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Domination of security

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Assume that you are currently holding security O, and that (E , ) = (7, 3).
You are considering a portfolio consisting of risk free security F with RF = 3, and a risky
security I with (ERI, ) = (10, 4). The objective is to equalize the risk of this portfolio to
the risk of security O.

Does a portfolio dominates security O.
If it does, decide can I decide how an investment of \$100,000 should be distributed among securities F and I.

https://brainmass.com/math/linear-programming/current-domination-security-19395

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Assume that you are currently holding security O, and that (E , ) = (7, 3).
You are considering a portfolio consisting of risk free security F with RF = 3, and a risky
security I with (ERI, ) = (10, 4). The objective is to equalize the risk of this portfolio to
the risk of security O.

Does a portfolio dominates security O.

Security I dominates security O.
If it does, decide can I decide how an investment of \$100,000 should be distributed among securities F and I.

Let us Invest x proportion in risk free security and y proportion in security I.

Risk is given by the standard deviation:

Total risk will be given by (x*0^2 + y* 4^2)^1/2 ( note when we combine 2 components with different standard deviations , the combined std dev is given by (a*std1^2 + b*std2^2)^1/2 where a and b are the proportions invested in security 1 & 2 respectively.

Here x+y =1 ( total of two proportions)

Or (16y)^1/2 = 3 ( risk of O)
Y = 9/16.

Hence Invest 9/16 * 100,000 in security I and 7/16*100,000 in security F.

Net Expected Value = 10*9/16 + 3*7/16 = 6.9375.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!