BUS5SBF Statistics For Business And Finance

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Question:

Create the line charts for each of S&P, Yahoo and Google series using Close prices against time in Excel and comment on your observations (focusing time series features).
a. Calculate returns for these three series in Excel using the transformation: rt = 100 ln[Pt/Pt-1]
Hints:
• We performed a similar task in Tutorial 01.
• These numbers would represent percentages after multiplication with 100 in the formula above. However,you would not put a percentage sign in your data. For example, returns for two periods are 0.35% and 0.41% but we omit % sign in our excel worksheet and use 0.35 and 0.41.
b. Obtain the summary statistics for your sample and briefly discuss the risk and average return relationship in each stock. Which stock (Google or Yahoo) is relatively riskier than the other
c. Perform the Jarque-Berra test of normally distributed returns for each of Yahoo, Google and S&P.

Write down the sampling distribution of sample means for both stocks when a sample of 36 months is taken. Use the sampling distributions of part (a) above to answer the following parts.
b. What is the probability of observing average return of at least 4% in both stocks
c. What is the likelihood of loss in a sample of 36 periods for both stocks

Before investing in one of the two stocks based on higher risk-return relationship, you further want to determine whether both stocks have same population average return. Perform an appropriate hypothesis test using information in your actual sample of 56 observations and report your findings. Also, which stock will you prefer and why

Create two new columns in Excel for excess return on your preferred stock (yt) and excess market return (xt) by subtracting the 10-year T-Bill rate from both series as follows.
Excess return on your preferred stock: yt = rt - rf,t
Excess return on market: xt = rM,t - rf,t

a. Estimate the CAPM using linear regression where the dependent variable is excess return on your preferred stock while the independent variable is excess market return (computed as return on S&P 500 minus the risk fee rate) and report your results.
b. Interpret the estimated coefficients in relation to the profitability of the Stock and its riskiness in comparison with the market.
c. Interpret the value of R2
d. Interpret 95% confidence interval for the slope coefficient.

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