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1、CHAPTER 6,Risk Aversion and Capital Allocation to Risky Assets风险厌恶与风险资产的配置,6-2,Allocation to Risky Assets风险资产的配置,Investors will avoid risk unless there is a reward.投资者是风险趋避的除非风险会产生收益The utility model gives the optimal allocation between a risky portfolio and a risk-free asset.效用模型认为最优的资产配置是风险组合和无风险资
2、产的一个最优搭配,6-3,Risk and Risk Aversion风险与风险趋避,Speculation投机Taking considerable risk for a commensurate gain考虑风险补偿Parties have heterogeneous expectations参与者有不同的期望，会对较高赢面的结果下较大的赌注，否则宁愿不做,6-4,Risk and Risk Aversion风险与风险趋避,Gamble 赌博Bet or wager on an uncertain outcome for enjoyment 享受为不确定性结果的下注Parties assi
3、gn the same probabilities to the possible outcomes 参与者对不同概率的结果下同样的赌注，为享受不确定性下的结果,6-5,Risk Aversion and Utility Values风险厌恶与效用价值,Investors are willing to consider:risk-free assets无风险资产speculative positions with positive risk premiums正值风险溢价的投机Portfolio attractiveness increases with expected return and
4、decreases with risk.收益越高风险越低组合就越吸引投资者What happens when return increases with risk?如果风险与收益同步上升？,6-6,Table 6.1 Available Risky Portfolios (Risk-free Rate = 5%)可供选择的风险组合,Each portfolio receives a utility score to assess the investors risk/return trade off效用分数就是用一个函数来对投资者获得的风险与收益进行打分排序，选择最好的组合,6-7,Utili
5、ty Function效用方程,U = utility效用E ( r ) = expected return on the asset or portfolio期望收益A = coefficient of risk aversion风险趋避系数s2 = variance of returns方差，或者风险 = a scaling factor尺度调节因子,6-8,Table 6.2 Utility Scores of Alternative Portfolios for Investors with Varying Degree of Risk Aversion几种投资组合对不同风险厌恶水平投
6、资者的效用,6-9,Mean-Variance (M-V) Criterion均值方差准则,Portfolio A dominates portfolio B if:And,6-10,Estimating Risk Aversion估计风险厌恶水平,Use questionnaires调查问卷Observe individuals decisions when confronted with risk观察面对风险时的个人决策选择Observe how much people are willing to pay to avoid risk观察人们是否愿意付钱来避免风险,6-11,Capital
7、 Allocation Across Risky and Risk-Free Portfolios 风险资产与无风险资产组合的资本配置,Asset Allocation:,Is a very important part of portfolio construction.构建投资组合时非常重要的步骤Refers to the choice among broad asset classes.是指大类资产的偏好，如股票、债券、货币市场证券或者其他资产,Controlling Risk:,Simplest way: Manipulate the fraction of the portfolio
8、 invested in risk-free assets versus the portion invested in the risky assets最简单的方法就是觉得多少份额投资于无风险资产，多少在风险资产上,6-12,Basic Asset Allocation基本资产配置,6-13,Basic Asset Allocation基本资产配置,Let y = weight of the risky portfolio, P, in the complete portfolio; (1-y) = weight of risk-free assets:,6-14,The Risk-Free
9、 Asset无风险资产,Only the government can issue default-free bonds.只有政府才能发行近似的无违约风险资产（俄罗斯除外）Risk-free in real terms only if price indexed and maturity equal to investors holding period.投资期限等于持有期时才能看做无风险（没有逼债&清偿风险）T-bills viewed as “the” risk-free asset美国短期国库券被看做是风险最低的资产Money market funds also considered r
10、isk-free in practice货币市场基金在实践中也是无风险,6-15,Figure 6.3 Spread Between 3-Month CD and T-bill Rates（ 3个月大额存单与短期国库券的收益差的历史数据）,6-16,Its possible to create a complete portfolio by splitting investment funds between safe and risky assets.将投资资金分配到安全和风险的资产中就可以创造一个完整的组合（意味着调整份额就可以复制其他任何组合）Let y=portion allocate
