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“Equity Premium Puzzle”(Mehra and Prescott, 1985)“The difference between the return on stocks and the return on a risk-free asset such as treasury bills is called the equity premium. [...] The fact that it is too large to be explained by standard economic models is called the equity premium puzzle.” (Siegel und Thaler, 1997, p. 192).Eine Anlage von $ 1000 im Jahr 1925 wäre 1995 wert gewesen: •=$ 12,720 (bei Anlage in Treasury bills).•=$ 842,000 (bei Anlage in Aktien).Warum lässt sich das nur schwer mit Standardmodellen erklären?Wieder beginnt man mit der Eulergleichung (1) und nimmt nun zusätzlich an, dass die Nutzenfunktion der CRRA-Klasse entstammt. Somit:)])1[(1111θθρ−++−++=t i t t t C r E C Das lässt sich umschreiben als:tt t c t c t i t C C C gg r E −=+=++++−++1111 ei wob ,1])1)(1[(ρθMittels einer Taylor-Approximation zweiter Ordnung (siehe unten) kann man dies schreiben als (unter Weglassung der Zeitindices):)()1(21),(][][c ci c i g Var g r Cov g E r E +−++≈θθθθρ Für ein risikoloses Asset kann man schreiben:)()1(21][c cg Var g E r +−+≈θθθρ Das führt zu:Relative Risikoaversion Risikoprämie Kovarianz von Konsum-wachstum und Aktienrenditen [] (,)i i c E r r Cov r g −≅θ× " "! " "! " "!Herleitung der Gleichung (7.37): Taylor-Approximation zweiter Ordnung des Ausdrucks: θ−++)1)(1(g r ander Stelle r=0, g=0. θθθθθθθθθθθθθ−=+−===+=+−−−+==+=−=+−+==++=++++++≈==−−==−−==−==−−−0,010,020,00,0122)1()0,0()0,0(0)0,0()1()1)(1)()(1()0,0(1)1()0,0()1)()(1()0,0(1)0,0()1)(1(),()0,0(21)0,0(21)0,0(21)0,0(21)0,0()0,0()0,0(),(g r rg gr rr g r gg g r r g r g rg gr rr gg r g g f f f g r f g f g r f f g r r g f rg f rg f r f g f r f g f f r g fEmpirie :Daten für 1890-1979Risikoprämie : 06.0][≅−r rE iKovarianz: 0024.0),()()(),(4.0036.0167.0≅="!" "!" "!" c i c i c i g r Corr g Var r Var g r CovDas impliziert einen Koeffizienten der relativen Risikoaversion von θ gleich 25, was unplausibel erscheint. Warum?Was bedeutet θ = 25?Ich bin sehr sehr risikoavers! Ich bin indifferent zwischen•=Einkommen 1000, das mit Wahrscheinlichkeit ½ um 50 % steigt und mit Wahrscheinlichkeit ½ um 50% sinkt.•=Sicheres Einkommen von 515.Bei θ = 25 ist man bereit, 48.5 % seines Einkommens mit Sicherheit bezahlen, um eine 50%-ige Möglichkeit eines Verlustes von 50% zu vermeiden!Versuche zu einer …Lösung” desEquity Premium Puzzles(folgt: J. Siegel und R. Thaler, …The Equity Premium Puzzle“, Journal of Economic Perspectives, Winter 1997)1. Empirisch:Man müsste zeigen, dass die “equity premium” (EP) in Wirklichkeit kleiner ist und/oder die Aktienerträge riskanter sind, als oben angenommen.1.1 Betrachtung anderer (längerer) ZeitperiodenWar die Periode 1890-1979 “speziell”?Siegel hat die Intervalle: 1802-1871, 1872-1925, 1926-1997 betrachtet. Die Aktienrenditen waren konstant (8 % - 9 %), während die Anleihenrenditen stetig gesunken sind. Die EP ist entsprechend angestiegen (von 2.9% auf 4.7% und 8.1%).Aber die EP über die gesamte Periode war mit 5.3% immer noch zu hoch, um durch …vernünftige“ RRA-Werte erklärt zu werden.1.2 …Survivorship-bias”Die tatsächliche Rendite auf Aktien wird durch die verfügbaren Daten überschätzt.Die heute noch bestehenden Börsen sind keine Zufallsstichprobe (“survivorship-bias”). Von den 36 zur Jahrhundertwende geöffneten Börsen hatten mehr als die Hälfte erhebliche Unterbrechungen oder wurden sogar gänzlich geschlossen. Anleger sind auch über die winzige Wahrscheinlichkeit eines katastrophalen Ereignisses (Börsenzusammenbruch, Totalverlust