# stock and t-bills

afrata

The market consists of two stocks: AD&5550 and 5550&AD. An investor can buy any of them in any

quantity. There is T-bill available with the rate of return 2.3% and the investor has to invest all money

he has, \$10 000 000, in market assets.

The investor believes that the prices are: for AD&5550 – \$47.40, for 5550&AD – \$91.42; expected

returns on stocks are: for AD&5550 – +2.11%, for 5550&AD – +6.13%; and the standard deviations

are: for AD&5550 – +7.13% and for 5550&AD – +13.17%. Correlation coefficient between stocks'

returns is -0.23. The investor's risk-averseness coefficient is 8. Both stocks just paid dividends of \$1.00.

Assume the investor can buy any fraction of a stock or T-bill (say, through mutual fund).

A. Assume the investor does not wish to buy T-bill at the moment, but can buy two other assets in any

combination. Plot the graph reward vs. risk. Show efficient frontier on your graph.

B. How much (approximately, with 10% accuracy) should the investor invest in stocks to maximize his

utility if he is not buying T-bill? What is his Utility in that case?

C. Assume, the investor may buy T-bill. Draw the Capital Market Line.

D. Identify Market (Balanced) Fund, MF. Show the composition of the MF and find its characteristics

(Expected Return and STD).

E. Assuming the constant growth of dividends, what are the expected growth rates of dividends for each

stock?

F. If the investor has a choice to buy either T-bill or Market Fund, which one does he prefer and why?

G. The investor can buy the following portfolio: invest \$3 700 000 into T-bill, \$5 600 000 in stock

AD&5550 and the rest of all money in stock 55500&AD. What is the expected return, STD and

associated utility of that portfolio?

H. What is the allocation of funds between stocks and T-bill to form the best optimal portfolio for the

investor?

• 7 years ago
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