Đang tải... (xem toàn văn)
Tiểu luận Đầu tư tài chính A CAPITAL ASSET PRICING MODEL WITH TIMEVARYING COVARIANCES The assumptions: All investors choose meanvariance efficient portfolios with a one period horizon, although the need not have identical utility functions All investors have the same subjective expectations on the means, variances, and covariances of returns The market is fully efficient in that there are no transaction costs, indivisibilities, taxes, or constraints on borrowing or lending at a riskfree rate.
A CAPITAL ASSET PRICING MODEL WITH TIME- VARYING COVARIANCES GVHD: TS. Trần Thị Hải lý Nhóm thuyết trình: 1.Trịnh Quang Công 2.Bùi Thị Thùy Dương 3.Mai Thị Huỳnh Mai 4.Chung Ngọc Nghi 5.Nguyễn Thị Ánh Ngọc Contents I. Introduction II. Econometric Methods III. Data Description IV. Model Estimates V. Diagnostic Tests VI. Conclusions I. Introduction The assumptions: 1. All investors choose mean-variance efficient portfolios with a one period horizon, although the need not have identical utility functions 2. All investors have the same subjective expectations on the means, variances, and covariances of returns 3. The market is fully efficient in that there are no transaction costs, indivisibilities, taxes, or constraints on borrowing or lending at a risk-free rate. In this paper we focus attention on the possibility that agents may have common expectations on the moments of future returns but what these are conditional expectations and therefore random variables rather than constants. y t : the vector of excess returns of all assets in the market measured as the nominal return during period t µ t and H t : vector and conditional covariance matrix of these returns give information available at the time t-1 ω t-1 : vector of value weights at the end of the previous period The excess return on the market: y Mt = y’ t ω t-1 . The CAPM requires: µ t = δ H t ω t-1 (1) With: δ = constant σ 2 Mt = ω’ t-1 H t ω t-1 µ Mt = ω’ t-1 µ t , (1) => µ Mt = δ σ 2 Mt (2) β t = H t ω t-1 /σ 2 Mt substituting in (1), (2) => µ t = β t µ Mt (3) In the special case: E (y t ) = δ V (y t )ω – δ 3 V(H t ω) ω II. Econometric Methods Model: The multivariate GARCH (GARCH-M) For y t N x 1, GARCH (p-q) – M: (4) (5) (6) The GARCH (1,1) model becomes: III. Data Description Bills (6-month Treasury bills), bonds (20-year Treasury bonds), stocks Quarterly percentage returns from the first quarter of 1959 through the second quarter of 1984 (102 observations) The Standard and Poor’s 500 equity series was used with Citibase interest rates. New York Stock Exchange value-weighted equity returns are used with Salomon Brothers bill and bond yields [...]... forecast return VI Conclusions The conditional covariance matrix of the asset returns is strongly autoregressive Information in addition to past innovations in asset returns is important in explaining premia and heteroscedasticity Lagged excess holding yields and innovations in consumption appear to have some explanatory power for asset returns The expected return or risk premia for the assets are... A better measure might be the nondiversifiable risk as given by the conditional covariance with the market The next test considers the lagged excess holding yields as explanatory variables for each of three risk premia => rejects the formulation of the CAPM given in (8) Use information in addition to past innovations in forming their expectations This ability of the lagged dependent variable... preferential tax treatment as previously mentioned Figures 4-6 are the estimated betas The beta for stocks is close to one, that for bonds is slightly above one and that for bills is close to zero Substantial movement over the sample period V Diagnostic Tests LM test involves the inclusion of the own conditional variances in each of the three equations for the conditional expectation of the...Mean of Excess holding yield Excess return Max Return Min Standard deviation Time Rate Time Rate Q1/1980 0.142% 0.356 Q2/1980 2.046% Bond 0.761% 6.255 Q2/1980 22.274% Stock 0.995 % 2.225 Q1/1975 3.746% Q3/1980 -0.777% Q4/1980 Bill (6 month) -0.462% -0.515% Q2/1980 -18.461% Q3/1980 -14.422% Q3/1974 -8.642% IV Model Estimates • The negative premia observed for bonds and equities in some... heteroscedasticity Lagged excess holding yields and innovations in consumption appear to have some explanatory power for asset returns The expected return or risk premia for the assets are significantly influenced by the conditional second moments of returns . A CAPITAL ASSET PRICING MODEL WITH TIME- VARYING COVARIANCES GVHD: TS. Trần Thị Hải lý Nhóm thuyết trình: 1.Trịnh Quang Công 2.Bùi Thị Thùy Dương 3. Mai Thị Huỳnh Mai 4.Chung. 0.142% 0 .35 6 Q2/1980 2.046% Q1/1980 Q3/1980 Q4/1980 -0.462% -0.777% -0.515% Bond 0.761% 6.255 Q2/1980 22.274% Q2/1980 Q3/1980 -18.461% -14.422% Stock 0.995 % 2.225 Q1/1975 3. 746% Q3/1974 -8.642% IV substituting in (1), (2) => µ t = β t µ Mt (3) In the special case: E (y t ) = δ V (y t )ω – δ 3 V(H t ω) ω II. Econometric Methods Model: The multivariate GARCH (GARCH-M) For y t