etc.) besorgt.Gegenargument: Selbst die NYSE hatte eine …Katastrophe“ (Crash 1929), und auch die Erträge von Ländern, deren Börsen zeitweilig (Zweiter Weltkrieg) geschlossen waren, sind vergleichsweise hoch. (Deutschland, 1926-1995: 5.9%; Japan, 1926-1990: 4%).2. TheoretischDas zugrundeliegende Modell beschreibt das Verhalten der Individuen (Anleger) schlecht. Die Annahmen bezüglich Nutzenfunktion und Eulergleichung sind möglicherweise falsch.2.1 Abgehen von der ErwartungsnutzentheorieVerwenden von Nutzenfunktionen, in denen der perfekte Zusammenhang von Risikoaversion und intertemporaler Substitutionselastizität durchbrochen wird. (Epstein und Zin, 1989).2.2 AggregationsproblemDie Theorie wird meist anhand von aggregierten Daten getestet, obwohl sie eigentlich nur für individuelle Entscheidungen zutreffen sollte. Mankiw und Zeldes (1991) betrachten die Daten für Aktienbesitzer und Nicht-Aktienbesitzer (3/4 der Bevölkerung) getrennt. Der Konsum der Aktienbesitzer ist tatsächlich 3 mal volatiler als der aggregierte Konsum. Dennoch bräuchte man auch hier noch ein θ=10, um die Daten zu erklären.2.3 Interdependente NutzenfunktionenDer Nutzen heute hängt auch vom Konsum der Umgebung (…Referenzgruppen“) oder vom eigenen vergangenen Nutzen ab (…habit-formation“). z.B. Campbell and Cochrane, “By Force of Habit”, 1999.Nutzen hängt ab von Konsumniveau relativ zu …Referenzkonsum“Konsumsenkungen haben grösseren Einfluss auf den Nutzenhohe kurzfristige Risikoaversion, langfristig Anpassung des Referenzniveaus2.4. Myopic Loss AversionBernartzi und Thaler (1995). Baut auf der Prospect Theory auf. Individuen erhalten Nutzen von Änderungen des Wertes ihres Portefeuilles, nicht von der Höhe des Wertes selber. Zusätzlich gilt Loss aversion: d.h. Verluste wiegen schwerer als Gewinne.Der Zeithorizont der Anlage spielt hier eine grosse Rolle. Über lange Zeiträume sind die Aktienrenditen höher als Zinsen auf sichere Anlagen. Bei kürzeren Anlagehorizont sind Verluste wahrscheinlicher. Jemand der ständig die Kurse verfolgt möchte für das …Wechselspiel der Gefühle“ kompensiert werden.。
复旦大学经济学院2013～2014学年第二学期期末考试试卷A卷答案（共4页）课程名称：投资学原理课程代码： ECON130031.01开课院系：经济学院考试形式：闭卷姓名：学号：专业：一、选择题（单选或多选:4’*5=20’）1、B2、A C3、B D4、ABD5、CDF二、名词（4’*5=20’）1、股权风险溢价股权风险溢价ERP(equity risk premium，ERP)是指市场投资组合或具有市场平均风险的股票收益率与无风险收益率的差额。
从这个定义可看出：一是市场平均股票收益率是投资者在市场参与投资活动的预期“门槛”，若当期收益率低于平均收益时，理性投资者会放弃它而选择更高收益的投资；二是市场平均收益率是一种事前的预期收益率，这意味着事前预期与事后值之间可能存在差异。
2、资本配置线正是由于无风险资产引入，才可以形成无风险资产和风险资产之间的资本配置线CAL(capital allocation line,CAL)，但是CAL仅仅为风险资产和无风险组合的“一般搭配”，并非“最优搭配”；而市场组合M与无风险资产构成全部资产组合的集合形成资本市场线（CML），是与“有效边界”相切的资本配置线，是一种“最优的”资本配置线。
3、市盈率增长因子（PEG）市盈率增长因子（PEG）是对P/E静态性缺陷的重要补充。
PEG是将一只股票的市盈率除以该公司的成长性。
其中，用估计盈利增长率除市盈率可以测算公司成长的速度，这就是著名的预期市盈率增长因子（Prospective PEG）。
市盈率增长因子越低，表示公司的发展潜力越大，公司的潜在价值也就越高。
市盈率/公司利润增长率，大于1说明估值高；小于1说明便宜。
4、动量效应投资者行为的研究表明，股票上涨得越多，就有也越多的投资者认为它继续上涨，因而股价的上涨存在一种自我实现机制，即存在动量效应（momentum effect）。
在股价的正反馈机制中，噪声交易这对股价上涨起到推动作用，而明智的专业投资者将从噪声交易者的追逐动能效应策略的过程中获取收益。
equity risk premium 公式(二)Equity Risk Premium公式什么是Equity Risk Premium？Equity Risk Premium（ERF），也称为股权风险溢价，是指投资者对股票投资相对于无风险投资的额外收益要求。
股权风险溢价是衡量市场风险的重要指标，它反映了投资者对未来股票市场表现的预期。
Equity Risk Premium公式的意义Equity Risk Premium公式是通过计算股票市场预期回报率减去无风险回报率，得出的预期股权风险溢价。
它可以帮助投资者评估股票投资的回报和风险之间的关系。
Equity Risk Premium公式根据经济学家们的研究和实践经验，有几种常用的Equity Risk Premium公式。
以下是其中三种常见的公式：1.Historical Equity Risk Premium公式： EPR = (Rp - Rf)–其中，EPR表示股权风险溢价，Rp表示股票市场的历史回报率，Rf表示无风险回报率。
–举例说明：假设过去年均股票市场回报率为10%，无风险回报率为5%，则历史股权风险溢价为5%。
–这个公式的缺点是只考虑了历史数据，没有考虑未来的预期回报率。
