第11章 套利定价理论 Arbitrage Pricing Theory 12-1
12-1 第11章 套利定价理论 Arbitrage Pricing Theory
套利定价理论 Arbitrage pricing Theory 11.1套利机会与利润 11.2套利定价理论与充分分散的资产组合 11.3单一资产与套利定价理论 11.4套利定价理论与CAPM模型 11.5多因素套利定价理论 12-2
12-2 套利定价理论 Arbitrage Pricing Theory 11.1 套利机会与利润 11.2 套利定价理论与充分分散的资产组合 11.3 单一资产与套利定价理论 11.4 套利定价理论与CAPM模型 11.5 多因素套利定价理论
套利定价理论 Arbitrage Pricing Theory 利用证券定价之间的不一致进行资金转移,从中 赚取无风险利润的行为称为套利 Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit ■无投资需要,投资者可建立大的头寸来获取高利润 Since no investment is required, an investor can create large positions to secure large levels of profit 1在有效市场内,有利的套利机会会很快消失 In efficient markets, profitable arbitrage opportunities will quickly disappear 12-3
12-3 套利定价理论 Arbitrage Pricing Theory 利用证券定价之间的不一致进行资金转移，从中 赚取无风险利润的行为称为套利 Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit. 无投资需要,投资者可建立大的头寸来获取高利润 Since no investment is required, an investor can create large positions to secure large levels of profit. 在有效市场内,有利的套利机会会很快消失 In efficient markets, profitable arbitrage opportunities will quickly disappear
套利举例 Arbitrage Example from Text 当前价格 期望收益 标准差关系矩阵 股票 Current Expected Standard Stock Prices Return Dev 10 25.0 29.58 B 10 20.0 33.91 10 32.5 48.15 D 10 22.5 8.58
12-4 当前价格 期望收益 标准差 关系矩阵 股票 Current Expected Standard Stock Price$ Return% Dev.% A 10 25.0 29.58 B 10 20.0 33.91 C 10 32.5 48.15 D 10 22.5 8.58 套利举例 Arbitrage Example from Text
套利组合 Arbitrage Portfolio 均值标准差相关系数 Mean S.D. Correlation ABC组合 Portfolio A.B.C 2583 640 0.94 D 22.25 8.58 12-5
12-5 均值 标准差 相关系数 Mean S.D. Correlation ABC组合 Portfolio A,B,C 25.83 6.40 0.94 D 22.25 8.58 套利组合 Arbitrage Portfolio
套利行为和收益 Arbitrage Action and Returns 预期收益 E Ret a D 标准方差 St. Dev 卖空3份D股票和A,B,C股票各买1份形成组合P Short 3 shares ofd and buy l ofA, b &c to form P. 投资者将获取比卖空更高额的回报 You earn a higher rate on the investment than you pay on the short sale 12-6
12-6 套利行为和收益 Arbitrage Action and Returns 预期收益 E. Ret. 标准方差 St.Dev. * P * D 卖空3份D股票和A,B,C股票各买1份形成组合P Short 3 shares of D and buy 1 of A, B & C to form P. 投资者将获取比卖空更高额的回报 You earn a higher rate on the investment than you pay on the short sale
套利定价理论和组合投资 aPt Well-Diversified portfolios E(rp+bF+ F=一些因素 some factor 对完善的资产组合 For a well-diversified portfolio ep约为零 approaches zero 类似 CAPM Similar to capm 12-7
12-7 套利定价理论和组合投资 APT & Well-Diversified Portfolios rP = E (rP) + bPF + eP F = 一些因素 some factor 对完善的资产组合 For a well-diversified portfolio: eP 约为零 approaches zero 类似CAPM Similar to CAPM
单个证券与投资组合的比较 Comparing a Portfolio with an Individual Security e(r)%o E(r)% F F 单个证券 证券组合 Individual security Portfolio 12-8
12-8 单个证券与投资组合的比较 Comparing a Portfolio with an Individual Security F E(r)% 证券组合 Portfolio F E(r)% 单个证券 Individual Security
非均衡举例 Disequilibrium Example E(r)% D 无风险6 口口圈 ■■ Risk Free 4 5 1.0 Beta for F 12-9
12-9 非均衡举例 Disequilibrium Example E(r)% Beta for F 10 7 6 无风险 Risk Free 4 D A C .5 1.0
非均衡举例 Disequilibrium Example ■卖空组合 Short portfolio c 用资金构建一个均衡风险高收益的组合D D与A和无风险资产相比 Use funds to construct an equivalent risk higher return portfolio d D is comprised of a Risk-Free Asset 百分之一的套利 Arbitrage profit of1% 12-10
12-10 非均衡举例 Disequilibrium Example 卖空组合C Short Portfolio C 用资金构建一个均衡风险高收益的组合D -D与A和无风险资产相比 Use funds to construct an equivalent risk higher return Portfolio D. – D is comprised of A & Risk-Free Asset 百分之一的套利Arbitrage profit of 1%