cash and carry q1 - r33

ok so the answer to 1C involves discounting the purchased gold at $300 to $295.5336. I understand how they are doing this (based on the lease rate). my question is – would you do the same discounting for a convenience yield?

I guess, I’m wondering how you treat convenience yield in these types of problems.

F = so*e^(r-d)*t -> when lease rate d is given

the other way

If they gave storage cost Lambda and Convenience yield c

F = so*e^(r+lambda - c )*t

lambda - c = -d

If the storage cost exceeds convenience yield - you are paying a lease rate.

thx. i understand the formulas. it’s pretty basic/intuitive.

but I fail to grasp (in plain english) why

  1. If we started with a So rate of $300 for gold (1a), why are we now discounting it by the lease rate value in (1c) down to $295.5336. Is it because we are immediately leasing it and getting the lease payment on day 0?

  2. Assuming we earn a convenience yield that exceeds storage, etc., say we were an industrial pipe maker and we had a pile of copper that gave us a convenience yield of 5% with 1% storage costs (both #s continuous compounding, etc.). Should we also discount the starting Spot by 4%?

If you are getting a lease payment on day 0 for question #1, then you would discount it, but not for #2 maybe ?? is my question.

when you got paid the lease rate - that is when you discounted it.

in the 2nd case - since the convenience yield exceeded the storage cost - you would actually be paying more?

makes sense. i dont know why, but I was trying to equate convenience yield with lease payment in the same functional sense. as in “these are both positive values to me as a long in a commodity” – so why aren’t I treating them the same way…

because they aren’t exactly the same, as you explained.

thanks much.