Jim has some money to invest for one year. He can choose to invest his money eit

Question

Jim has some money to invest for one year. He can choose to invest his money either in a
mutual fund, or in a savings account, or in a combination of both. The guaranteed interest rate
on a savings account is 6%(his bank also accepts to lend money at 6% interest rate). The mutual
fund 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 of
the mutual fund today is $80.
Based on historical data and his view of the current economic situation, Jim makes the following
scenario. There is a chance that the economy will boom, with rms making high pro ts. In this
case 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. With
probability 0.5 the economy will follow its current trend. In this case the dividends will $4 a share
and the price next year will be $84. However a downturn is not impossible given that the economy
lacks strength. In this case the dividends will be the same at $4 per share, but the price next year
will 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 of
return of the mutual fund in each state.
(b) Compute the expected rate of return on the mutual fund, its standard deviation and its
Sharpe ratio.
(c) Compute the expected rate of return and standard deviation of Jim's portfolio if he invests a
proportion 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? What
is the risk (standard deviation) of the portfolio?

Explanation / Answer

State of the economy Probability Dividend Price Cost of Mutual Fund (X-M)^2*Probbility Boom 0.3 5 115 4.348 0.135 Current Trend 0.5 4 84 4.762 0.033 Downturn 0.2 4 60 6.667 0.543 Expected Rate of Return=0.3*4.348+0.5*4.762+0.2*6.667 5.019 0.711 SD=Square Root(0.711) 0.843 Let Y is the proportion of MF or Y*5.019+(1-y)*6=10 or (5.019-6)Y=10-6=4 or Y=4/5.019 80 Proportion of Savings A/c 20

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