Hello All,

Let’s say I am being given a semi-annual yield of 4.5130%. Therefore, if I have to find yield per quarter, I would first find the yield for six months, i.e. 4.5130/2 => r = 0.022565. Now, to calculate yield per quarter (rq), I would do {(1+rq)^.5 -1} => rq=1.12195% Hence, EAY = 4.4880. I am good with this.

However, why can’t we calculate like this:

We are given semi-annual yield for six months, r = 0.022565. Therefore, we can calculate r/2 = 0.0112825. This is yield for 3 months. Hence, EAY using this newly calculated,r, is equal to ((1+0.0112825)^4-1) = 4.5899%. What’s wrong with this method? Essentially, what I am asking is that if we can halve the annual yield to get a semi-annual yield (i.e. we divided 4.5130 by 2), why can’t we divide the given annual yield by 4 and then annualize it using ()^4? I am curious. Moreover, I see that EAY using this method is a little higher than the previous method because we are compounding over 4 periods, as opposed to compounding over 2 periods (i.e. while computing the square root) in the earlier method. It’s not that we never divide the given annual yield to get a lower multiple yield. We do so. For instance, given a 90-day T-bill with annualized discount of 1.2%, I would calculate 90-day discount rate by dividing 1.2% by 4. So, I think we do divide the annualized rate to get a rate for a lower interval, but I am not sure why we don’t use this method for calculating EAY as shown above.

I would appreciate any help.