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1. The estimate of β is 1.4626.
2. A 95% confidence interval for β is [0.9671, 1.9581].
3. r- 0.04=1.4626*0.06, r=0.1278.
4. A 95% confidence interval for the interest rate is [0.0980, 0.1575].
5. NPV=-100,000+8000/(1+r)+…+8000/(1+r)^132=-100,000+8000/r=-37380
6.  [-18387.41,- 49202.46] 

All values in this interval are negative. The investment has high risk of loss.

1. r<8%
2. H0: r≥8%,  H1: r<8%

As r- 0.04=0.06β,

1. 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.

1. They claim that the idiosyncratic risk of these investments generates positive returns, while it is treated as a gamble by CAPM.
2. 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.

1. 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.

1. 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.
2. 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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