Lecture 2 Discount Factors and Interest Rates_handouts固收

【2020CFA二级高清讲义】CFA二级高清-衍生品CFA Level IIDerivativesCONTENTS目录Pricing and Valuation of ForwardCommitmentsValuation of Contingent ClaimsWarm-up●Pricing:确定远期价格（t=0）.●Valuation:签订合约期间的某一时刻是否赚钱（t=t）.●合约签订期初时，双方的价值都为0（forward commitment ）。

Warm-upt=0Pricingt=t Valuationt=T Settlement●No-Arbitrage Rule ●Equity Forward and Futures●Interest Rate Forward and Futures (FRA)●Fixed-income Forward and Futures●Currency Forward and Futures●Interest Rate Swap●Currency Swap●Equity SwapPricing and Valuation of Forward Commitments Non-Arbitrage Principle●Arbitrage:在不同市场同时买卖相同资产并获利（低买高卖）.●Arbitrage opportunities:相同的东西卖不同的价格.●The no-arbitrage principle(Law of one price):不存在任何套利机会.●T he no-arbitrage principle 可以用来对衍生品进行定价。

FP=S 0×(1+R f )T●Cash-and-carry Arbitrage:正向套利。

If FP>S0×(1+Rf)TNon-Arbitrage PrincipleAt initiation At settlement date1.借钱S2.买资产3.Short一份远期合约1.把资产交割给long方2.获得FP的现金3.偿还本金和利息Profit=FP-S0×(1+R f)T●Reverse-cash-and-carry Arbitrage: 反向套利。

Essentials of Investments (BKM 5th Ed.)Answers to Suggested Problems – Lecture 7Bond Pricing Examples for Exam 3:Problem 9(a) in Chapter 9 provides an example of a bond price calculation (answer shown below). As additional examples, page 69 in your course packet provides several bond pricing problems for bonds with various maturity, yield, and coupon characteristics. The bond prices for these examples are as follows (note all bonds pay coupons semi-annually):8% coupon, 8% market yield, 10 years to maturity: B = $1,000.008% coupon, 10% market yield, 10 years to maturity: B = $875.388% coupon, 6% market yield, 10 years to maturity: B = $1,148.778% coupon, 8% market yield, 20 years to maturity: B = $1,000.008% coupon, 10% market yield, 20 years to maturity: B = $828.418% coupon, 6% market yield, 20 years to maturity: B = $1,231.156% coupon, 8% market yield, 10 years to maturity: B = $864.106% coupon, 10% market yield, 10 years to maturity: B = $750.766% coupon, 6% market yield, 10 years to maturity: B = $1000.00Chapter 9:4. Lower. Interest rates have fallen since the bond was issued. Thus, the bond is selling at apremium and the price will decrease (toward par value) as the bond approaches maturity.5. True. Under the Expectations Hypothesis, there are no risk premia built into bond prices.The only reason for an upward sloping yield curve is the expectation of increased short-term rates in the future.7. Uncertain. Liquidity premium will increase long-term yields, but lower inflationexpectations will reduce long-term yields compared to short-term rates. The net effect is uncertain.8. If the yield curve is upward sloping, you cannot conclude that investors expect short-terminterest rates to rise because the rising slope could either be due to expectations of future increases in rates or due to a liquidity premium.9. a) The bond pays $50 every 6 monthsCurrent price = $1052.42Assuming that market interest rates remain at 4% per half year:the price 6 months from now = $1044.52b) Rate of return = [1044.52 - 1052.42 + 50]/1052.42 = .04 or 4% per 6 months14. Zero 8% coupon 10% coupona) Current prices $463.19 $1,000 $1,134.20b) Price in 1 year $500.25 $1,000 $1,124.94change $37.06 $0.00 $-9.26PriceCouponincome $0.00 $80.00 $100.00$37.06 $80.00 $90.74incomeTotalRate of return 8.00% 8.00% 8.00%33. a) The forward rate, f, is the rate that makes rolling over one-year bonds equally attractiveas investing in the two-year maturity bond and holding until maturity:(1.08)(1 + f) = (1.09)2 which implies that f = 0.1001 or 10.01%b) According to the expectations hypothesis, the forward rate equals the expected shortrate next year, so the best guess would be 10.01%.c) According to the liquidity preference (liquidity premium) hypothesis, the forward rateexceeds the expected short-term rate for next year (by the amount of the liquiditypremium), so the best guess would be less than 10.01%.35. a. We obtain forward rates from the following table:Maturity(years)YTM Forward rate Price (for part c)($1000/1.10)1 10.0% $909.09[(1.112/1.10) – 1] $811.62 ($1000/1.112)12.01%2 11.0%[(1.123/1.112) – 1] $711.78 ($1000/1.123)14.03%3 12.0%b. We obtain next year’s prices and yields by discounting each zero’s face value at theforward rates derived in part (a):Maturity(years)Price YTM1 $892.78 [ = 1000/1.1201] 12.01%2 $782.93 [ = 1000/(1.1201 x 1.1403)] 13.02%Note that this year’s upward sloping yield curve implies, according to theexpectations hypothesis, a shift upward in next year’s curve.c.Next year, the two-year zero will be a one-year zero, and it will therefore sell at: ($1000/1.1201) = $892.78Similarly, the current three-year zero will be a two-year zero, and it will sell for $782.93. Expected total rate of return:two-year bond: %00.101000.0162.811$78.892$==− three-year bond: %00.101000.0178.711$93.782$==−37. d) 2e) 3f) 2g) 4Chapter 10:1. ∆∆B B D y y =−⋅+1 -7.194 * (.005/1.10) = -.03272.If YTM=6%, Duration=2.833 years If YTM=10%, Duration=2.824 years6.a) Bond B has a higher yield since it is selling at a discount. Thus, the duration of bond B is lower (it is less sensitive to interest rate changes).b) Bond B has a lower yield and is callable before maturity. Thus, the duration of bond B is lower (it is less sensitive to interest rate changes).9.a) PV = 10,000/(1.08) + 10,000/((1.08)2) = $17,832.65Duration = (9259.26/17832.65)*1 + (8573.39/17832.65)*2 = 1.4808 yearsb) A zero-coupon bond with 1.4808 years to maturity (duration=1.4808) would immunize the obligation against interest rate risk.c) We need a bond position with a present value of $17,832.65. Thus, the face value of thebond position must be:$17,832.65*(1.08)1.4808 = $19,985.26If interest rates increase to 9%, the value of the bond would be:$19,985.26/((1.09)1.4808) = $17,590.92The tuition obligation would be:10,000/1.09 + 10,000/((1.09)2) = $17,591.11or a net position change of only $0.19.If interest rates decrease to 7%, the value of the bond would be:$19,985.26/((1.07)1.4808) = $18,079.99The tuition obligation would be:10,000/(1.07) + 10,000((1.07)2) = $18,080.18or a net position change of $0.19.