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We are planning to invest 60000$ to a bank that yields 30% (expected return after one year), bonds that yield 40% and stocks that yields 90%. We know in advance, however, that 2 of the above 3 investment choices will go bankrupt at some point before year-end but we don't know which ones. This, of course, will result to total loss of any amount that has been invested in each of these two options, along, of course with any earnings. Knowing this, our investment consultant suggested that we build a balanced portfolio so as to spread the risk and ensure some guaranteed profit.
What is the maximum guaranteed profit we can achieve?
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Are we tied to use all 3 options?
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It is not explicitly specified but obviously you must spread the amount to all three options; otherwise, if you leave one aside and the other two go bankrupt, then you will have nothing!
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If it were my money I would lock it up in a cupboard and not invest in these ventures. However if I were to advise somebody for a fee it is o.k.
The investment must be such that the yield from each of these will be same after a year.
let x,y,z be the investment in these avenues. Then
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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If the goal is to maximise the minimum amount retained, then thickhead is correct and given $60k you should invest precisely $22,964.03 in the bank, $21,323.74 in bonds, and $15,712.23 in stock. This guarantees a final amount of exactly $29,853.24 irrespective of which investments go bankrupt.
In general, you should invest whatever capital you have, if you have this silly goal, as near as possible to the proportion 266:247:182 in the 30%:40%:90% ventures, which guarantees a final amount 1729/3475 of the capital (about 49.755%).
If your goal is instead to maximise the minimum yield or profit of any given investment, which seems a likely interpretation of the problem, this changes things. I think now it is 0.3x=0.4y=0.9z, and given $60k you should now invest $28,800 in bank, $21,600 in bonds and $9600 in stock, guaranteeing a yield on any investment of precisely $8640.
In general, if this even sillier goal is yours, you should again invest any capital you have, and as near as possible to the proportion 12:9:4, which guarantees a profit on one investment exactly 14.4% of the capital.
Of course, the reasonable goal is to maximise expectation, in which case you should not invest a dime in any of it (unless you have the hopeless desperation for riches and disregard for losses of a gambler). Given two out of three investments must go bankrupt, but one of them is guaranteed not to, your expectation is to lose [edit: corrected] 17/30, 8/15 and 11/30 of any amount you invest in the 30%, 40% and 90% options respectively.
Under these conditions, only investments that give strictly greater than [corrected] 200% profit are worthwhile.
Last edited by Relentless (2016-04-29 18:11:03)
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You are talking of more than 100% profit ,not possible even without any avenue going bankrupt.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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I don't understand. I mean that whenever there are any three investment options and a random two of them will go bankrupt, only those yielding over 100% profit may be worth considering.
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Precisely speaking only those yielding over 200% may be worth considering.
{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}
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Correct!! Thank you!
If it were my money I would lock it up in a cupboard and not invest in these ventures. However if I were to advise somebody for a fee it is o.k.
The investment must be such that the yield from each of these will be same after a year.
let x,y,z be the investment in these avenues. Then
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Oh! Thank you thickhead, that is correct. I made a logical error. Which means all my expectations were calculated to be 1/3 of the investment better than they in fact are. You would actually expect to lose 17/30, 8/15 and 11/30 of any amount invested in 30%, 40% or 90% profit ventures respectively. Much worse!
Last edited by Relentless (2016-04-29 18:12:15)
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