The stock of Business Adventures sells for $$40$ a share. Its likely dividend payout and end$$of$$year price depend on the state of the economy by the end of the year as follows: Dividend Stock price Boom $$2\mathrm{.}00$ $$50$ Normal economy $1\mathrm{.}0043$ Recession $0\mathrm{.}5034$ Calculate the expected holding$$period return and standard deviation of the holding$$period return. All three scenarios are equally likely. Q$2$: Suppose you want to estimate the risk of the IBM stock using its historical return data. Its monthly return over the past three months are: $-7\%,10\%,12\%.$ What is its standard deviation? Q$3$: Assume that you manage a risky portfolio with an expected rate of return of $17\%$ and a standard deviation of $27\%.$ The T$$bill rate is $7\%.$ a$.$ A client prefers to invest in your portfolio a proportion $($y$)$ so that his complete portfolio's standard deviation is $20\%.$ What is his investment proportion, y$?$ What is the expected rate of return on this complete portfolio? b$.$ Suppose your risky portfolio includes the following investments in the given proportions: Stock A $27\%$ Stock B $33\%$ Stock C $40\%$ Your client decides to invest in your risky portfolio a proportion $($y$)$ of his total investment budget with the remainder in a T$$bill money market fund so that his complete portfolio will have an expected rate of return of $15\%.$ b$\mathrm{.}1$ What is the proportion y$?$ What are your client's investment proportions in your three stocks and the T$$bill fund? b$\mathrm{.}2$ What is the standard deviation of the rate of return on your client's portfolio? c$.$ What is the CAL on this market?