the house is a large proportion of your wealth.CAPITAL ALLOCATION TO RISKY ASSETS2. a. With insurance coverage for one-half the value of the house, the premiumis $100, and the investment in the safe asset is $49,900. By year end, theinvestment of $49,900 will grow to: $49,900 × 1.06 = $52,894If there is a fire, your insurance proceeds will be $100,000, and theprobability distribution of end-of-year wealth is:Probability WealthNo fire 0.999 $252,894Fire 0.001 $152,894For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(252,894)] + [0.001 × ln(152,894)] = 12.4402225 The certainty equivalent is: W CE = e 12.4402225 = $252,766.77b.With insurance coverage for the full value of the house, costing $200, end-of-year wealth is certain, and equal to:[($50,000 – $200) × 1.06] + $200,000 = $252,788Since wealth is certain, this is also the certainty equivalent wealth of the fullyinsured position.c.With insurance coverage for 1? times the value of the house, the premiumis $300, and the insurance pays off $300,000 in the event of a fire. Theinvestment in the safe asset is $49,700. By year end, the investment of$49,700 will grow to: $49,700 × 1.06 = $52,682The probability distribution of end-of-year wealth is:Probability WealthNo fire 0.999 $252,682Fire 0.001 $352,682For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(252,682)] + [0.001 × ln(352,682)] = 12.4402205 The certainty equivalent is: W CE = e 12.440222 = $252,766.27Therefore, full insurance dominates both over- and under-insurance. Over-insuring creates a gamble (you actually gain when the house burns down).Risk is minimized when you insure exactly the value of the house.6-14。

Human Development and Economic Sustainability*SUDHIR ANANDSt.Catherine's College,Oxford,UKandAMARTYA SENTrinity College,Cambridge,UKSummary.ÐThis paper attempts to integrate the concern for human development in the presentwith that in the future.In arguing for sustainable human development,it appeals to the notion ofethical``universalism''Ðan elementary demand for impartiality of claimsÐapplied within andbetween generations.Economic sustainability is often seen as a matter of intergenerational equity,but the speci®cation of what is to be sustained is not always straightforward.The addendumexplores the relationship between distributional equity,sustainable development,optimal growth,and pure time preference.Ó2000Elsevier Science Ltd.All rights reserved.1.FUTURE PROSPECTS AND PRESENTLIVES``It is justice,not charity,that is wanting in the world,''wrote Mary Wollstonecraft,the pioneering feminist,in A Vindication of the Rights of Woman,published in1792,the same year in which her friend Thomas Paine published the second part of the Rights of Man. Both were concerned with giving everyoneÐwomen and menÐpower over their own lives and opportunities to live the way they had reasons to value.One particular feature of their common approach is particularly worth emphasizing in the context of policy discussions today,viz.the implicit``universalism''that characterizes both the approaches.The domain of concern is not arbitrarily restricted to,say, men,or men of a certain class or background. This shared aspect of the original contributors to the human rights approach is of speci®c interest in interpreting the task of``human development''in a world that is marked,on the one hand,by enormous inequities in contem-porary living conditions,and on the other,by real threats to the prospects of human life in the future.Appeals to rights and entitlements that have moved the world forcefully have often tended to ignore the freedoms of particular groups.For example,while ancient Greek philosophers presented some of the most far-reaching ana-lyses of individual independence and auton-omy,they typically did not hesitate to leave out the slavesÐand often women tooÐfrom the discourse.The language and the rhetoric as well as the reality of rights in the contemporary world are often characterized by the neglect of particular sections of the populationÐless privileged ethnic groups,exploited classes, sequestered women.The basic idea of expanding``human capa-bility,''or of``human development,''which has been pursued in di erent forms in recent years, involves the assertion of the unacceptability of such biases and discrimination.1We shall not spend any time here on the issue of whether formalisms used in successive Human Develop-World Development Vol.28,No.12,pp.2029±2049,2000Ó2000Elsevier Science Ltd.All rights reservedPrinted in Great Britain0305-750X/00/$-see front matterPII:S0305-750X(00)00071-1/locate/worlddev*This paper draws on an earlier discussion paper``Sustainable Human Development:Concepts and Prior-ities''prepared by the authors for the United NationsDevelopment Programme(Anand&Sen,1996).Forhelpful conversations and