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Hull page 84

S

sonnyshook

Member
Year 1
Zero rate = 3.0

Year 2
Zero Rate = 4.0
Forward rate = 5.0

If an investor borrows £100 at 3% for 1 Year and then invests the money at 4% for 2 years the result is an outflow of 100e0.03x1 = $103.05 at the end of year 1 and an inflow of 100e0.04x2 = $108.33 at the end of year 2. Since 108.33= $103.05 e0.05 , a return equal to 5% is earned on $103.05 during the second year.


I understand the concept of forward rates but this doesn’t make sense to me because if he has returned $103.55 at the end of year one how can he earn a forward rate on money he no longer has. I hate problems like this because I spend hours aching to figure out what he is talking about hours better spent studying difficult stuff like the ugly Radon-Nikodym derivative.
 
At time 0, you borrow 100 and invest 100, ie nil effect
At time 1, you pay back the 103.05 (from the loan)
At time 2, you receive 108.33 (from the investment)

This is the same as investing 103.05 at time 1 and receiving 108.33 in return.
Compare this to paying 100 now to receive 105 in a year.

Yes you have to pay back the loan, but you can't expect to earn something for nothing. You'll be out of pocket for second year only (over which you earn interest)

A simpler replicating portfolio would be to invest 100 now for 1 year then reinvest at forward rate and compare this to investing 100 now for 2 years. Then again you can't always find a simple replicating portfolio, so it's useful to try to understand it.

Just try to think of all transactions in the simplest of terms, ie individual cash flows (a simple investment is two cash flows), and eventually you should get the hand of replicating portfolios.
 
So at the end of year 1 do you at any point use money from your investment to pay back the money you owe the lender or you use money from other sources.
 
thanks ...I guess it makes some sense. I am now going try to figure out why you don't use your own money in the first place.
 
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