2.Implied Equity Risk Premium公式： EPR = Rp - Rf–其中，EPR表示股权风险溢价，Rp表示股票市场的预期回报率（通过市场定价模型计算得出），Rf表示无风险回报率。
–举例说明：假设市场定价模型预测未来股票市场回报率为8%，无风险回报率为3%，则预期股权风险溢价为5%。
–这个公式考虑了未来的预期回报率，更符合实际情况。
3.Country Risk Premium公式： CRP = Default Spread +Equilibrium Spread–其中，CRP表示国家风险溢价，Default Spread表示违约风险溢价，Equilibrium Spread表示平衡风险溢价。
上海金融学院2009--2010 学年度第二学期《投资学》课程A卷代码：23330295（集中考试考试形式：闭卷考试用时: 90 分钟）考试时只能使用简单计算器(无存储功能)试题纸一、单项选择题（每题1分，共10分；在答题纸上相应位置填入正确选项前的英文字母）：1、证券持有人面临预期收益不能实现，是证券的( )特征。
A、期限性B、收益性C、流通性D、风险性2、证券交易所内证券交易的竞价原则是( )。
A、时间优先，客户优先B、价格优先，时间优先C、数量优先D、市价优先3、以追求当期高收入为基本目标，以能带来稳定收入的证券为主要投资对象的证券投资基金是（）。
A、指数基金B、成长型基金C、收入型基金D、平衡型基金4、企业对其产品的未来需求的预期相对悲观，于是决定减少投资。
这往往会造成实际利率（）A、下降B、不变C、上升D、不确定5、风险厌恶程度越强的投资者，其效用无差异曲线越（）A、平缓B、陡峭C、水平D、下倾6、零贝塔值证券的期望收益率为（）。
A、市场收益率B、零收益率C、负收益率D、无风险收益率7、收益率曲线向右下方倾斜意味着在同一时点上，长期债券收益率( )短期债券收益率。
A、高于B、等于C、低于D、不能判断是否高于8、一张5年期零息票债券的久期是( )。
A、小于5年B、多于5年C、等于5年D、等同于一张5年期10%的息票债券9、考虑单指数模型，某只股票的阿尔法为0%。
市场指数的收益率为16%。
无风险收益率为5%。
尽管没有个别风险影响股票表现，这只股票的收益率仍超出无风险收益率11%。
那么这只股票的贝塔值是多少？（）A、0.67B、0.75C、1.0D、1.3310、已知一张3年期零息票债券的收益率是7.2%，第一年、第二年的远期利率分别为6.1%和6.9%，那么第三年的远期利率应为多少？( )A、7.2%B、8.6%C、6.1%D、6.9%二、多项选择题（每题1分，共10分；在答题纸上相应位置填入正确选项前的英文字母）：1、( )是金融资产。
CHAPTER 2: ASSET CLASSES AND FINANCIALINSTRUMENTSPROBLEM SETS1. Preferred stock is like long-term debt in that ittypically promises a fixed payment each year. In thisway, it is a perpetuity. Preferred stock is also likelong-term debt in that it does not give the holdervoting rights in the firm.Preferred stock is like equity in that the firm is under no contractual obligation to make the preferred stock dividend payments. Failure to make payments does not set off corporate bankruptcy. With respect to the priority of claims to the assets of the firm in the event of corporate bankruptcy, preferred stock has a higher priority than common equity but a lower priority than bonds.2. Money market securities are called cash equivalentsbecause of their high level of liquidity. The prices ofmoney market securities are very stable, and they canbe converted to cash ., sold) on very short notice andwith very low transaction costs. Examples of moneymarket securities include Treasury bills, commercialpaper, and banker's acceptances, each of which ishighly marketable and traded in the secondary market.3. (a) A repurchase agreement is an agreement whereby theseller of a security agrees to “repurchase” it from the buyer on an agreed upon date at an agreed upon price. Repos are typically used by securities dealers as a means for obtaining funds to purchase securities.4. Spreads between risky commercial paper and risk-freegovernment securities will widen. Deterioration of the economy increases the likelihood of default on commercial paper, making them more risky. Investors will demand a greater premium on all risky debt securities, not just commercial paper.5.6. Municipal bond interest is tax-exempt at the federallevel and possibly at the state level as well. Whenfacing higher marginal tax rates, a high-incomeinvestor would be more inclined to invest in tax-exemptsecurities.7. a. You would have to pay the ask price of:% of par value of $1,000 = $b. The coupon rate is % implying coupon payments of$ annually or, more precisely, $ semiannually.c. The yield to maturity on a fixed income security isalso known as its required return and is reported byThe Wall Street Journal and others in the financialpress as the ask yield. In this case, the yield tomaturity is %. An investor buying this security todayand holding it until it matures will earn an annualreturn of %. Students will