Stock Market and Market Portfolio Essay

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Part 1

Dependent Variable: Y | | | Method: Least Squares | | | Date: 08/27/12 Time: 19:37 | | | Sample (adjusted): 9/10/1984 8/29/2011 | | Included observations: 7034 after adjustments | | | | | | | | | | | | Variable | Coefficient | Std. Error | t-Statistic | Prob. | | | | | | | | | | | C | 0.010895 | 0.036165 | 0.301259 | 0.7632 | X | 1.192214 | 0.030519 | 39.06480 | 0.0000 | | | | | | | | | | | R-squared | 0.178318 | Mean dependent var | 0.033510 | Adjusted R-squared | 0.178201 | S.D. dependent var | 3.345379 | S.E. of regression | 3.032690 | Akaike info criterion | 5.057061 | Sum squared resid | 64674.77 | Schwarz criterion | 5.059012 | Log likelihood | -17783.69 | Hannan-Quinn criter. | 5.057733 | F-statistic | 1526.059 | Durbin-Watson stat | 1.964847 | Prob(F-statistic) | 0.000000 | | | | | | | | | | | | | |

Question 1

Regression equation: yt=0.0109+1.1922xt
Alpha(hat)=0.0109.
Interpretation: The excess return on stock will be 1.09% when then excess return on market portfolio is 0.
Beta(hat)=1.1922.
Interpretation: If the excess return on market portfolio increases by 1 percent, then the excess return on stock increases by 1.1922%.
Question 2 Procedures
(1) H0: αd=0 stock perform as good as portfolio
H1: αd≠0 stock is not perform as good as portfolio (2) Get a test statistic (TS) t=0.010895/0.036165=0.3012
(3) Significant level : α=0.05 P-value =0.7632. Thus P-value>α. We fail to reject the null hypothesis. Our decision is in favour of H0 meaning that the excess return on the IT stock is what the CAPM model predicts.

(4) I would not invest my money in this portfolio. I will only invest my money in a portfolio When the IT stocks are underpriced, which means that the abnormal return has effect on the excess return on the IT stocks. Based on the test result, we know that the portfolio of IT stocks is fairly priced because there is no extra return made from the portfolio of IT stocks. Moreover, its Beta is greater than 1. This means that IT stocks are more risky than market portfolio. I am risk aversion, and then I will not invest his/her money in this portfolio.

Question 3
Procedures
(1) H0: βd=1 The IT stock tracks the market portfolio
H1: βd>1 The IT stock is more risky (2) Test statistic (TS)=(1.192214-1)/0.030519=6.29 (3) Critical value: α=0.05 tcritical=tα,n-2=t0.05,7032=1.645( refer table) tstat=6.29>1.645 We reject βd=1 at 5% significant level. Therefore, the IT stock is more risky then the market portfolio.

Part 2
Head tutor is right. In CAPM model, there is only one explanatory variable which is excess return on market portfolio. Hence, this model is too simple so that it cannot capture everything that is going on in the market. Thus the result may not be accurate. In order for better estimated return to be obtained, Fama-French model should be used. The Fama-French three factor model is based on CAPM model. It include extra two explanatory variables which may explain the variation of the excess return. The two variables are firm size and book to market equity. These two firm-characteristic variables are chosen because of long-standing observations that firm size and book-to-market ratio predict deviations of average stock returns from levels consistent with the CAPM (Bodie, 2011). Thus, by including the extra variables, this model can be better to capture sensitivity to risk factors in the macroeconomy. Then the estimated excess return can be more accurate.
The Fama-French three factor model is ‘Rit-Rft=β0+β1(Rmt-Rft)+β2SIZE+β3Book+ut’. Hence in order to run the suggested Fama-French three factor model, the following data within a specific period should be obtained. The first one is market index and risk free rate for a specific period so that we can get the market index excess
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