suggestions,we thank SisselaBok,Robert Dorfman,Mahbub ul Haq,Robert Solow,Paul Streeten,and the referees of this journal.Researchsupport from the John D.and Catherine T.MacArthurFoundation is gratefully acknowledged.Final revisionaccepted:5May2000.2029ment Report s do full justice to the idea.But its focus on universalism is something of impor-tance for contemporary debates on public policy.The growing concern with``sustainable development''re¯ects a basic belief that the interests of future generations should receive the same kind of attention that those in the present generation get.2We cannot abuse and plunder our common stock of natural assets and resources leaving the future generations unable to enjoy the oppor-tunities we take for granted today.We cannot use up,or contaminate,our environment as we wish,violating the rights and the interests of the future generations.The demand of ``sustainability''is,in fact,a particular re¯ec-tion of universality of claimsÐapplied to the future generations vis- a-vis us.That universalism also requires that in our anxiety to protect the future generations,we must not overlook the pressing claims of the less privileged today.A universalist approach cannot ignore the deprived people today in trying to prevent deprivation in the future. One of the strongest arguments in favor of giving priority to the protection of the envi-ronment is the ethical need for guaranteeing that future generations would continue to enjoy similar opportunities of leading worthwhile lives that are enjoyed by generations that precede them.This,as we discuss in Section3 of this paper,is the central idea underlying the demand for``sustainable development,''and it has many important implications.But this goal of sustainabilityÐincreasingly recognized to be legitimateÐwould make little sense if the present life opportunities that are to be``sus-tained''in the future were miserable and indi-gent.Sustaining deprivation cannot be our goal,nor should we deny the less privileged today the attention that we bestow on genera-tions in the future.The living standard of a substantial part of humanity has radically moved forward in a way that would have been hard to anticipate in Paine's or Wollstonecraft's time.While it would have been,then,di cult to dispute that human life everywhere was``nasty,brutish and short''(as Thomas Hobbes had put it in Levi-athan),people today in many countries in Europe,North America and elsewhere have lives that are much longer,less miserable,and far less battered by forces beyond the person's control.Yet a great many people in the world continue to su er from the absence of funda-mental opportunities to lead decent and satis-fying lives.The continued high incidence of premature mortality,ill-health,undernourish-ment,illiteracy,poverty,insecurity,and other forms of deprivation indicate the failure of the modern world to bring even the most basic capabilities within the reach of all.A newborn child may be doomed to a life of extreme brevity or intense misery if that child happens to be born in a``wrong class,''in a``wrong country,''or to be of the``wrong sex.'' Ethical universalism is basically an elemen-tary demand for impartialityÐapplied within generations and between them.It is,in the present context,the recognition of a shared claim of all to the basic capability to lead worthwhile lives.Not working toward guaran-teeing the basic capabilities to the future generations would be scandalous,but in the same way,not working toward bringing those elementary capabilities within the reach of the deprived in the present generation would also be outrageous.Given the implicit biases in many policy debates,there is a real need for jealously guarding that universalist perspective. As the full signi®cance of the issues forcefully discussed in the environmental conference (UNCED)in Rio in1992begins to be more fully understood,the integration of human progress and environmental conservation has emerged as one of the central challenges faced by the modern world(Pronk&Haq,1992; Speth,1992;Brundtland,1993).The moral value of sustaining what we now have depends on the quality of what we have,and the entire approach of sustainable development directs us as much toward the present as toward the future.There is,in principle,no basic di culty in broadening the concept of human develop-ment to accommodate the claims of the future generations and the urgency of environmental protection.2.ALTERNATIVE DEVELOPMENTAPPROACHES(a)Human development and wealth The foundational task of scrutinizing the demands of sustainable human development also provides an appropriate occasion to see how the``human development''approach relates to the more conventional analyses to be found in the standard economic literatureÐfrom Adam