Thread: Fractions ---- please help me figure this one

1. A Financial Advisor helps (FA) one of the firm’s clients to diversify their portfolio. According to the clients profile the FA recommends the following plan.



Investment / Fraction of Total Portfolio



Technology Stocks 1/5



Pharmaceutical stocks 1/10



Banking & Finance 2/7



Real Estate 1/5



Bonds 1/10



The remainder is in cash in money market accounts.



a) What fraction of the portfolio is in cash ?


b) If the cash holdings are $7,000 what is the total value of the portfolio?



c) Six months later due to the volatility in the market the Financial Advisor instructs

the client to sell two thirds() of his technology holdings and deposit the money in a

money market account. What fraction of the portfolio is represented by the

technology stocks after the investor (client) completes the transaction

You're told that various holdings are 1/5, 1/10, 2/7, 1/5, 1/10 and you want the remainder. Remembering that 1/5 is the same as 2/10, 3/15, 4/20 and so forth, we want to express the holdings all as multiples of the same part (a common denominator). The denominators (bottom lines) are 5,10 and 7, so a common multiple is 70: that is, any number of 5ths, 7ths or 10ths can be expressed as 70ths. (70 is the smallest number we can use, so its the least common denominator.) Since 70 = 14 times 5, 1/5 = 14/70: 1/10 = 7/70, 2/7 = 20/70. The various holdings are now 14, 7, 20, 14 and 7 in units of 1/70, so total 62/70. Hence the remaining holding is 70-62 = 8 in units of 1/70, that is, 8/70 = 4/35.

If the total holding is X (try to find the quantity you're being asked for and give it a letter), then the cash holding is 4X/35. You're told this = 7000. Solve this equation for X.

a) What fraction of the portfolio is in cash ?

Cash = 1 -(1/5 +1/10 +2/7 +1/10 +1/5)
= 1 -[(14*1 +7*1 +10*2 +7*1 +14*1) / 70]
= 1 -[62 / 70]
= 8/70
= 4/35 -----------answer.

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b) If the cash holdings are $7,000 what is the total value of the portfolio?

Let x = total value of the portfolio
(4/35)x = $7,000
Divide both sides by 4/35,
x = ($7,000) / (4/35)
x = ($7,000)*(35/4) = $61,250 --------answer.

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c) "Six months later due to the volatility in the market the Financial Advisor instructs the client to sell two thirds() of his technology holdings ....."

Original Technology holdings = (1/5)($61,250)
2/3 of that is (2/3)[(1/5)($61,250)] = (2/15)($61,250)

"... and deposit the money in a (the?) money market account. What fraction of the portfolio is represented by the technology stocks after the investor (client) completes the transaction?"

What is left after selling of (2/15)($61,250) :

a) New Tecnology stocks = (1/3)[(1/5)($61,250)] = (1/15)($61,250)
b) New value of portfolio = $61,250 -(2/15)($61,250) = (13/15)($61,250)
So,
[(1/15)($61,250)] / [(13/15)($61,250)]
= (1/15) / (13/15)
= (1/15)*(15/13)
= 1 / 13 -----------answer.

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***Oopps, something wrong. Let me correct it.

The (2/15)($61,250) is still a part of the portfolio of the client. It is just changed from technology to money market. So there is no new value for the portfolio--it is still $61,250.

Therefore, the new technology stock now is
[(1/15)($61,250)] / ($61,250) = 1/15 of the portfolio ----answer.
Not the 1/13 above.