learn in a later chapterhow to compute both the price and the yield to maturitywith a financial calculator.8. Treasury bills are discount securities that mature for$10,000. Therefore, a specific T-bill price is simply the maturity value divided by one plus the semi-annual return:P = $10,000/ = $9,9. The total before-tax income is $4. After the 70% exclusionfor preferred stock dividends, the taxable income is: $4 = $Therefore, taxes are: $ = $After-tax income is: $ – $ = $Rate of return is: $$ = %10. a. You could buy: $5,000/$ = shares. Since it is notpossible to trade in fractions of shares, you could buy77 shares of GD.b. Your annual dividend income would be: 77 $ = $c. The price-to-earnings ratio is and the price is $.Therefore:$Earnings per share = Earnings per share = $d. General Dynamics closed today at $, which was$ hi gher than yesterday’s price of $11. a. At t = 0, the value of the index is: (90 + 50 + 100)/3= 80At t = 1, the value of the index is: (95 + 45 + 110)/3 =The rate of return is: 80) 1 = %b. In the absence of a split, Stock C would sell for110, so the value of the index would be: 250/3 =with a divisor of 3.After the split, stock C sells for 55. Therefore,we need to find the divisor (d) such that: = (95+ 45 + 55)/d d = . The divisor fell, which isalways the case after one of the firms in an indexsplits its shares.c. The return is zero. The index remains unchangedbecause the return for each stock separatelyequals zero.12. a. Total market value at t= 0 is: ($9,000 + $10,000 +$20,000) = $39,000Total market value at t= 1 is: ($9,500 + $9,000 + $22,000) = $40,500Rate of return = ($40,500/$39,000) – 1 = %b.The return on each stock is as follows:r A = (95/90) – 1 =r B = (45/50) – 1 = –r C = (110/100) – 1 =The equally weighted average is:[ + + ]/3 = = %13. The after-tax yield on the corporate bonds is: (1 – == %Therefore, municipals must offer a yield to maturity of at least %.14. Equation shows that the equivalent taxable yield is: r = r m/(1 –t), so simply substitute each tax rate in the denominator to obtain the following:a. %b. %c. %d. %15. In an equally weighted index fund, each stock is given equalweight regardless of its market capitalization. Smaller cap stocks will have the same weight as larger cap stocks. The challenges are as follows:Given equal weights placed to smaller cap andlarger cap, equal-weighted indices (EWI) will tendto be more volatile than their market-capitalization counterparts;It follows that EWIs are not good reflectors ofthe broad market that they represent; EWIsunderplay the economic importance of largercompanies.Turnover rates will tend to be higher, as an EWImust be rebalanced back to its original target. Bydesign, many of the transactions would be amongthe smaller, less-liquid stocks.16. a. The ten-year Treasury bond with the higher coupon ratewill sell for a higher price because its bondholderreceives higher interest payments.b. The call option with the lower exercise price has morevalue than one with a higher exercise price.c. The put option written on the lower priced stock hasmore value than one written on a higher priced stock.17. a. You bought the contract when the futures price was$ (see Figureand remember that the number to the right of theapostrophe represents an eighth of a cent). Thecontract closes at a price of $, which is $ more thanthe original futures price. The contract multiplier is5000. Therefore, the gain will be: $ 5000 = $b. Open interest is 135,778 contracts.18. a. Owning the call option gives you