Interest rates

[wrongsaidfred]

Hi David,

I think you have already addressed this, but I just looked at some old FRM questions in a Schwesser book and some of the interest rate conventions were really strange. For instance, one question says "the one year US dollar interest rate is 3 percent..." and we were supposed to assume annual compounding because they don't say otherwise. And one of the answers is almost exactly correct if you assumed continuous compounding. Then it goes on to say that we should be prepared for these types of ambiguities. Are there any rate conventions that do not need to be stated explicitly?

There was one other question where a "3 month interest rate of 2%" meant that the total amount of interest gained on $100 over that 3 months is $2. Is this a normal convention? For instance, "a 3 month LIBOR rate of 4%." Would this mean that the rate for those 3 months is 1% per 90 days or 4% for those 90 days?

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

1. No, there really are not rate conventions that can or should be assumed (that old question is an example of something I think we've helped get rid of by persistence). I thought i shared GARP's last reply to me on this, in a previous thread, but the FRM program Director agrees that the compound conventions need to be explicitly stated. The only assumption, as we've discussed, that is valid is the sort: "A $100 face value bond with a 6% coupon that pays semi-annually." In this case, you should assume semi-annual (although I prefer "a $100 face value bond with a 6% semi-annual coupon."

2. A good example, too. That is NOT normal convention (e.g., $2 over three months) and also something I pointed out to GARP as incorrect. Technically that is a "simple interest rate," but using that convention leads to all sort of confusion. GARP should, following Hull's good example, only use "per annum" rates. If we think about just two examples

1. cost of carry: what's the three month forward price if the riskfree rate is 4%? We always assume per annum, such that F(0) = S*exp(4%*3/12), we don't assume S*exp(4%)
2. Eurodollar price of 96 corresponds to a 4% LIBOR which is NOT 16% per annum (4% over three months), it is 4% per annum compounded quarterly (1% over 90 days). In the case of a ED contract, it is okay to infer from the "96" alone that it is implicitly as 4% per annum (because that is always the assumption!) and quarterly compounding because it's a 90 day instrument

Hopefully that explains why my position is that interest rates should always be "per annum" (best if explicitly stated; but assumed if not) and the compound frequency should also be explicitly stated (the only exception being when the instrument already conveys that information; e.g., bond coupons; Eurodollar futures)

Hope that helps, David

 

[wrongsaidfred]

It certainly does.

Thanks,
Mike