Smith(1776,1790)onwards. Interest in human development is not new inWORLD DEVELOPMENT 2030economics.Indeed,this motivating concern is explicitly present in the writings of the early founders of quantitative economics(such as William Petty,Gregory King,Francßois Ques-nay,Antoine Lavoisier,and Joseph Lagrange) as well as the pioneers of political economy (such as Adam Smith,David Ricardo,Robert Malthus,Karl Marx,and John Stuart Mill).3 There is,in this sense,no foundational depar-ture in making economic analysis and policy take extensive note of the demands of human development.The approach reclaims an old and established heritage,rather than importing or implanting a new diversion. Economics has never been a subject of one tradition only.The interest in human develop-ment has had to compete with other priorities and pursuits within the same body of main-stream economics.The preoccupation with commodity production,opulence and®nancial success can also be traced in professional economics through several centuriesÐinvolv-ing many leading economists as well as busi-nessmen and bureaucrats,who have preferred to concentrate more on the characteristics of overall material success than on the deprivation and development of human lives.Indeed,the dominant contemporary tradition of focusing on such variables as per capita gross national product or national wealth is a continuationÐperhaps even an intensi®cationÐof the old opulence-oriented approach.The focus on wealth maximization can be taken at di erent levels,and at the common aggregative level,the spotlight is put entirely on making the community as a whole as opulent as possible,irrespective of distribution and irre-spective of what that wealth does to human lives.It is,of course,true that being rich, wealthy and a uent can be among the most important contributory factors in generating well-being,and the opulence-oriented approach to economic progress certainly cannot be criti-cized for being irrelevant to the success of human living.On the other hand,insofar as it neglects other crucial factors,such as public care and social organization,which also contribute to the well-being and freedom of individuals,the approach is deeply limited and defective.4Insofar as the concern is with overall wealth maximizationÐirrespective of distributionÐthere is a serious disregard of individual predicaments in favor of some conglomerative achievement,which can be blind to the most extreme deprivations su ered by many,while others make useÐpossibly excellent useÐof the accomplishment of wealth and opulence.Thus,the fundamental di culty with the approach of wealth maximization and with the tradition of judging success by overall opulence of a society is a deep-seated failure to come to terms with the universalist unbiasedness needed for an adequate understanding of social justice and human development.In this sense,the wealth-based approach is not,by any means, inconsequential,but it certainly is signi®cantly partisan.The most basic problem with the opulence view is its comprehensive failure to take note of the need for impartial concern in looking at the real opportunities individuals have.The exclusive concentration only on incomes at the aggregative or individual levels ignores the plurality of in¯uences that di er-entiate the real opportunities of people,and implicitly assumes away the variationsÐrelated to personal characteristics as well as the social and physical environmentÐin the possibility of converting the means of income into the ends of good and livable lives which people have reason to value.(b)Objectives and instrumentsHow illuminating is the di erence between the two traditions of focusing respectively on(i) development of human capability,or human development,and(ii)overall wealth and opu-lence?These traditions can be seen as di ering, directly or indirectly,in two distinct respects. The®rst concerns divergences in the ultimate objectives,and the second relates to di erences in the e ectiveness of distinct instruments. While the human development approach has conformed broadly to the line of reasoning enunciated by Aristotle more than two millennia ago(``wealth is evidently not the good we are seeking,for it is merely useful and for the sake of something else''),there have been many professional experts who have seen their task as being con®ned to the maximiza-tion of opulence(an old illustration is the17th century monograph by the pioneering mercantilist author,Thomas Mun,England's Treasure by Foreign Trade,or the Balance of Our Foreign Trade is the Rule of Our Treasure). That division about our basic objectives still surfaces in the debates on current policies in di erent parts of the world,and also in discussions about what importance to attach to various indicators and criteria of progress (such