Hull's cost of carry

[yjhirad]

David,

In spreadsheet 3a8 theres an example of Hull Long Bond Forward. Is the $40 coupon given or is iot being backed out? I dont see am indication of coupon payment ...is the interest rate of 4% assumed to be the coupon?

jy

 

[David Harper CFA FRM]

Hi jy,

That is Hull's example 5.5: $900 bond that pays a single $40 in 4 months.
(unlike the more typical COC examples where income/dividend is expressed as constant %)
So it's a $40 (lump sum) coupon and we need a 3% discount rate assumption to convert to a PV lump sum:
$39.60 = $40*exp (-3%*4 months/12 months)

The PV lump sum, then, is the (I) is the version of cost of carry:
Forward = (Spot - I)*EXP(rT)

...so just to give color to this: the dividend/income is a benefit of ownership that, b/c it is forgone by the long forward and accrues to the commodity owner, reduces the forward price. It can find input as either constant (%) or lump sum.

I can solve for the "equivalent" constant %, to this lump sum.
Assuming (S-I)*EXP(rt) = S*EXP*(r-q)*T), then given I = 40, we can solve for the "associated" (q), which in this case happens to equal 0.5% monthly or 6% annual, such that:
900*EXP*(4% - 6%)*9/12)= $886.60
i.e., in this case, a $40 lump sum in 4 months has the same effect as a 6% dividend/coupon yield

so you can see, in a way, it's almost just a "formatting" issue

David