11、d to the risky portfolio, P(1-y)=portion to be invested in risk-free asset, F.,Portfolios of One Risky Asset and a Risk-Free Asset单一风险资产与无风险资产的投资组合,6-17,Example Using Chapter 6.4 Numbers案例,6-18,Example (Ctd.)期望收益,The expected return on the complete portfolio is the risk-free rate plus the weight of
12、P times the risk premium of P该组合的期望收益等于无风险资产的收益乘以它的份额再加上风险资产的收益乘以它的份额,6-19,Example (Ctd.)期望的风险,The risk of the complete portfolio is the weight of P times the risk of P:期望的风险就是风险资产的风险乘以它的份额,6-20,Example (Ctd.)期望的风险收益,Rearrange and substitute y=sC/sP:,6-21,Figure 6.4 The Investment Opportunity Set 投资
13、集合,6-22,Lend at rf=7% and borrow at rf=9%Lending range slope = 8/22 = 0.36Borrowing range slope = 6/22 = 0.27CAL kinks at P在借贷利率发生变化的一点发生歪曲连接,Capital Allocation Line with Leverage资本配置线与杠杆,6-23,Figure 6.5 The Opportunity Set with Differential Borrowing and Lending Rates投资集合（借贷利率不同）,6-24,Risk Toleranc
14、e and Asset Allocation风险容忍度与资产配置,The investor must choose one optimal portfolio, C, from the set of feasible choices投资者必须从可选集中择出最优Expected return of the complete portfolio:Variance:,6-25,Table 6.4 Utility Levels for Various Positions in Risky Assets (y) for an Investor with Risk Aversion A = 4风险厌恶系数
15、4时投资不同风险资产的效用水平,6-26,Figure 6.6 Utility as a Function of Allocation to the Risky Asset, y效用值作为风险资产比例y的函数,6-27,Table 6.5 Spreadsheet Calculations of Indifference Curves无差异曲线的计算,6-28,Figure 6.7 Indifference Curves for U = .05 and U = .09 with A = 2 and A = 4风险厌恶系数为2、4时效用水平为0.05、0.09的无差异曲线,6-29,Figure
16、6.8 Finding the Optimal Complete Portfolio Using Indifference Curves使用无差异寻找最优投资组合,6-30,Table 6.6 Expected Returns on Four Indifference Curves and the CAL四条无差异曲线和资本配置线对不同风险的期望收益,6-31,Passive Strategies: The Capital Market Line被动策略：资本市场线,The passive strategy avoids any direct or indirect security anal
17、ysis被动策略中投资者避免任何直接或者间接的证券分析Supply and demand forces may make such a strategy a reasonable choice for many investors供给和需求的力量将使得这类策略对很多投资者来说是可行的,6-32,A natural candidate for a passively held risky asset would be a well-diversified portfolio of common stocks such as the S&P 500.被动投资策略中的一个合适的投资品是分散得很好的投
18、资组合比如标普500The capital market line (CML) is the capital allocation line formed from 1-month T-bills and a broad index of common stocks (e.g. the S&P 500).资本配置线就是1月短期国库券和股票价值指数的搭配,Passive Strategies: The Capital Market Line被动策略：资本市场线,6-33,The CML is given by a strategy that involves investment in two
19、passive portfolios:两个被动的投资资产构成的策略 virtually risk-free short-term T-bills (or a money market fund) 安全资产a fund of common stocks that mimics a broad market index.风险资产,Passive Strategies: The Capital Market Line被动策略：资本市场线,6-34,From 1926 to 2009, the passive risky portfolio offered an average risk premium of 7.9% with a standard deviation of 20.8%, resulting in a reward-to-volatility ratio of .38.从1926年到2009年被动的风险组合提供了平均收益为7.9%标准差为20.8%的回报，收益风险比为0.38为什么会有效？一是积极策略需要付出成本而被动策略不需要，二是有搭便车的效应；,Passive Strategies: The Capital Market Line被动策略：资本市场线,