the right, but notthe obligation, to buy at $180, while the stock istrading in the secondary market at $193. Since thestock price exceeds the exercise price, you exercisethe call.The payoff on the option will be: $193 - $180 = $13The cost was originally $, so the profit is: $13 - $ = $b. Since the stock price is greater than the exerciseprice, you will exercise the call. The payoff on theoption will be: $193 - $185 = $8The option originally cost $, so the profit is $8 - $ =-$c. Owning the put option gives you the right, but not theobligation, to sell at $185, but you could sell in thesecondary market for $193, so there is no value inexercising the option. Since the stock price is greaterthan the exercise price, you will not exercise the put.The loss on the put will be the initial cost of $.19. There is always a possibility that the option will be in-the-money at some time prior to expiration. Investors will pay something for this possibility of a positive payoff.20.Value of Call aInitial Cost ProfitExpirationb.04-4c.04-4d.541e.1046Value of Put aInitial Cost ProfitExpirationb.56-1c.06-6d.06-6e.06-621. A put option conveys the right to sell the underlyingasset at the exercise price. A short position in a futures contract carries an obligation to sell the underlying asset at the futures price. Both positions, however, benefit if the price of the underlying asset falls.22. A call option conveys the right to buy the underlyingasset at the exercise price. A long position in a futures contract carries an obligation to buy the underlying asset at the futures price. Both positions, however, benefit if the price of the underlying asset rises.CFA PROBLEMS1.(d) There are tax advantages for corporations that ownpreferred shares.2. The equivalent taxable yield is: %/(1 = %3. (a) Writing a call entails unlimited potential losses asthe stock price rises.4. a. The taxable bond. With a zero tax bracket, the after-tax yield for thetaxable bond is the same as the before-tax yield (5%),which is greater than the yield on the municipal bond.b. The taxable bond. The after-tax yield for thetaxable bond is:0.05 (1 – = %c. You are indifferent. The after-tax yield for thetaxable bond is:(1 – = %The after-tax yield is the same as that of the municipal bond.d. The municipal bond offers the higher after-tax yieldfor investors in tax brackets above 20%.5.If the after-tax yields are equal, then: = × (1 –t)This implies that t = =30%.。
Chapter 15 the equity market (cross-section patternsand time-series patterns)Fan LongzhenIntroduction•In this class, we again look at the stock return data, but with a very different view point;•Previously, we examined the data through the “eyes”of CAPM. We had a noble intension, although it didn’t work very well;•Now we are going to get our hands “dirty”, and plunge right into the data, without a formal model;•In particular, we will look at some well-established patterns---size,value, and momentum—that have beensuccessful in explaining the cross-sectional stock returns.Multifactor-regressions•For each asset i, we use a multi-factor time-series regression to quantify the asset’s tendency to move with multiple risk factors:• 1. Systematic factors:•:risk premium•：risk premium • 2 idiosyncratic factors:•: no risk premium • 3. Factor loadings:•beta(i): sensitivity to market risk;•: sensitivity to the factor risk.i tt i f t M t i i f t i t e F f r r r r ++−+=−)(βαM t r )(f t M t M r r E −=λtF )(t F F E =λi t e 0)(=i t e E i fThe pricing relation•Given the risk premia