The following are monthly rates of return for two companies during a six-month period: Month Firm A Firm B 1 − 0.04 0.07 2 0.06 − 0.02 3 − 0.07 − 0.10 4 0.12 0.15 5 − 0.02 − 0.06 6 0.05 0.02 Compute the following. i. Average monthly rate of return i R for each stock ii. Standard deviation of returns for each stock iii. Covariance between the rates of return (20 marks)
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To compute the average monthly rate of return, standard deviation of returns, and covariance between the rates of return for Firm A and Firm B, we will follow these steps: Show more…
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Consider the annual returns of stock $\mathrm{A}$ and $\mathrm{B}$, as given in the following table. $$ \begin{array}{crr} \hline \text { Year } & \text { Stock } A & \text { Stock } B \\ \hline 1 & 80.95 \% & 58.26 \% \\ 2 & -47.37 \% & -33.79 \% \\ 3 & 31.00 \% & 29.88 \% \\ 4 & 132.44 \% & 30.35 \% \\ 5 & 32.02 \% & 2.94 \% \\ 6 & 25.37 \% & -4.29 \% \\ 7 & -28.57 \% & 28.86 \% \\ 8 & 0.00 \% & -6.36 \% \\ 9 & 11.67 \% & 48.64 \% \\ 10 & 36.19 \% & 23.55 \% \\ \hline \end{array} $$ a. Estimate the average and standard deviation in annual returns in each company. b. Estimate the covariance and correlation in returns between these companies.
Statistical analysis
Problem
17) Investment Portfolio Analysis A portfolio manager is analyzing two stocks, Stock A and Stock B. The manager has compiled the following historical data on the monthly returns of each stock: • Stock A: Expected monthly return E(RA) = 8%, with a standard deviation σA = 5%. • Stock B: Expected monthly return E(RB) = 12%, with a standard deviation σB = 7%. • The correlation coefficient between the returns of Stock A and Stock B is ρAB = 0.3. The manager plans to allocate 60% of the portfolio to Stock A and 40% to Stock B. (a) What is the expected return of the portfolio? (b) What is the standard deviation of the portfolio? (c) What is the probability that the portfolio will return less than 0% in a given month, assuming the portfolio returns are normally distributed?
Daniel C.
Danielle F.
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