单一指数模型.pptVIP

Chapter 10 Single index model 单一指数模型 The main goal of this chapter is to introduce Sharpe’s Single Index Model of Capital Asset Pricing. According to the Single Index Model, by using observable realized returns on a security to regress a relationship between realized returns on that security and the market index, we can examine how the returns on a particular asset or portfolio changes with respect to the returns of the market. 10.1 Guidelines 证券的收益与方差 “均值-方差模型“的局限性 单一指数模型的主要假设 估计单一指数模型 单一指数模型与多样化 多样化组合对比单一资产 Security’s returns and its variance The limitation of the “mean, variance approach” Main assumptions for single-index model Estimating the single index model Single index model and diversification Well-diversified portfolio versus single assets 1. Security’s Returns and its Variance 1) The limitation of the “mean, variance approach” “The mean, variance approach” to portfolio analysis involves estimating and then selecting the portfolio that offers the best mean-variance combination. With “The mean, variance approach”, Consider what we need to do: (1) Mean and variance of each asset. (2) Correlation between each asset. (3) Mean and variance differing combinations of assets. This is fine when the portfolio consists of only two assets. What if there are 20 assets to construct? you need the information: n = 20 estimates of E(Ri) n = 20 estimates of variances n(n - 1)/2 = 190 estimates of covariances 230 estimates So for each combination we need 230 estimates. In light of the fact that a 20-security portfolio is relatively small, if n = 200 we need 20,300 estimates per combination. Single-index model enables us to dramatically reduce the number of parameters required to perform portfolio analysis. 2) Main Assumptions of Single-index model (1) The returns on stocks tend to change in a similar fashion as an average return on the market, because the same economic factors affect almost all firms. This implies the exce