Trying to check this 1Y1Y forward treasuries calculation

Question

here is a screenshot of the FWCM screen on Bloomberg:

https://i.stack.imgur.com/2BT3y.jpg

I'm trying to check that I understand this by calculating the 1Y1Y which according to this matrix is 3.6877%.

So the inputs are 1Yr rate at 2.7737% and 2Yr rate is 3.2756%.

((2*.032756)-(1*.027737))/(2-1) = 3.78%

Bloomberg says they calculate it using discount factors and those rates are here:

https://i.stack.imgur.com/Y7pFZ.jpg

1 year discount rate is .972146

2 year discount rate is .935587

I can calculated the rate by this https://i.stack.imgur.com/CxyT3.jpg

which I take to mean below

.935587/.972146 = 1/(1+r)

r = 3.91%

Both 3.91% and 3.78% are different from bloombergs 3.6877%. Am I doing something wrong? I asked bloomberg and they only gave me the formula I was using.

Answer 1

I pulled up the Bloomberg page you referenced in your question. The rates you are referencing are not zero rates but yields on the coupon note/bond that are used to construct the curve. Toggle the spot from coupon to zero to get the zero rates.

When I do this, I get a 1Yr rate of 3.0386% and a 2Yr rate of 3.4119%.

Using the formula:

$$(1+1Yr/100)^1 * (1+1Yr1Yr/100)^1 = (1+2Yr/100)^2 $$

I get a 1Yr1Yr forward of 3.7866%, while Bloomberg is showing 3.7833%.

As for the discount factors you use in the second part of your calculations, it looks like the rates have moved since you snapped the first page and therefore your discount factors are for different rates.