**The slight differences result from the fact that duration is only a linear approximationof the true convex relationship between fixed-income values and interest rates.11. a) The duration of the perpetuity is 1.05/.05 = 21 years. Let w be the weight of the zero-coupon bond. Then we find w by solving:w × 5 + (1 – w) × 21 = 1021 – 16w = 10w = 11/16 or .6875Therefore, your portfolio would be 11/16 invested in the zero and 5/16 in theperpetuity.b) The zero-coupon bond now will have a duration of 4 years while the perpetuity willstill have a 21-year duration. To get a portfolio duration of 9 years, which is now theduration of the obligation, we again solve for w:w × 4 + (1 – w) × 21 = 921 – 17w = 9w = 12/17 or .7059So the proportion invested in the zero has to increase to 12/17 and the proportion in theperpetuity has to fall to 5/17.12. a) The duration of the perpetuity is 1.1/.1 = 11 years. The present value of the payments is$1 million/.10 = $10 million. Let w be the weight of the 5-year zero-coupon bond andtherefore (1 – w) will be the weight of the 20-year zero-coupon bond. Then we find wby solving:w × 5 + (1 – w) × 20 = 1120 – 15w = 11w = 9/15 = .60Therefore, 60% of the portfolio will be invested in the 5-year zero-coupon bond and 40%in the 20-year zero-coupon bond.Therefore, the market value of the 5-year zero must be×.60 = $6 million.$10millionSimilarly, the market value of the 20-year zero must be$10× .40 = $4 millionmillionb) Face value of the 5-year zero-coupon bond will be× (1.10)5 = $9.66 million.$6millionFace value of the 20-year zero-coupon bond will be$4 million × (1.10)20 = $26.91 million.18. a) 4b) 4c)42d)21. Note that we did not discuss swaps in detail. For that reason, I would not expect you to beable to answer this type of question on the exam. The question is meant to provide youwith a brief summary of some potential motivations for swaps.a) a. This swap would have been made if the investor anticipated a decline in long-terminterest rates and an increase in long-term bond prices. The deeper discount, lowercoupon 6 3/8% bond would provide more opportunity for capital gains, greater callprotection, and greater protection against declining reinvestment rates at a cost of only amodest drop in yield.b. This swap was probably done by an investor who believed the 24 basis point yield spreadbetween the two bonds was too narrow. The investor anticipated that, if the spreadwidened to a more normal level, either a capital gain would be experienced on theTreasury note or a capital loss would be avoided on the Phone bond, or both. Also, thisswap might have been done by an investor who anticipated a decline in interest rates, andwho also wanted to maintain high current coupon income and have the better callprotection of the Treasury note. The Treasury note would have unlimited potential forprice appreciation, in contrast to the Phone bond which would be restricted by its callprice. Furthermore, if intermediate-term interest rates were to rise, the price decline ofthe higher quality, higher coupon Treasury note would likely be “cushioned” and thereinvestment return from the higher coupons would likely be greater.c. This swap would have been made if the investor were bearish on the bond market. Thezero coupon note would be extremely vulnerable to an increase in interest rates since theyield to maturity, determined by the discount at the time of purchase, is locked in. This isin contrast to the floating rate note, for which interest is adjusted periodically to reflectcurrent returns on debt instruments. The funds received in interest income on the floatingrate notes could be used at a later time to purchase long-term bonds at more attractiveyields.d. These two bonds are similar in most respects other than quality and yield. An investorwho believed the yield spread between Government and Al bonds was too narrow wouldhave made the swap either to take a capital gain on the Government bond or to avoid acapital loss on the Al bond. The increase in call protection after the swap would not be afactor except under the most bullish interest rate scenarios. The swap does, however,extend maturity another 8 years and yield to maturity sacrifice is 169 basis points.e. The principal differences between these two bonds are the convertible feature of the Zmart bond and the yield and coupon advantage, and the longer maturity of the LuckyDucks debentures. The swap would have been made if the investor believed somecombination of the following: First, that the appreciation potential of the Z martconvertible, based primarily on the intrinsic value of Z mart common stock, was nolonger as attractive as it had been. Second, that the yields on long-term bonds were at acyclical high, causing bond portfolio managers who could take A2-risk bonds to reach forhigh yields and long maturities either to lock them in or take a capital gain when ratessubsequently declined. Third, while waiting for rates to decline, the investor will enjoyan increase in coupon income. Basically, the investor is swapping an equity-equivalentfor a long- term corporate bond.23. Choose the longer-duration bond to benefit from a rate decrease.a) The Aaa-rated bond will have the lower yield to maturity and the longer duration.b) The lower-coupon bond will have the longer duration and more de facto call protection.c) Choose the lower coupon bond for its longer duration.30. The price of the 7% bond in 5 years is:PVA(C=$70, N=25, r=8%) + PV($1000, N=25, r=8%) = $893.25You also get five $70 coupon payments four of which can be reinvested at 6% for a total of $394.59 in coupon income.HPR = ($893.25 - 867.42 + 394.59)/867.42 = 48.47%The price of the 6.5% bond in 5 years is:PVA(C=$65, N=15, r=7.5%) + PV($1000, N=15, r=7.5%) = $911.73You also get five $65 coupon payments four of which can be reinvested at 6% for a total of $366.41 in coupon income.HPR = ($911.73 - 879.50 + 366.41)/879.50 = 45.33%**The 7% bond has a higher 5-year holding period return.。

