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 $12,000 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 $510. How much did you invest in each of the three funds?

Question

Ibrahim Hammond

Mathematics

27 December, 18:27

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 $12,000 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 $510. How much did you invest in each of the three funds?

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Answers (1)

Know the Answer?

Kamron · Answer 1

Let SHPIX = x = $6000

Let RYURX=y=$3000

Let RYIHX=z = $3000

Step-by-step explanation:

y=z eqn ... 1

x+y+z=$12000 eqn ... 2

0.06x+0.05y=$510 eqn ... 3

From equation 2, x=12000-y-z eqn ... 4

Since y=z, eqn ... 1 becomes x=12000-2y ... eqn 4

Substitute equation 4 into equation 2

0.06 (12000-2y) + 0.5y=510

720-0.12y+0.5y=510

720-0.07y=510

0.07y=720-510

0.07y=210

divide both sides by 0.07

y=210/0.07

y=$3000

since y=z

Then z=$3000 as well

Finally x+$3000+$3000=$12000

x+$6000=$12000

x=$12000-$6000

x=$6000