Jim has some money to inv

Jim has some money to inv

Jim has some money to invest for one year. He can choose to invest his money either in amutual fund, or in a savings account, or in a combination of both. The guaranteed interest rateon a savings account is 6%(his bank also accepts to lend money at 6% interest rate). The mutualfund is a portfolio of stocks. Like an ordinary stock, investors can buy shares of this mutual fund,which give right to receive dividends and which can be sold at any time. The price of a share ofthe mutual fund today is $80.Based on historical data and his view of the current economic situation, Jim makes the followingscenario. There is a chance that the economy will boom, with rms making high pro ts. In thiscase the dividends per share of the mutual fund over the next year will be $5 a share and the shareprice in one year from now will be $115. Jim attributes a probability of 0.3 to this possibility. Withprobability 0.5 the economy will follow its current trend. In this case the dividends will $4 a shareand the price next year will be $84. However a downturn is not impossible given that the economylacks strength. In this case the dividends will be the same at $4 per share, but the price next yearwill be as low as $60 a share. Jim attributes a probability 0.2 to this possibility.(a) Draw a table with the possible states of the economy, their probabilities, and the rate ofreturn of the mutual fund in each state.(b) Compute the expected rate of return on the mutual fund, its standard deviation and itsSharpe ratio.(c) Compute the expected rate of return and standard deviation of Jim’s portfolio if he invests aproportion y of his money in the mutual fund and 1-y in the savings account.(d) What is the proportion y which guarantees an expected return of 10% for the portfolio? Whatis the risk (standard deviation) of the portfolio?

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