as GNP per capita).5HUMAN DEVELOPMENT AND ECONOMIC SUSTAINABILITY2031At the level of objectives,the case for following Aristotle rather than Mun is not hard to appreciate.How can we possibly give priority to the means of living,which is what treasures and wealths are,over the ends of good and free human lives?While much of economic and®nancial writing proceeds as if there is nothing beyond opulence with which we need be concerned,it is fair to see that as a problem of presentation,rather than a re¯ec-tion of some deep-seated eccentricity about ends and means.The really interesting debates must relate to instrumental e ectiveness of overall wealth and opulence in promoting those things for which wealth and opulence are sought.There is,in fact,much more substance in the opulence-centered approach than the implau-sible view that opulence is an end in itself.This takes us to the second di erence,which relates to the cause±e ect relationships in the pursuit of the deeper objectives.Some have taken the view that while opulence is not to be valued at all for its own sake,it still is the most important instrument in promoting the more basic objec-tivesÐeven the Aristotelian one of rich and ful®lling lives.To take a prominent example,W.Arthur Lewis,one of the leading modern development economists,did not entertain much doubt that the appropriate objective to pursue is increas-ing``the range of human choice.''He also acknowledged the causal role of many factors in advancing the freedom to choose.But nevertheless he decided to concentrate speci®-cally on``the growth of output per head,'' because it``gives man greater control over his environment,and thereby increases his free-dom''(Lewis,1955,pp.9±10,420±421).Indeed, the focus of his classic book was su ciently precise to permit him to assert:``Our subject matter is growth,and not distribution.'' Lewis's faith in the instrumental e cacy of total growth has proved to be quite disputable in terms of the experiences observed in the actual world.Many countries have grown fast without a commensurate impact on living conditions,and more importantly,some coun-tries have achieved high quality of life despite relatively moderate growth of GNP or GDP per head.It has also been observed that even when there is a generally positive and statisti-cally signi®cant relationship between GNP per head and indicators of quality of life in the gross intercountry data,much of that rela-tionship turns on the use of extra income in the speci®c®elds of public education and health, and in reducing absolute poverty.It is certainly true that the higher the average income of a country,the more likely it isÐgiven other thingsÐthat it will tend to have a higher average life expectancy,lower infant and child mortality rates,higher literacy,and in fact,a higher value of the``human development index.''A number of recent studies have con®rmed this general pattern.The associa-tions are,however,far from perfect.For example,in intercountry comparisons,income di erences tend to explain not much more than half the variations in life expectancy,or in infant or child mortality,and they explain a smaller proportion of variation in adult literacy rates.6Many countries,such as Sri Lanka, China,Jamaica,Costa Rica,and the state of Kerala in India,have achieved levels of human development that are enormously higher than what would be expected on the basis of their GNP or real income per head.What is also of importanceÐperhaps even more soÐis the route through which growth of GNP most e ectively in¯uences human devel-opment.Economic growth not only involves increase in private incomes,it can also signi®-cantly contribute to generating resources that can be marshalled to improve social services (such as public healthcare,epidemiological protection,basic education,safe drinking water, etc.).In some cases such marshalling is e ec-tively done,while in other cases,the fruits of growth are put to little use of this kind.7This can make a big di erence to the outcome in terms of the expansion of basic human capa-bilities.Similarly,while the expansion of private income certainly is of instrumental importance in enhancing basic capabilities,the e ectiveness of that impact depends much on the distribution of the newly generated incomes.In particular, the biggest impact may be expected to occur if the rise in average GNP per head goes with a sharp reduction in the poverty of the worst-o people,rather than going in other directions.To what extent this will happen depends on a variety of economic and social circumstances related to the labor-intensive nature of tech-niques of production,the sharing of education and skills across the population,the success of land reforms and the sharing of rural resources, and so on.Here again the experiences of