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#1
09-11-2007, 09:04 PM
 ybern Member SOA Join Date: May 2007 Location: Canada Studying for ever Favorite beer: anyone Posts: 97
Profit question

I was wondering if my understanding of the profit is right:

Let say I enter a one-year long forward with a \$104 forward price and buy a zero-coupon bond at a risk free interest of 4% for \$100 to get \$104 in 1 year and that the spot price in 1 year is \$109.

My profit would be 109 - 104 = \$5

I have 2 questions:

1- Why isn't it 109 - 100 = \$9?

Is it because the 4% risk free is not a profit since I would have to pay 4% as well if I would borrow the \$100?

2- Would it be different if the risk free coupon would give me 5% and I had borrow \$100 at 4% interest?
#2
09-12-2007, 02:12 AM
 jraven Member Join Date: Aug 2007 Location: New Hampshire Studying for nothing! College: Penn State Posts: 1,262

Quote:
 Originally Posted by ybern I was wondering if my understanding of the profit is right: Let say I enter a one-year long forward with a \$104 forward price and buy a zero-coupon bond at a risk free interest of 4% for \$100 to get \$104 in 1 year and that the spot price in 1 year is \$109. My profit would be 109 - 104 = \$5 I have 2 questions: 1- Why isn't it 109 - 100 = \$9? Is it because the 4% risk free is not a profit since I would have to pay 4% as well if I would borrow the \$100?
You generally take time-value-of-money into account when determining profit. Given that the risk free rate is 4%, if we spend \$100 at time 0 and make \$109 at time 1, that makes our profit at time 1 come out to
$109 - 100 (1.04) = 109 - 104 = 5$

Quote:
 2- Would it be different if the risk free coupon would give me 5% and I had borrow \$100 at 4% interest?
It's a little strange to have two risk-free interest rates going on in a problem, since that would allow for arbitrage.
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