Cash to Synthetic Equity Index

This is generally pretty straightforward, but I can see CFAI throwing a bit of a curveball in there, and so my question is actually about a pretty basic concept in the curriculum. Say a manager wants cash funds to have the exposure to an equity index for a period of 6 months, without actually buying stock. We’re generally given the annual risk-free rate and dividend yield of the index. Say we’re given the annualized 6-month risk-free rate in a problem. Would we then use in the numerator for N*

N* = V(1+RF(1/2)) instead of N* = V(1+RF)^(1/2)?

I know this is pretty fundamental stuff, but just wanna be sure about it. If anyone can sort this out that would be great.

Thanks!

  1. is it a LIBOR? From what you say it does not seem to be. So do not think you should multiply by 1/2 as you have done.

  2. It is the 6 month risk free rate. so shouldn’t it be used directly? (as V*(1+rf) ?

I am confused about this too. When do we use exponent and when multiplication?

Hey cpk - not talking about LIBOR here. Say they tell you that the current yield on the 6-month T-bill is 1.0%, for example. The thing is the rate is quoted as an annualized rate, so it needs to be adjusted, because the synthetic holding perid is 6 months. So the question is - is it halved and used directly, or not halved and “compounded” for half a year? I’d think it’s the former, but def not positive.

In the Fixed income readings - they tell you Coupon is 6% semiannual.

CPN=6% semiannual, for us PMt=3, N=N*2

CPN=6% Annual -> PMT=6 for N periods.


so if current yield is 1% on a 6-month T-Bill - it will be 1.01^0.5. The 1% is the annualized yield. I have not seen them provide a semi-annual yield e.g. before.


Maybe S2000 or someone else can correct me if I am wrong (and I have been known to be wrong).

Unless they tell you that it’s a nominal interest (e.g., they specify LIBOR), I’d assume that it’s an effective rate. In my experience, they always use effective rates for this stuff.

(Note: for equity indices, they generally assume continuous dividends, so they usually convert the annual (effective) risk-free rate to a continuously compounded rate.)