第6罩 风险与风险厌恶 Risk and risk aversion
6-1 第6章 风险与风险厌恶 Risk and Risk Aversion
风险与风险厌恶 Risk and risk aversion 6.1风险与风险厌恶 62资产组合风险 6-2
6-2 风险与风险厌恶 Risk and Risk Aversion 6.1风险与风险厌恶 6.2 资产组合风险
风险与风险厌恶 Risk and risk aversion 风险的存在意味着可能产生一个以上的结果, 单一前景是指将某一初始财富被用于投资时面 临着风险,这一投资机会只产生两种可能的结 果 The presence of risk means that more than one outcome is possible. A simple prospect is an investment opportunity in which a certain initial wealth is placed at risk, and there are only two possible outcomes 6-3
6-3 风险与风险厌恶 Risk and Risk Aversion 风险的存在意味着可能产生一个以上的结果， 单一前景是指将某一初始财富被用于投资时面 临着风险，这一投资机会只产生两种可能的结 果。 The presence of risk means that more than one outcome is possible. A simple prospect is an investment opportunity in which a certain initial wealth is placed at risk, and there are only two possible outcomes
风险-不确定收益 Risk- Uncertain outcomes 概率1:p=.6 收益W1=150利润 Profit=50 W=100 初始投资额 概率2:1=4收益W2=80利润 Profit=20 预期收益E(W) pW1+(1-p)W2=06(150)+0.4(80)=122 预期盈利( expected profit=122-100=22 方差σ2 variance)=pW1-E(W)2+(1p)[W2-E(W =0.6(150-122)2+0.4(80-122)2=1,176000 标准差σ=34,293
6-4 W = 100 初始投资额 收益W1 = 150 利润Profit = 50 概率2: 1-p = .4 收益W2 = 80 利润Profit = -20 预期收益E(W) = pW1 + (1-p)W2 =0.6 (150) +0.4(80) = 122 预期盈利(expected profit)=122-100=22 方差 s2 (variance) = p[W1 - E(W)]2 + (1-p) [W2 - E(W)]2 =0.6 (150-122)2 + 0.4(80-122)2 = 1,176,000 标准差 s = 34,293 风险-不确定收益 Risk - Uncertain Outcomes
风险投资与无风险投资 Risky Investments with risk-Free Investment p W=150 Profit= 50 风险投资 Risky Inv 100 p Wo=80 Profit=-20 无风险投资 Risk Free t-bills Profit=5 预期盈利( The expected profit)=122-100=22 风险溢价 Risk premium=风险投资预期盈利22-国库券盈利5=17 6-5
6-5 W1 = 150 Profit = 50 W2 = 80 Profit = -20 1-p = .4 100 风险投资Risky Inv. 无风险投资Risk Free T-bills Profit = 5 预期盈利(The expected profit) = 122-100=22 风险溢价Risk Premium =风险投资预期盈利22 – 国库券盈利5 = 17 风险投资与无风险投资 Risky Investments with Risk-Free Investment
风险厌恶与效用价值 Risk Aversion& Utility ■投资者的风险观 nvestor's view of risk 风险厌恶型 Risk Averse 风险中性 Risk Neutral 风险爱好型 Risk Seeking ■效用价值 Utility ■效用价值方程 Utility Function U=E(r)-.005A2 A是投资者风险厌恶系数 a measures the degree of risk aversion 6-6
6-6 投资者的风险观 Investor’s view of risk – 风险厌恶型 Risk Averse – 风险中性 Risk Neutral – 风险爱好型 Risk Seeking 效用价值 Utility 效用价值方程 Utility Function U = E ( r ) - .005 A s 2 A 是投资者风险厌恶系数 A measures the degree of risk aversion 风险厌恶与效用价值 Risk Aversion & Utility
风险厌恶与价值:投资举例 Risk Aversion and value: Using the Sample Investment U=E(r)-005Ao2 22-.005A(34%)2 风险厌恶度效用值 Risk Aversion a value High 53 6.90 4.66 Tbill= 5%o LOW 116.22
6-7 风险厌恶与价值:投资举例 Risk Aversion and Value: Using the Sample Investment U = E ( r ) - .005 A s 2 = .22 - .005 A (34%) 2 风险厌恶度 效用值 Risk Aversion A Value High 5 -6.90 3 4.66 Low 1 16.22 T-bill = 5%
风险厌恶、风险与收益的权衡 Equilibrium of risk aversion Risk and return ■如果证券A可以无风险的获得回报率为10%, 而证券B以50%的概率获得20%的收益, 50%的概率的收益为0,你将选择哪一种证 券 ■对于一个风险规避的投资者,虽然证券B的 期望收益为10%,但它具有风险,而证券A 的无风险收益为10%,显然证券A优于证券 B 6-8
6-8 风险厌恶、风险与收益的权衡 Equilibrium of Risk Aversion、Risk and return 如果证券A可以无风险的获得回报率为10％， 而证券B以50％的概率获得20％的收益， 50％的概率的收益为0，你将选择哪一种证 券？ 对于一个风险规避的投资者，虽然证券B的 期望收益为10％，但它具有风险，而证券A 的无风险收益为10％，显然证券A优于证券 B
均值方差标准(Mean- variance criterion) 若投资者是风险厌恶的,则对于证券A和证 券B,当且仅仅当 E(r)≥E(r 时成立 2 < 2 B 则该投资者认为“A占优于B”,从而该投资者是 风险厌恶性的。 6-9
6-9 均值方差标准（Mean-variance criterion) 若投资者是风险厌恶的，则对于证券A和证 券B，当且仅仅当 2 2 s s A B 时成立 则该投资者认为“A占优于B”，从而该投资者是 风险厌恶性的
占优原则 Dominance Principle 预期收益 Expected Return 2 方差或标准差Ⅴ ariance or standard deviation 2占优 dominates1;有更高收益 has a higher return ·2占优 dominates3;有更低风险 has a lower risk 4占优 dominates3;有更高收益 has a higher return 6-10
6-10 占优原则 Dominance Principle 1 2 3 4 预期收益Expected Return 方差或标准差Variance or Standard Deviation • 2占优dominates 1; 有更高收益has a higher return • 2占优dominates 3; 有更低风险has a lower risk • 4占优dominates 3; 有更高收益has a higher return