高考英语听力必备场景词汇精选听力的短对话和长对话部分，其话题范围涉及学习、工作、衣食住行等场景。

英语是模式化的语言，固定场景只会用固定词汇，所以分场景总结记忆听力词汇，效果更佳。

A.校园1. subject n. 学科2. major n. 专业3. course n. 课程4. math/maths/mathematics 数学5. physics n. 物理6. chemistry n. 化学7. biology n. 生物8. politics n.政治9. history n.历史10. geography n.地理11. computer n. 电脑12. literature n.文学13. art n. 艺术14. P.E.（physical education） n. 体育15. science n. 科学16. middle-term exam n. 期中考试17. final exam n. 期末考试，18. test n. 测验19. quiz n. 小测验20. marks/grades 分数21. homework/assignment n. 家庭作业22. task n. 任务23. lecture n. 演讲24. text book 课本25. campus n. 校园26. public school 公立学校，27. private school 私立学校，28. term/semester 学期29. president/headmaster/principal 校长，30. professor 教授31. lecturer 讲师32. primary school student小学生33. middle school student中学生34. freshman 大一新生35. monitor n. 班长36. assistant n. 助手，助理37. scholarship 奖学金38. tuition n. 学费39. classroom n. 教室40. playground n. 操场41. dormitory n.寝室42. dining-hall n. 食堂，餐厅43. lab/laboratory n. 实验室44. library n. 图书馆45. language lab 语音室46. reading room 阅览室46. Bachelor’s degree 学士学位47. Master’s degree 硕士学位48. Doctor’s degree 博士学位49. Students’ card 学生证50. have a lesson 上课51. cut a class 逃课52. be absent from class 缺课53. preview vt. 预习54. go over/review vt 复习55. take an exam 参加考试56. pass the exam 考试及格57. fail(in) the exam 考试不及格58. take part in the English Speech contest参加英语演讲比赛B. 图书馆1. library n. 图书馆2. librarian n. 图书管理员3. library card借书证4. bookshelf n.书架5. author/writer 作者/作家6. novel小说7. story-book故事书8. picture book图画书9. science fiction科幻小说10. newspaper报纸11. magazine杂志12. reference book参考书13.borrow books借书14. keep the books for two weeks 书借两周15. renew vt 续借16. return the books 还书17. overdue借书逾期18. pay a fine 交罚款C.交通运输1. means transportation 交通工具2. by plane/airplane/air 乘飞机3. by train/express train 乘火车/特快列车4. by taxi/cab 乘出租车5. by bus 乘公交车6. by coach 乘长途汽车7. by bike /bicycle 乘自行车8. by boat/ship/sea 乘船9. by subway/underground 乘地铁10. walk/on foot 步行11. airport n. 机场12. railway station /train station 火车站13. subway station 地铁站14. bus stop 公交站点15. booking office/ticket office 售票处16. waiting room 候车室17. platform 站台18. fare 车费19. ticket 罚单，车票20. driver’s license 驾照21. driver n. 司机22. conductor n. 售票员23. passenger 乘客24. policeman 警察25. officer n. 警官26. pedestrian/passer-by 路人，行人27. garage 修车库29. parking lot 停车场30. tunnel 隧道31. carriage 车厢32. express way/high way 高速公路33. one way street 单行道34. sidewalk/pavement 人行道35. rush hours 交通高峰期36. traffic jam 交通堵塞37. traffic rules 交通规则38. traffic lights 交通灯39. heavy traffic 拥挤的交通40. car accident 事故41. over speed 超速42. run the red light 闯红灯43. park vt. 停车44. give sb a ride让某人搭便车45. break down汽车抛锚46. flat tire爆胎47. fix/repair修理48. depart vi 出发 departure n.出发49. see sb off 给某人送行50. meet sb/pick sb up 接某人51. drop sb off 中途载某人D.机场1. airport 机场2. flight 航班3. flight number航班号4. Welcome on board 欢迎登机5. plane/airplane 飞机6. book a ticket 订票7. one way ticket 单程票8. round trip ticket 往返票9. timetable 时间表10. destination 目的地11. nonstop/direct flight 直航12. take off 起飞13.departure time 起飞时间14. check in 登记15. boarding card 登机牌16. security check 安检，17. fasten the safety / seat belt 系好安全带18. land 着陆19. behind schedule 晚点20. cancel 取消21. luggage/baggage 行李22. suitcase 行李箱23. passport 护照24. visa 签证25. captain 机长26. pilot 飞行员27. flight attendant/airhostess 空姐28. first class/business class/economy cabin头等舱/商务舱/经济舱D.电话1. telephone 电话2. mobile phone/cellphone 手机3. smartphone 智能手机4. pay phone 公用电话5. telephone box/booth 电话亭6. operator 接线员7. long-distance call 长途电话,8. answering machine留言机9. put/get through 接通电话10. dial the wrong number拨错号码11. hold on/hang on 不要挂断12. hang up 挂断13. leave a message 留言14. take a message 捎口信15. charge vt. 充电16. give sb a call / ring 给某人打电话17. The line is bad/ busy / engaged. 电话占线18. Who’s speaking?/Who’s that? 请问是哪位？19. Hello! This is …speaking 喂，我是。

统计学Reading 11 相关和回归Reading 12 多元线性回归1. 相关分析:1) 协方差和相关系数的计算;2) 相关系数的检验(ρ = 0): t = r ((n - 2) / (1 – r2))1/2, df = n – 2.2. 线性回归:1) 模型及假设, dependent variable (Y) and independent variable (X).2) 参数估计(min SSE): b i = Cov(X i, Y) / Var(X i), b0 = E(Y) –Σb i * E(X i).3) 回归系数的置信区间和统计检验: t = (b i–βi) / s bi, df = n – k – 1.注：k为independent variable的数目, 不要求计算标准误s bi.3. 线性模型的显著性检验:1) Total sum of squares (SST) = Σ(Y – E(Y))2, Y –观测值;Regression sum of square (RSS) = Σ(y – E(Y))2, y –拟合值;Sum of squared error (SSE) = Σ(Y - y)2;SST = RSS + SSE.2) 方差分析表(ANOV A):Source of variation Sum of squares Degree of freedom Mean sum of square Regression RSS k (# independent variable) MSR = RSS / k Error SSE n – k – 1 MSE = SSE / (n – k -1) Total SST n – 1 Var(Y) = SST / (n - 1)Standard error of estimate SEE = (MSE)1/2.3) Determination coefficient R2 = RSS / SST,Adjusted R2 = 1 – (n - 1)/(n – k - 1) * (1 – R2): adjust the impact of additional variables.4) F-检验：F = MSR / MSE, df = (k, n – k - 1).4. 模型前提假设的检验:1) Heteroskedasticity:A) Effect :Unconditional: heteroskedasticity is unrelated to the level of X, no major problem;Conditional: coefficient estimates are not affected, but s.e. and F-test are unreliable.B) Detecting:a) Residual plot: residual = actual – predicted.b) Breusch-pagan test (H0: no heteroskedasticity):n * R resid2 ~ χ2(k), 其中R resid2是residual对X回归的决定系数.C) Correcting: using robust or corrected s.e.2) Serial correlation: residual terms are correlated with each other:A) Effect:Positive serial correlation: underestimating s.e., unreliable F-test;Negative serial correlation: overestimating s.e., unreliable F-test.B) Detecting:a) Residual plot.b) Durbin-Watson test (H0: no serial correlation):DW ≈ 2(1 - r), 其中r是残差的自相关系数, 0 ≤ DW ≤ 4.C) Correcting: corrected s.e. for both serial correlation and heteroskedasticity.3) Multicollinearity: independent variables are highly correlated with each other:A) Effect: individual variables are not significant (large s.e.) but their combination is.B) Detecting:a) None of individual coefficient is significant, but F-test is.b) Correlations between variables (> 0.7).