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Essay by XIAOQING LUO • November 5, 2017 • Coursework • 435 Words (2 Pages) • 940 Views
1.
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- The estimate of β is 1.4626.
- A 95% confidence interval for β is [0.9671, 1.9581].
- r- 0.04=1.4626*0.06, r=0.1278.
- A 95% confidence interval for the interest rate is [0.0980, 0.1575].
- NPV=-100,000+8000/(1+r)+…+8000/(1+r)^132=-100,000+8000/r=-37380
- [-18387.41,- 49202.46]
All values in this interval are negative. The investment has high risk of loss.
- r<8%
- H0: r≥8%, H1: r<8%
As r- 0.04=0.06β,
- That’s mean it is the same to test H0: β ≥0.6667, H1: β <0.6667
t= (1.4626-0.6667)/0.2505=3.1772
p=T.DIST(F22,130,TRUE)= 0.99907>0.01
Thus, we cannot reject H0 at 99% significant level, the interest rate is higher than the upper bound of this region.
6.
- They claim that the idiosyncratic risk of these investments generates positive returns, while it is treated as a gamble by CAPM.
- Those with Β=0 are uncorrelated with the market, reducing the variation in returns of the portfolio.
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By regressing Berkshire returns on market returns, we can learn that the 95% confidence interval for the intercept is [0.00483, 0.01751. Since the 0 lies outside the 95% confidence interval, the claim stands a good chance to be true.
- The 95% confidence interval for the β is [0.53505, 0.80319]. After checking that 1 lies outside the confidence interval, we can conclude that the claim is very likely to be false.
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The associations of market return and Berkshire stock return appears linear. The linear fit is Berkshire Stock Return = 0.0112 + 0.6691*Market Return with r^2=0.2013 and Se=0.0618, the linear pattern is weak. There are some positive outliers that are in loose agreement with SRM.
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This plot shows no pattern.
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We use a time plot of the residuals to check independence. The residuals vary around 0 consistently over time, with no drifts.
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The distribution of residuals is nearly normal as the residuals track the diagonal reference line and remain inside the adjacent bands.
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The estimate slope from this equation is 0.66380, the estimate intercept is 0.00982, with r^2=0.19964 and Se=0.6175. the reason why the differences are so small is that the risk free returns are almost 0 constantly compared with market and stock returns.
- The t ratio of intercept is 3.09 with p=0.0021, which is far less than the common threshold 0.05. The 95% confidence interval for the intercept is [0.00358, 0.01606]. Both of these tell us that α is statistically significantly larger than 0, thus Berkshire Hathaway produce excess α.
- Since 95% confidence interval for β is [0.53010, 0.79750] and the estimate β=0.66380<1, Berkshire Hathaway is not a growth stock.
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