please solve number 2 from above photo. Please show all the work Statistics I Ho
ID: 3316934 • Letter: P
Question
please solve number 2 from above photo. Please show all the work
Statistics I Homework (Deadline: 2017/12/07) Exercise 1 - Stock price data In this exercise, we are interested in the daily price returns (i.e. price variation over one day) of three stocks (A, B and C), expressed in arbitrary units. Table 1 shows the first 8 daily returns that we observed for these stocks. I. (a) For stocks A, B and C, calculate returns) for the first 8 days. (sample mean of returns) and 2 (sample variance of (b) For a set of observations, we call coeficient of variation the ratio u = . A stock with a high coefficient of variation is risky with poor average returns whereas a stock with a low coefficient of variation performs well and is not (too) risky. Using the coefficient of variation, rank A, B and C from the best stock to the worst. 2. We look now to a larger data set containing 100 daily returns. Figure 1 shows scatter plots associated to the couples (Stock A, Stock B) and (Stock A, Stock C) (a) Let be the sample correlation coefficient between Stock A and Stock B. Based on figure 1, can you tell which of the following values of PAB is correct ? Explain. (b) Same question as (a) with pAc, sample correlation coefficient between Stock A and Stock C. 3. In practice, using n = 100 daily returns we find that 4, 36 for Stock A, and 5, ~ 25 for Stock C. We are interested in predictions for tomorrow's returns for stocks A and C. Write XA and Xc the corresponding random variables. We assume that . Sample mean and sample variance are good approximations for A.40, and 8, so that we may assume ,-4, ¾-36, le = 5, 8-25. (a) Calculate P(XA 20) (ie. probability that Stock A's price increases) (b) Calculate P(2.5 S Xc S 7.5). 4. For this question, we recall that if X ~ N(,) and Y ~ N(u2, ) are two independent + 2, 1 +of). An index on a stock market is an average normal variables, then X + Y ~N( value of several stocks. For example, 1 = a+xe is the index associated to the stocks A and C. (e) Assume that Stock A and Stock C are completely independent. Explain why we have (b) Deduce P(2.5 I 6.5).Explanation / Answer
We use Excel to find correlations,
a)
PAB = 0.9
PAC = -0.4302
StockA StockB StockC StockA 1 S 0.974535 1 Column 3 -0.43202 -0.55654 1Related Questions
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