注：两变量间的相关系数并未考虑变量线性组合的相关性，因此低相关系数并不一定意味着不存在multicollinearity.C) Correcting: omit correlated variables or take stepwise regression.4) Model misspecification: 不合适地选取解释变量（实际意义不对或不满足线性模型的前提假设）或不恰当的变量转换等.5. Dummy variable (0 – 1 variable):1) Independent dummy variable: linear regression is appropriate.注：n classes → (n - 1) dummy variable.2) Qualitative dependent variable (Y取0, 1): ordinary regression may not be appropriate, use logit regression model or discriminate model.Reading 13 时间序列分析1. Trend model:1) Linear: x t = b0 + b1t + εt;2) Log-linear: ln(x t) = b0 + b1t + εt, 常用于为增长率建模.2. Autoregressive model (AR):1) AR(p): x t = b0 + b1x t-1 + … + b p x t-p + εp, lag: 1, … , p.2) Covariance stationarity:a) Constant and finite E(X t): mean-reverting level for AR(1) E(X t) = b0 / (1 – b1).Random walks (unit root process): x t = b0 + x t-1 + εt不是平稳过程.b) Constant and finite Var(X t);c) Constant and finite Cov(X t, X t-k):对AR平稳序列, 自相关系数Cor(X t, X t-k) = ρk→ 0.3) Forecasting:a) In-sample (within the range of data) and out-sample forecasts.b) Short time series: more stable (no dramatic change);Long-time series: more reliable.c) Predicting power: root mean squared error (RMSE) on the out-sample data.3. AR模型的检验与修正:1) Nonstationarity:a) Detecting: Dickey-Fuller (DF) test or unit root test:For AR(1): x t– x t-1 = b0 + (b1 - 1)x t-1 + εt, H0: b1 = 1, t-test with modified s.e.b) Correcting - differencing:For random walks: 令y t = x t– x t-1, 有y t = b0 + εt.2) Serial correlation (residual terms should not exhibit serial correlation):a) Detecting:H0: Cor(εt, εt-k) = 0 for any lag k; t = Cor(εt, εt-k) / (1 / T) 1/2, df = T – p - 1.注: T – number of effective observations, T = n – p.一般线性回归中的DW检验不适用于AR模型。

THE JOURNAL OF FINANCE•VOL.LV,NO.1•FEBRUARY2000The Cost of Diversity:The Diversification Discount and Inefficient InvestmentRAGHURAM RAJAN,HENRI SERVAES,and LUIGI ZINGALES*ABSTRACTWe model the distortions that internal power struggles can generate in the allo-cation of resources between divisions of a diversified firm.The model predicts thatif divisions are similar in the level of their resources and opportunities,funds willbe transferred from divisions with poor opportunities to divisions with good op-portunities.When diversity in resources and opportunities increases,however,re-sources can f low toward the most inefficient division,leading to more inefficientinvestment and less valuable firms.We test these predictions on a panel of diver-sified U.S.firms during the period from1980to1993and find evidence consistentwith them.T HE FUNDAMENTAL QUESTION IN THE THEORY of the firm,raised by Coase~1937! more than60years ago,is how decisions taken inside a hierarchy differ from those taken in the marketplace.Coase suggested that decisions within a hierarchy are determined by power considerations rather than relative prices.If this is indeed the case,why,and when,does the hierarchy domi-nate the market?A major obstacle to progress in this area has been the lack of data.Data on internal decisions made by firms are generally proprietary.Even when they are available to researchers,it is difficult to find a comparable group of decisions taken in the market.A notable exception is the capital allocation decision in diversified firms.Since1978,public panies have been forced to disclose their data on sales,profitability,and investments by major lines of business~segments!.An analysis of a small sample of multisegment firms reveals that segments correspond,by and large,to distinct internal *Rajan is from the University of Chicago,Servaes is from the London Business School and University of North Carolina at Chapel Hill,and Zingales is from the University of Chicago. Rajan and Zingales acknowledge financial support from the Center for Research on Security Prices at the University of Chicago.Servaes acknowledges financial support from the O’Herron and McColl faculty fellowships,University of North Carolina at Chapel ments from Sugato Bhattacharya,Judy Chevalier,Glenn Ellison,Milton Harris,Steven Kaplan,Owen La-mont,Colin Mayer,Todd Milbourn,Vikram Nanda,Jay Ritter,RenéStulz,Robert Vishny,Ralph Walkling,Wanda Wallace,two anonymous referees,and especially Mitchell Petersen are grate-fully ments from participants in seminars at AT Kearney~London!,the University of Chicago,Cornell University,the University of Georgia,the University of Florida, the University of Illinois,the London School of Economics,New York University,Northwestern University,Ohio State University,the College of William&Mary,Vanderbilt University,and Yale University were useful.3536The Journal of Financeunits of the firm.Since the investment decision is perhaps the most impor-tant of corporate decisions,these data allow researchers an opportunity to compare decisions taken by units within hierarchies with decisions taken by independent units in the same industry,and thus obtain insights on how hierarchies and markets differ.Previous research~Lamont~1997!and Shin and Stulz~1998!!has shown that resource allocation in diversified firms does appear different from that in focused firms and seems to ignore traditional market indicators of the value of investment such as Tobin’s q.Moreover,there seems to be a con-nection between resource~mis!allocation and the value of diversified firms. Berger and Ofek~1995!find that investment by diversified firms in seg-ments that have low q is correlated with the discount at which these firms trade.So perhaps such misallocation explains why diversified firms trade, on average,at a discount relative to a portfolio of single-segment firms in the same industries~Lang and Stulz~1994!,Berger and Ofek~1995!,Ser-vaes~1996!,Lins and Servaes~1999!!.But these facts simply heighten the puzzle.What is it in a hierarchy that makes diversified firms misallocate funds?Moreover,what accounts for the wide dispersion in diversified firm values,with fully39.3percent trading at a premium in1990?1To answer these questions,we first need a theoretical framework to un-derstand the phenomenon.At least three kinds of models have been pro-posed to explain how the divisions of diversified firms behave