Tiểu luận Đầu tư tài chính A CAPITAL ASSET PRICING MODEL WITH TIMEVARYING COVARIANCES

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

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

 yt: the vector of excess returns of all assets in the

market measured as the nominal return during period t

these returns give information available at the time t-1

period

 The CAPM requires:

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

bonds), stocks

1959 through the second quarter of 1984 (102

observations)

 The Standard and Poor’s 500 equity series was used with Citibase interest rates.

returns are used with Salomon Brothers bill and bond

yields

Mean of Excess holding yield Excess return

-0.462% -0.777% -0.515%

Q3/1980

-18.461% -14.422%

IV Model Estimates

• The negative premia observed for bonds and equities in some periods could be due to the preferential tax

treatment as previously mentioned

 Figures 4-6 are the estimated betas.

slightly above one and that for bills is close to zero

V Diagnostic Tests

variances in each of the three equations for the

conditional expectation of the excess holding yields

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)

forming their expectations

forecast return

VI Conclusions

 The conditional covariance matrix of the asset returns is

strongly autoregressive.

 The expected return or risk premia for the assets are

significantly influenced by the conditional second moments of returns.

 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.