di erent countries and of di erent policy regimes have been quite divergent.There is signi®cant evidence that the statis-tical correlation between GNP per head andWORLD DEVELOPMENT 2032human development tends to work through the impact of GNP expansion on higher public expenditure and lower poverty.For example,it is found in Anand and Ravallion(1993)that when life expectancy variations are linked with public health spending per person and an index of poverty,the addition of GNP per person as a further explanatory variable yields a coe cient that is not signi®cantly di erent from zero.8 ThisÐand related results that focus on other characteristics of quality of lifeÐmust not,of course,be interpreted to imply that economic growth does not matter in expanding the quality of life.Rather,what they indicate is that the connections are seriously contingent, and much depends on how the fruits of economic growth are shared(in particular what the poor get)and how far the additional resources are used to support public services (for example,public spending on health servi-ces,which are particularly crucial in in¯uencing life expectancy).Thus the opulence-oriented view of progress, which has little intrinsic merit(as was discussed earlier),has a conditionally important instru-mental roleÐand that conditionality relates speci®cally to features on which the human development approach has tended to focus,to wit,public action and poverty reduction.There is no basic con¯ict between regarding economic growth to be very important,and taking it to be in itself an insu cient basis of human devel-opment.Insofar as growth of GNP or GDP promotes enhancement of living conditions,its biggest impact comes through the expanded ability to undertake public action to promote human development,and the share of the additional income that is enjoyed by the poor. In recognizing the importance of economic growth as a means for human development,we must also take full note of(i)the contingent nature of its e ectiveness as means(depending on the use of the means for promoting human development),and(ii)its nonuniqueness as means(there are other means as well,including social organization).3.THE ENVIRONMENT ANDSUSTAINABLE DEVELOPMENT(a)The environmental challengeThe idea of sustainable development arose essentially from concerns relating to the over-exploitation of natural and environmental resources.Early discussions stressed the limits to economic activity imposed by the physical environment,and concluded that species and ecosystems should be utilized in ways that allow them to go on renewing themselves inde®nitely (IUCN,1980).The anxieties expressed by environmental scientists and ecologists were recognized by policymakers and economists, who attempted to formulate concepts of``sus-tainable development.''An early formulation by Robert Repetto(1985,p.10)was as follows:At the core of the idea of sustainability,then,is the con-cept that current decisions should not damage the pros-pects for maintaining or improving living standards in the future...This implies that our economic systems should be managed so that we live o the dividend of our resources,maintaining and improving the asset base so that the generations that follow will be able to live equally well or better.This principle also has much in common with the ideal concept of income that accountants seek to determine:the greatest amount that can be consumed in the current period without reducing prospects for consumption in the future.As we shall presently argue,this connection between the ideal of sustainable development and the economic accountant's concept of maintaining the income level(discussed,in particular,by Hicks,1946)is an important one to explore.A more recent characterization has been suggested by Robert Solow(1992,p.15):The duty imposed by sustainability is to bequeath to posterity not any particular thingÐwith rare excep-tions such as Yosemite,for exampleÐbut rather to endow them with whatever it takes to achieve a stan-dard of living at least as good as our own and to look after their next generation similarly.We are not to consume humanity's capital,in the broadest sense.In this section and the next,we follow this characterization,but we subject it to critical scrutiny in Section3(c).The term``sustainable development,''in fact, owes its widespread usage to the Brundtland Commission Report(WCED,1987),Our Common Future,which de®ned it as``develop-ment that meets the needs of the present with-out compromising the ability of future generations to meet their own needs.It contains within it two key concepts:Ðthe concept of`needs,'in particular the essential needs of the world's poor,to which overriding priority should be given;andÐthe idea of limitations imposed by the state of technology and social