differently from stand-alone firms.Efficient Internal Capital Market models typically suggest that diversification creates value.By forming an internal capital market where the internally generated cash f lows can be pooled,diversified firms can allocate resources to their best use~e.g.,see Li and Li~1996!, Matsusaka and Nanda~1997!,Stein~1997!,Weston~1970!,and Williamson ~1975!!.2Clearly,these models do not explain the misallocation of resources to divisions with poor opportunities.Agency cost models have sometimes been offered as explanations for the potential investment distortions in diversified firms.Because top manage-ment in the diversified firm has greater opportunities to undertake projects, and potentially greater resources to do so if diversification relaxes con-straints imposed by imperfect external capital markets,it might overinvest1Also,the evidence on the value of diversification,as indicated by the stock price reaction to the decision to diversify,is decidedly mixed.Morck,Shleifer,and Vishny~1990!show that acquiring firms in the1980s experience negative returns when they announce unrelated ac-quisitions.John and Ofek~1995!find that announcement returns are greater when diversified firms in the late1980s announce asset sales that increase focus.By contrast,Schipper and Thompson~1983!document positive announcement period returns when conglomerates an-nounced acquisition programs in the1960s,and Matsusaka~1993!and Hubbard and Palia ~1999!find positive returns to announcements of diversifying acquisitions in the1960s and 1970s during the conglomerate merger wave.2Also see Billett and Mauer~1997!,Denis and Thothadri~1999!,Gertner,Scharfstein,and Stein~1994!,Milbourn and Thakor~1996!,and Harris and Raviv~1996,1997!for other recent papers on the costs,benefits,and workings of internal capital markets.The Cost of Diversity37 resources~e.g.,see Stulz~1990!and Matsusaka and Nanda~1997!!.Though we believe that agency theories could explain generic overinvestment—for example,the decision to diversify could be viewed as an attempt by the CEO to entrench herself~e.g.,Shleifer and Vishny~1989!!—it is more difficult to see how these theories could explain the internal misallocation of funds;the CEO should exploit all potential sources of value inside the firm,skimming her agency rents only from the overall pie.Inf luence cost models are a third class of models that attempt to explain the decisions of diversified firms.In Meyer,Milgrom,and Roberts~1992!, managers of divisions that have a bleak future have an incentive to attempt to inf luence the top management of the firm to channel resources in their direction.Of course,in the spirit of inf luence cost models,top management sees through these lobbying efforts.Thus,no resources are,in fact,misal-located to the divisions,though costs are incurred in lobbying activities.As a result,it is again hard to explain the evidence on misallocation with these models.3Since existing theories need substantial embellishment to explain the mis-allocation of funds in diversified firms and the cross-sectional variation in value,Occam’s Razor suggests a different approach.We develop a model of capital allocation under two basic assumptions.First,headquarters has lim-ited power over its divisions:it can redistribute resources ex ante,but it cannot commit to a future distribution of surplus.Second,surplus is distrib-uted among divisions through negotiations,and divisions can affect the share of surplus they receive through their choice of investment.4Questions of how the power to take decisions,or capture surplus,is distributed within the firm then become central to determining whether the firm does better or worse than the market.A brief description of our model may help fix ideas.We assume that the diversified firm consists of two divisions,each led by a divisional manager. Each manager starts with an endowment of resources that the headquarters can either transfer to the other division or leave in place.The retained re-sources can be invested in one of two projects:an“efficient”investment and a“defensive”investment.The former is the optimal investment for the firm in a world where all contracts can be perfectly enforced.The latter offers lower returns,but protects the investing division better against poaching by the other division.53Hard,though not impossible.The prospect of enhanced inf luence costs can lead to changes, ex ante,in real decisions like allocations or organizational structure.These ideas have been separately explored in Fulghieri and Hodrick~1997!,Scharfstein and Stein~1997!,and Wulf ~1997!.As we will argue later,the precise nature of the misallocation we document is hard to reconcile with inf luence cost models.4Our model is best characterized as a model of power-seeking,and is most related to papers by Shleifer and Vishny~1989!,Skaperdas~1992!,Hirshleifer~1995!,and Rajan and Zingales ~2000!.5That managers have a choice between investments that alter their power is well recognized in the literature;see Shleifer and Vishny~1989!and Stole and Zwiebel~1996!.38The Journal of FinanceDivisional managers have autonomy in choosing investments and are self interested.Even though the efficient investment maximizes firm value, a divisional manager may prefer the defensive investment that would ben-efit her more directly,especially when her resources and opportunities are much better than the other division’s.The reason is quite simple.Once the divisional manager makes the unprotected,albeit efficient,investment,she will have to share some of the surplus created with the other division.Of course,if the other division also makes the efficient investment,our man-ager will get a piece of the surplus created by the other division.If the surplus created by the other division is not too small relative to what she is giving up,the divisional manager will prefer the efficient investment. Thus appropriate incentives are created for both divisions only when they do not differ too much in the