# 1-year theoretical spot rate Q.

1 year, 10% semiannual coupon bond is priced at \$975 6-month T-bill holding period yield = 6% What’s the theoretical 1-year spot rate on a bond-equivalent basis? A. 6.4% B. 8.7% C. 9.9% D. 12.8% I get 13.1%

I guess it’s D. I just used the Excel-Solver, because I’m a little bit lazy…: total 97.50 cf rate df df x cf 0.5 5.00 12% 0.943396226 4.72 1 105.00 0.12760 0.883649341 92.78

you have to solve: PV = sum(cf_t x df_t) where cf_t is the relevant cashflow, t is 0.5 and 1, df_0.5 = 1/(1+12%/2)^(2*0.5) and df_1 = 1/(1+y/2)^(2*1). Now solve for y.

I got 12.74% with a BAII+, so I’d go D too.

Farina Wrote: ------------------------------------------------------- > I got 12.74% with a BAII+, so I’d go D too. Farina, can you or anyone else explain how you calculated this?

Farina Wrote: ------------------------------------------------------- > I got 12.74% with a BAII+, so I’d go D too. Your calculator can do that? That’s unfair!

I used the 1y note rate. TVM keys: N: 2 PV: -975 PMT: 50 FV: 1000 CPT — I/Y = 6.37, which is over a SA period so to get a BEY just x2 = 12.74.

it’s D.

a la boostrapping: 975 = 50/(1+.03) + 1050/(1+x/2)^2 975 - 50/(1+.03) = 1050/(1+x/2)^2 926.456 = 1050/(1+x/2)^2 (1+x/2)^2 = 1.33351 (1+x/2) = 1.0646 x/2 = 0.0646 x ~ .128

Farina Wrote: ------------------------------------------------------- > I used the 1y note rate. > > TVM keys: > N: 2 > PV: -975 > PMT: 50 > FV: 1000 > > CPT — I/Y = 6.37, which is over a SA period so > to get a BEY just x2 = 12.74. but that’s only the right answer by chance, right? I guess the question was to bootstrap a zero-curve, or am I wrong?

yosh Wrote: ------------------------------------------------------- > a la boostrapping: > > 975 = 50/(1+.03) + 1050/(1+x/2)^2 > 975 - 50/(1+.03) = 1050/(1+x/2)^2 > 926.456 = 1050/(1+x/2)^2 > (1+x/2)^2 = 1.33351 > (1+x/2) = 1.0646 > x/2 = 0.0646 > x ~ .128 but replace the .03 with a .06, because it is meant to be a holding period return. result is similar, though.

Yes, you should bootstrap. 50/(1,06) + 1050/(1+x)^2=975 Solve for x and multiply by 2 to get the BEY. It’s actually not that difficult but i usually write down the equation not to do a silly mistake. And it takes less than 1,5 minutes;).

yeah, you’re all right, bootstrap it, not a simple ^0.5 BEY fix.