calculation of implied fwd price

[noalv4]

Hi David,

Regarding the examples that you gave in the study notes which are demonstrated in spreadsheet P1.T3.3b:

Why the EXP is in terms of monthes insted of terms of years? for example page 74, the bond with price of $900 with time to maturity if 9 monthes, the EXP of time is 9 and not 9/12.

Thanks,
Noa.

 

[David Harper CFA FRM]

Hi Noa,

It should be better labelled (tagged for future revision). This is an example of the convenience of time-additive property of continuous compounding: you can do it monthly or annually, it doesn't matter. Forgetting the lump sum and just using the financing cost (interest rate):

• Annually: $900 spot*exp(4.0% per annum rate * 9/12 year) = $927.41, which is the same as:
• Monthly: 900 *exp(0.33% per month rate * 9 months) = $927.41

so, either way we have in the exponent the same: 4%*9/12, although the continuous assumption allows us to be so "cavalier" in treating time like it can be added without further attention. Thanks,