Question

Inverse mutual funds, sometimes referred to as "bear market" or "short" funds, seek to deliver the opposite of the performance of the index or category they track, and can thus be used by traders to bet against the stock market. This question is based on the following table, which shows the performance of three such funds as of August 12, 2011.

	Year-to-date Loss
SHPIX (Short Smallcap Profund)	6%
RYURX (Rydex Inverse S&P 500)	5%
RYIHX (Rydex Inverse High Yield)	7%

You invested a total of $8,000 in the three funds at the beginning of 2011, including an equal amount in RYURX and RYIHX. Your year-to-date loss from the first two funds amounted to $340. How much did you invest in each of the three funds?

SHPIX	$
RYURX	$
RYIHX	$

Answer 1

Let the Amount of investment in SHPIX = x ,

Now equal amount is invested in RYURX and RYIHX

So Let the amount of investment in RYURX = amount of investment in RYIHX = y

total amount investment = Amount of investment in SHPIX + amount of investment in RYURX + amount of investment in RYIHX

8000 = x + y + y

x + 2y = 8000                   

x = 8000 - 2y                (Equation 1)

It it given that loss from first two funds is $340

6%(x) + 5%(y) = 340

(6/100)(x) + (5/100)(y)= 340

6x + 5y = 34000          (equation 2)

Substituting the value of x from equation1 into equation 2, we get

6(8000 - 2y) + 5y = 34000

48000 - 12y + 5y = 34000

7y = 14000

y = 14000 / 7 = 2000

Now substituting the value of y in in equation 1 to find x

x = 8000 - 2(2000) = 8000 - 4000 = 4000

So we now have

Amount of investment in SHPIX = x = $4000

Amount of investment in RYURX = y = $2000

Amount of investment in RYIHX = y = $2000