surplus—which is the product of resources and opportunities—they create.Diversity in resources and opportunities is costly for investment incentives.Clearly,the investment distortions would not arise if headquarters could design precise rules to share ex post surplus.In practice,sharing rules are likely to be determined by factors other than considerations of ex ante optimality—such as the ex post bargaining power of the divisions. Although headquarters cannot contract on how divisions will share the surplus ex post,it can transfer funds ex ante.Some transfers will certainly be made because one division has better opportunities than the other.If stand-alone divisions face imperfect capital markets and cannot borrow as much as they need,the transfers to deserving divisions~“winner-picking”in Stein’s~1997!felicitous language!is one way the diversified firm adds value.But transfers will also be made so as to improve the incentives to un-dertake the efficient investment.Since incentives are distorted away from the optimal because of diversity~of opportunities and resources!,transfers will be made in a direction that makes divisions less diverse—from divi-sions that are large and have good opportunities to divisions that are small and have poor investment opportunities.Thus,the diversified firm may misallocate some funds at the margin~relative to the first-best!to prevent greater average investment distortions.The more diverse a firm’s divisions are,the greater the need to reallocate funds in this way.Thus corporate redistribution may be a rational second-best attempt to head off a third-best outcome.We are not the first to argue that politics inf luences investment decisions in firms.6However,our simple model of internal capital allocation based on power considerations has the advantage of identifying a clear proxy for what6For example,Chandler~1966,p.166!describes the capital budgeting process at General Motors under Durand’s management in the following way:“When one of them@Division Man-agers#had a project why he would vote for his fellow members;if they would vote for his project,he would vote for theirs.It was a sort of horse trading.”The Cost of Diversity39 drives inefficient allocations:the diversity of investment opportunities and resources among the divisions of the firm.Moreover,it offers detailed test-able implications on the direction of f lows between divisions.We test the implications of the theory for a panel of diversified U.S.firms during the period1980to1993using the segment data on COMPUSTAT. Our theory suggests that whether a segment receives or makes transfers in a diversified firm depends not so much on its opportunities~proxied for by Tobin’s q)as on its size-weighted opportunities,and the way these are dis-persed across segments in that firm.We show that our theory has a greater ability to predict internal capital allocation than the Efficient Internal Mar-ket theory.Moreover,allocations toward the relatively low q segments of a diversified firm,on average,outweigh allocations to its relatively high q segments as the dispersion in weighted opportunities~which we call diver-sity!increases.Of course,this may simply ref lect the channeling of funds to low q seg-ments that are inefficiently being rationed by the market.For this reason, we test the relationship between diversity and value.We find the greater the diversity,the lower the diversified firm’s value relative to a portfolio of single-segment firms.This effect persists even after we correct for the ex-tent to which the diversified firm is focused in specific industries,so our measure of diversity captures something different from traditional measures of diversification.The empirical results,taken together,provide striking evidence that diver-sity in investment opportunities between segments within firms leads to dis-torted investment allocations and hence value differences between diversified firms.Diversified firms can trade at a premium if their diversity is low.As a case in point,General Electric,perhaps the most admired U.S.conglomerate, is at the8th percentile of our sample over the entire sample period in terms of diversity,and at the75th percentile in terms of relative value.More generally,we believe that our evidence sheds light on how decisions within firms can differ from decisions made in markets.A firm is a collec-tion of commonly held,and mutually specialized critical resources.7Though the common control of key resources gives certain agents in the firm the power to shape transactions that would otherwise not be possible in the marketplace~such as the transfer of resources!,the absence of a clear de-marcation to property rights within the firm can create inefficient power struggles~also see Rajan and Zingales~1998a!!.Thus,our finding that a measure of the distortions created by power~i.e.,diversity!relates to the discount diversified firms trade at suggests,first,that the use of power may indeed explain why transactions within firms are different from transac-tions in markets and,second,that neither hierarchies nor markets need dominate.Coase’s emphasis on power is far from empty!7See Kumar,Rajan,and Zingales~1999!for a more detailed exposition of Critical Resource theories of the firm.40The Journal of FinanceThe rest of the paper is organized as follows.In Section I we present the framework of our simple stripped-down model.In Section II we derive some testable implications from the model.Section III describes the sample,the tests,and the results.Conclusions follow.I.The ModelWe want to analyze resource allocation in diversified firms.Therefore,we focus on firms operating in different lines of business.For the purposes of our analysis,the distinction between vertically integrated divisions and un-related divisions is unimportant.In fact,the distortions we want to study may arise whenever different organizational units operate within the same hierarchy,so long as at least one dimension of their operations~e.g.,raising and allocating resources!is