Inverse mutual funds, sometimes referred to as \"bear market\" or \"short\" fund

Question

Inverse mutual funds, sometimes referred to as "bear market" or "short" funds, are designed to deliver the opposite of the performance of the index or category they track, and so can be used by traders to bet against the stock market. The following table shows the performance of three such funds as of August 12, 2011.

You invested a total of $9,000 in the three funds at the beginning of 2011, including an equal amount in SHPIX and RYURX. Your total year-to-date loss amounted to $540. How much did you invest in each of the three funds?

SHIPX

RYURX

RYIHX

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

Explanation / Answer

Answer:

Let the investment in SHIPX is x

investment in RYURX is y

and

investment in RYIHX is x (as it has same investment as SHIPX)

Total investment in three funds = $9,000

Therefore:

x + y + x = $9000

2x + y = $9,000     …………. (1)

Now total loss in these funds = $540

So,

6% of x + 5% of y + 7% of x = $540 or 6x + 5y + 7x = $54000

13x + 5y = $54,000    ……….(2)

Solving (1) and (2) for x and y, we get:

x = $3000 and y = $3000

So investment in:

SHIPX = $3000

RYURX = $3000

RYIHX = $3000

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