B)(1 mark) Which of the 3 machines nas e 22 CXI 1 mark) Suppose your first-choic
ID: 2615110 • Letter: B
Question
B)(1 mark) Which of the 3 machines nas e 22 CXI 1 mark) Suppose your first-choice machine is NOT available? Which machine would you now choose? Why? 3. (4 marks) Suppose there are only 2 risky securities in the entire market. The expected return on security A is 5% and the expected return on security B is 11%. The market capitalizations of securities A and B are equal. a) (1 mark) What is the expected return on the market portfolio? b) (1 mark) How would you construct an optimal portfolio with an expected return of 2%, assuming there is no risk-free asset, what are the weights on the two risky securities 2(1 mark) How would you construct an optimal portfolio with an expected return of 5%, assuming there is a risk-free asset returning 296, what are the weights on the two risky securities. (1 mark) Suppose you form a portfolio by making a $25 investment in the risk- free asset and a $75 investment in the market-portfolio. The standard deviation of this portfolio is 0.20. What must be the standard deviation of the market portfolio? d) 1 Page 2 of7Explanation / Answer
Answer a) Expected return from market Porfolio
E(R) = w1r1 + w2r2 = 0.5 * 5% + 0.5 *11% = 8%
Answer b) As required rate of return of portfolio (2%) < either of the two asset class , so the optimal portfolio will be combination of long and short position of the available stocks
w1 + w2 = 1, E(R) = w1r1 + (1-w2) r2
=> 2 = w * 5 + (1-w) *11
=> w = 9/6 = 1.5
indicate , w1 = 1.5 and w2 = 1-1.5 = - 0.5 i.e short position
Answer 3)
As the risk ( standard deviationis not given in the question ) , so the siad problem solved by use of linear programming problem (LPP) model in excel solver
E(R)= w1r1 + w2r2 +w3r3
ST
w1+ w2+w3 <= 1
E(R) = 5% solving the out come
0.4*5+0.2*11+0.4*2 , i.e, Asset with 5% = 40% ,Asset with 11% = 20% and Risk free asset = 40% of the total portfolio.
Answer d)
?(Rp) = w1?(R1) + w2?(R2)
Here , w1 = 25/100 = 0.25 similarly , w2 = 75/100 = 0.75
?(R1) = 0 , as risk free asset , ?(R2) =?
as per question , ?(Rp) =0.2
=>0.2 = 0+ 0.75* ?(R2) => ?(R2) = 0.2/0.75 = 0.2666= 0.27 .
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