When I invest money in bonds and interest rates decrease, the value of
the bond increases in inverse relationship.  Is there an
investment which goes up in value in direct relationship when
interest rates increase?

Hello.

First of all, I must note that Google Answers provides general
information and is not a substitute for professional investment
advice. No warranties are expressed or implied. You should carefully
research all investments and proceed with extreme caution.

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Yes, there are a number of investments that go up in value in direct
relationship to rising interest rates.


(1) Funds that short-sell bonds

From Forbes:
"When rates finally rise--and they will--you can still make money in
the bond market. How? By selling bonds short. A couple of mutual funds
are experts at this game."
"How to Short T Bonds"  / James Grant, 08.11.03
Read the article at forbes.com:
http://www.forbes.com/markets/free_forbes/2003/0811/106.html

More about the funds mentioned in the Forbes article:

Profunds Rising Rate Opportunity Fund
http://www.profunds.com/profiles/profile.asp?id=69

Rydex Juno fund:
http://www.rydexfunds.com/website/fund_info_fset.cfm?rydexfundid=14&show=none

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(2) Prime-Rate Funds

From BusinessWeek:

"...it's prime time for prime-rate funds. Also known as bank loan
funds, these portfolios are comprised of loans made to corporate
borrowers that are pegged to the prime lending rate, now 4%; the rates
on the loans are usually prime plus 3% or so. That means the funds'
yields rise along with rates."
source: BusinessWeek, October 20, 2003
http://www.businessweek.com/magazine/content/03_42/b3854130.htm

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(3) Interest Rate Options

 "Interest rate Options are European-style, cash-settled options on
the yield of U.S. Treasury securities. Available to meet your needs
are options on short-, medium-, and long-term rates. These options
give you an opportunity to invest based upon your views of the
direction of interest rates.
  In general, when yield-based options are purchased, a call buyer and
a put buyer have opposite expectations about interest rate movements.
A call buyer anticipates interest rates will go up, increasing the
value of the call position. A put buyer anticipates that rates will go
down, increasing the value of the put position."
source: Chicago Board Options Exchange
http://www.cboe.com/OptProd/InterestRateOptions.asp

Note well that "options involve risk and are not suitable for all
investors."

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search terms:
"rising rates," "make money"
"rates rise," profit
"when interest rates", "go up"

I hope this helps.

Using interest rate futures, which have the same payoff as the
underlying bond, you can have a short position in different maturities
of bonds.

http://www.cbot.com/cbot/www/page/0,1398,12+31,00.html

The payoff is directly opposite of that of an investment in bonds.
Commonly used to hedge the risk of a bond portfolio it can also be
used to profit from rising interest rates or declining bond values.