integrated.Our model,therefore,does not apply to a leveraged buyout fund,where each subunit is a firm that operates sep-arately from the other subunits on every dimension,including financing~see Jensen~1989!!.A.TimingConsider a world with four dates,0,1,2,and3.A firm is composed of two divisions,A and B,each of which is headed by a manager who,for simplicity, will be thought of as representing the entire human capital of her division. Each manager wants to maximize the surplus that accrues to her division at date2.We assume,by contrast,that headquarters maximizes the surplus created by the entire firm.8The two divisions interact on three dimensions.At date0,the headquar-ters can reallocate resources between the two divisions.At date1,divisions choose investments.The type of investment chosen affects the“property right”a division has on the cash f low produced because,depending on it,a division may have the opportunity to poach on the surplus created by the other division.At date2,the divisions split the total surplus according to their relative power.Everything is predetermined at date3:Production takes place and surplus is shared according to the date2contract.So date 3is only for completeness.To summarize,the sequence of events is pre-sented in Figure1.We now detail the interactions on the previous three dates.8In Rajan,Servaes,and Zingales~1997!,we model this more precisely by assuming that headquarters controls the physical assets of the firm~which are crucial for production!,and thus gets a share of the total surplus in bargaining with the divisions.If we assume that headquarters first bargains with the divisions after which the divisions further subdivide the surplus,headquarters will always get a constant share of the surplus,and hence has an in-centive to maximize the surplus created by the firm.The Cost of Diversity41Figure1.Timing of the events.B.Resources and TransfersEach division j starts with an initial endowment of resources,l0j,that can be invested.We assume that these resources include any potential borrow-ing from outside.The initial level of resources could also be thought of as the resources the division would be able to invest if it were a stand-alone firm. The quantity of these resources are assumed to be limited despite unlimited investment opportunities~see later!because external capital markets are imperfect.For simplicity,we assume that headquarters can transfer all of a divi-sion’s resources to the other,though we will see that in equilibrium it will not always choose to do so.The total resources division A has available for investment at date1is then l1Aϭl0AϪt,and division B has l1Bϭl0Bϩt.C.InvestmentEach division can allocate its date1resources,l1j,to one of two kinds of investments.One investment is technologically efficient in that it maximizes returns;however,it leaves the surplus exposed to potential expropriation by the other division.Alternatively,the division could make a defensive invest-ment,which protects the surplus created at the cost of lower returns. Some examples are useful to fix ideas.The protective investment could be overly specialized~as in Shleifer and Vishny~1989!!so that only the division knows how to run it.This prevents the project from ever being turned over to the other division.Moreover,the durable resources employed on the project, such as employees,would also become so specialized that they could never be poached by the other division.Of course,the excess specialization would reduce the returns of such a project relative to a more general investment that could be subject to interference by the other division.The protective investment could reduce a division’s dependence on the other division.One of the authors once worked in a commercial bank with three subunits.One subunit had leased dedicated long-distance telephone lines to connect its representatives in each of the bank’s branches.The lines were barely used and since the subunits shared space in the branches,it would have been a simple matter for the other subunits to share access to the lines and also connect their representatives.Rather than spending resources to42The Journal of Financeaugment the common usage of the existing lines~efficient!,the other sub-units decided to lease their own lines~protective!because they felt their dependence on the first subunit would compromise their ability to bargain over issues such as transfer prices for funds.The protective investment could be one that stays within the well-defined turf of a division,even though it is efficient for the division to venture out.Bertelsmann,the German conglomerate,had separate divi-sions for publishing and new media.The development of book sales through the Internet provided a wonderful opportunity to the book division,as well as a substantial threat to its existing business.Yet the book division ig-nored the opportunity,preferring to focus on book sales through traditional channels,which were clearly its protected turf,and ignoring the efficient Internet investment that could well become part of the new media divi-sion’s empire.9Let the gross return at date3per dollar invested in efficient investment at date1be a j.Since defensive investments are wasteful of resources,the gross return to them is then a jϪg,where g is a positive quantity.To tie our hands,we assume that there are no savings or diseconomies from joint production.We only assume that if two divisions are under common ownership,resources can be reshuff led between the two.As we shall show,this reshuff ling has a positive side~the possibility that re-sources can be reallocated to their highest value use as in Stein~1997!! and a negative side~that a division may distort its investment in order to obtain“property rights”in the surplus it creates!.Thus,both the benefits and costs of a diversified firm spring from the same source:the use of power rather than arm’s length contracts to govern transactions within the firm.D.ContractibilityAccounting controls can ensure that the funds transferred