organizationHUMAN DEVELOPMENT AND ECONOMIC SUSTAINABILITY2033on the environment's ability to meet present and future needs''(WCED,1987,p.43). The Brundtland Commission de®nition is often cited and has become very in¯uential.9 As a general statement,it reminds us that sustainability is about an obligation to future generations(toward meeting their``needs''), and thus it is necessarily about intergenera-tional allocation.Unlike some earlier state-ments,it also helpfully shifts attention away from conserving speci®c resources and``leaving the world as we found it''in every particular. The latter would appear to be neither feasible nor necessarily sensible:resources are basically fungible and can be substituted for one another.The Brundtland Commission's notion of sustainable development is indeed broader and invites examination even independently of environmental concerns.Moreover,the obligation of sustainability cannot be left entirely to the market.The future is not adequately represented in the marketÐat least not the distant futureÐand there is no reason that ordinary market behavior will take care of whatever obligation we have to the future.Universalism demands that the state should serve as a trustee for the interests of future ernment policies such as Pigouvian taxes,subsidies,and regulation can adapt the incentive structure in ways that protect the global environment and resource base for people yet to be born.As Pigou(1932, pp.29±30)had noted,there is wide agreement that the State should protect the interests of the future in some degree against the e ects of our irrational discounting and of our prefer-ence for ourselves over our descendants.The whole movement for`conservation'in the United States is based on this conviction.It is the clear duty of Government,which is the trustee for unborn genera-tions as well as for its present citizens,to watch over, and,if need be,by legislative enactment,to defend, the exhaustible natural resources of the country from rash and reckless spoliation.(b)Intergenerational equity and sustainabledevelopmentWhat are our obligations to future genera-tions?Joseph Addison,writing in The Spectator of1714was dismissive of any duty to posterity:Most people are of the humour of an old fellow of a college,who,when he was pressed by the Society to come into something that might redound to the good of their successors,grew very peevish;`We are alwaysdoing,'says he,`something for posterity,but I would fain see posterity do something for us.'10Yet,of course,there is something posterity can do for us:it can inherit less physical and natural capital,and thus allow us to achieveÐthough not out of its choiceÐa higher standard of living at its expense.How much capital should the future inherit from us?This has been the subject matter of optimal growth theory since the pioneering article of Frank Ramsey(1928).The theory has formed the basis of development policy and social cost-bene®t analysis in the less-developed countries.In Section5we present a simple two-period model which captures the central features of intergenerational allocation as seen in this approach.This framework is founded on the essentially utilitarian criterion of maximizing the sum total of welfare of di erent generations.It allows the welfare of one generation to be traded o one-for-one against that of another generation.If the bene®t to us from economic activities which continue to emit greenhouse gases at the present rates outweighs the harm done to future generations from global warming,then the criterion would recommend no change in our activities.Other ethical notions of the total ``good''may allow for di erent tradeo sÐfor example,those that take account of welfare inequality between generations(see Section 5(a)).Yet others may allow no tradeo in certain rangesÐfor example,those based on the``rights''of future generations to the same quality of environment and levels of clean air as the present generation has.This latter view of justice would give priority to speci®c rights that generations have over decisions based on a calculation of aggregate welfare(Rawls,1971; Dworkin,1978;Sen,1982a,b).Within the broadly welfarist framework of optimal growth theoryÐby far the main economic approach used to analyze questions of intergenerational justiceÐit is relevant to enquire whether sustainable development is necessarily a consequence of growth being optimal.If it were,then a(derived)justi®cation for sustainability could be found in maximizing the total good.Let us take sustainable devel-opment to mean nondeclining welfare over timeÐalthough other de®nitions are formu-lated in terms of nondeclining income, consumption,or capital stock.Even though Ramsey(1928)had argued for treating the welfare of di erent generationsWORLD DEVELOPMENT 2034。