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You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 8%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y, respectively.

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Answer:

The total investment in P should be $405.40 which is further divided in X and Y as $243.24 and $162.16 respectively.

Explanation:

Expected return of risky portfolio is given as

E(P)=W(X)E(X)+W(Y)R(Y)

     = 0.60*14% + 0.40*10 % = 12.40%

So the expected return of risky portfolio is 12.40%.

Let the investment in risky portfolio be p

(1-p)*5% + p*12.40% = 8%

Solving this gives

p = 0.4054*$1000=$405.4

So the amount to be added in the risky portfolio is $405.4. This is further divided in X and Y as follows

amount invested in X = 0.4054*0.60*1000 = $243.243

amount invested in Y 0.4054*0.40 * 1000 = $162.162

So the total investment in P should be $405.40 which is further divided in X and Y as $243.24 and $162.16 respectively.

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