of the systematic factors, the determinants of expected returns:•What are the additional systematic factors?FiM i f t i t f r r E λλβ+=−)(Size: small or big•We sort the socks by their market capitalization: share price* number of shares outstandingValue or growth•We can sort the cross-section of stocks by their book-to-market ratios: growth stocks:firm with low book-to-market ratios;•Value stocks:firms with high book-to-market ratios.Other factors•Price-to-earining ratios,•The market skewness fcator•---Havey and Siddique(JF,2000) report that systematic skewness is economically important and commands an average risk premium of 3.6% per year.Time-series behavior•For the time-series behavior of stock returns, we focus in particular on the time-varying nature of expected return and volatility;•We are interested in building dynamic models that explicitly incorporate conditioning information to best describe the behavior of future stock returns.Predictability and marketefficiency•In addition to the random walk test, there is mounting evidence that stock returns are predictable;•Some argue that predictability implies market inefficiency. What do you think?•Others contend it is simple a result of rational variation in expected returns;•Suppose this is true. Can we find a coherent story that relates the variation through time of expected returns to business conditionsWhat cause expected returns to vary?•Using the intuition of CAPM, expected returns canvary for two reasons:• 1. Varying risk aversion;• 2. Varying exposure to market risk, or varying market risk.•When income is high, investor want save more, higher saving lead to lower expected returns;•Empirical implication?Variables related to business condition •Default spreads: difference in yields between defaultable bonds and treasury bonds with similar maturities. When the business condition is bad, the systematic default risk increases, widening the default spread.•Term premiums: difference in yields between long-and short-term treasury bonds. This is a forward-looking variable predictive of future inflation, and is found to be important in forecasting real economic activity.•Financial ratios: book-to-market, dividend yields, ect. Variables that are important in fundamental valuationTime-varying volatility---volatility also changes with time •If the rate of information arrival is time-varying, so is the rate of price adjustment, causing the volatility to change over time;•The time-varying volatility of the market return is related to the time-varying volatility of a variety of economic variables, includinginflation, money growth, and industrial production;•Stock market volatility increases with financial leverage: a decrease in stock price causes an increase in financial leverage, cause volatility to increase;•Investors’s sudden changes of risk attitudes, changes in market liquidity, and temporary imbalance of supply and demand could all cause market volatility to change over time.•What are the testable empirical implications?Stochastic volatility•More generally, volatility is a stochastic process of its own, this is an active area of research in academics and in industry.•Some well-known facts about stochastic volatility:• 1. It is persistent: volatile periods are followed by volatile periods;• 2. It is mean-reverting: over time, volatility converges to its long-run mean.• 3. There is a negative correlation between volatility and return: large negative price jumps are coupled with large positive volatility jumps.。