to a division are invested,but a division~and the headquarters!cannot contract on the type of investment that is to be made by the other division.Myers~1977!has a detailed discussion as to why it is difficult to contract on investment;the nature of the“right”physical investment is based on the division’s judgment about the state,which is hard to specify ex ante or verify ex post.Also,much of the investment may not be in physical assets but may enhance the divi-sion’s human capital which,again,is hard to contract upon.We also make another assumption that is standard in the incomplete con-tract literature~see Grossman and Hart~1986!!:The surplus that is to be produced at the final date cannot be contracted on before date2because the state will be realized then and the state-contingent surplus that will be pro-9See the survey in The Economist,November211998,p.10.The Cost of Diversity43 duced may be hard to specify up front.As shown by Hart and Moore~1999!, this incompleteness of long-term contracts can be rationalized in a world where all contracts can be renegotiated.At date2,however,after the uncertainty about the state that will prevail is resolved,it is possible to strike deals,after bargaining,over the division of date3cash f low.Date3is separated from date2only for expositional convenience,and these dates could be thought of as very close together so that the deals could be thought of as enforceable spot deals.E.Date2PayoffsA divisional manager who chooses the defensive investment ensures that the surplus his division creates is well protected against any actions by the other division.Moreover,since the investment does not consume all his time and resources,he can attempt to poach on the surplus created by the other division if the other division made the efficient,albeit unprotected, investment.Thus,if each divisional manager chooses the defensive investment,there is no room for power seeking inside the firm and each division will retain its product—that is,~a jϪg!l1j.If one divisional manager,say A,chooses the defensive investment and B does not,then A will have the opportunity of trying to grab some of B’s surplus.If A attempts such a grab,B can defend himself,but at substan-tially greater cost than if he had chosen the defensive investment up front. Specifically,a fraction of the surplus produced by B is dissipated in ex post jockeying for advantage.The payoff B gets is then~a BϪu!l1B where u.g. For simplicity,we assume that the surplus division A grabs is almost fully matched by its cost of poaching,and it gets~a AϪg!l1Aϩe where e is a small number.Finally,if both divisional managers choose the technologically efficient investment,both are fully involved in productive activity,and neither has the time to poach.Of course,knowing this,neither bothers to defend.Thus, when both divisions choose the efficient investment,dissipation will be avoided and we assume the total surplus~a A l1Aϩa B l1B!is split equally between the two divisions.10The assumption of equal split is not crucial.We will discuss the robustness of the result to changes in this assumption in Section II.D.1110That headquarters does not get any of the surplus is only for simplicity.None of our results would be changed if headquarters gets a constant fraction of the surplus because of its control of the firm’s physical assets~see footnote7!.11It is possible to formalize all this.For example,let poaching consume real resources.Skaper-das~1992!shows that when the opportunity cost of poaching is high,cooperation~i.e.,no poach-ing!is an equilibrium.When division A makes the defensive investment and division B does not,A’s opportunity cost of poaching is low since the defensive investment has low returns.By contrast,when A makes the efficient investment,the opportunity cost of poaching is high,and both divisions would be content not to poach.44The Journal of FinanceF.First BestIdeally,all the resources should be transferred to the division with the highest return a j.12This division should allocate all the resources to the efficient investment.As we will show,resources may not all be transferred to the division with the highest use for them because such a transfer can destroy the division’s incentive to make the efficient investment.In what follows,we will examine how transfers and allocations are distorted away from the first-best.II.Equilibrium ImplicationsGiven the anticipated payoffs from date2bargaining,at date1division j ~jʦA,B!has the incentive to make the efficient investment if division k is expected to do so,and1Ϫ@a j l1jϩa k l1k#Ն~a1jϪg!l1j.~1!2Since a similar inequality should hold for division k also,both divisions have the requisite incentives if1Ϫ@a j l1jϩa k l1k#ՆMax@~a1jϪg!l1j,~a1kϪg!l1k#.~2!2It is easily checked that this is a necessary and sufficient condition for the efficient investment to be an equilibrium at date1.Now let us effect a sim-ple change of variables so that b jϭa jϪg.Furthermore,without loss of generality,let b j l1jՆb k l1k.Then the right-hand side of inequality~2!sim-plifies to b j l1j and the whole expression can be rewritten asg~l1jϩl1k!Ն~b j l1jϪb k l1k!.~3!For a fixed total amount of resources,~l1Aϩl1B!,this inequality implies that the product of resources and potential returns cannot be too diverse across divisions.The intuition is straightforward.Division j~which is the division that can contribute the most to surplus in the following period!will choose the effi-cient investment only if division k contributes enough surplus to make it worthwhile.Division k will not be able to contribute enough if its resource-weighted opportunities,b k l1k,are small relative to j’s.If so,division j will not make the efficient investment,and neither will k.Therefore,too much diversity in potential contributions to the common pool will lead to a break-12Of course,in practice,returns will not be constant with scale.Some resources will be retained by the division with lower a j so as to undertake essential investments such as maintenance.。