MotoTrojan wrote: ↑Tue Aug 13, 2019 9:43 pm
Lee_WSP wrote: ↑Tue Aug 13, 2019 9:39 pm
HEDGEFUNDIE wrote: ↑Tue Aug 13, 2019 9:36 pm
Lee_WSP wrote: ↑Tue Aug 13, 2019 9:35 pm
HEDGEFUNDIE wrote: ↑Tue Aug 13, 2019 9:30 pm
2. I also acknowledge that at 2%, TMF’s upside from here is capped. Which is why I made my AA change to 55/45.

I do not know of any reason bond funds cannot go up in value even if rates go negative. In fact, they should go up by a very large amount if rates indeed went negative.

I agree, but I do think there is a cap on how negative rates can go, it’s probably in the low single negative digits.

True, but the increase in bond fund price is also exponential as rates go lower, so even a single basis point change past zero could mean a 10 or 20% gain in LTT.

If rates rise, TMF is going to look like stocks in 1999.

Doesn't that phenomenon's derivative peak at 0% rates and then start to reduce symmetrically as the rates go to negative? Ie the change from 0.5% to 0% is the same as 0% to -0.5%.

We can just do some bond math to see what happens as rates drop through 0%.

If yields go negative, the lowest coupon rate would be 0%, since I don't think there's a way to implement a negative coupon rate. I recall someone posting that the minimum coupon rate for a US Treasury is 0.125%, and a negative yield would be implemented by selling the bond at a sufficient premium (price > 100). The results of the math aren't much different for 0% and 0.125% coupon rates, and with a zero-coupon bond, we don't have to factor in coupon return (it's all capital return), so I'll just use a 0% coupon rate.

As someone pointed out, price of a 0% coupon bond at 0% yield is 100--I'll normalize 100 to 1 for use in the PV function to calculate price (and hence return). Continuing to use a constant maturity 25-year bond:

p(0%) =-PV(0%,25,0%,1) = 1.00

To calculate the return for a change of yield from 1% to 0%, we first calculate the price at 1% yield:

p(1%) =-PV(1%,25,0%,1) = 0.78

Then we calculate the return as:

r(1%->0%) = p(0%) / p(1%) - 1 = 1.00 / 0.78 = 28.2%

Similarly, to calculate the return for 0% -> -1%, we first calculate the price at -1% yield:

p(-1%) =-PV(-1%,25,0%,1) = 1.286,

and the return for 0% to -1% is:

r(0%->-1%) = 1.286/1.000 - 1 = 28.6%

So 28.6% is a little higher than 28.2%, but not that much higher.

Doing similar calculations for all one-percentage-point changes from 10%->9% to -9%->-10%, and graphing the results, we get this:

So as yields drop, return increases with slight curvature, but pretty close to linear, and nothing special happens at 0% yield.

Kevin