Not sure whether this type of calculation will appear in real test. If I can’t figure it out again by your help, I’ll probably just skip it… Thx. A bank loan depart. is trying to determine the correct rate for a 2-yr loan to be made two years from now. If current implied Treasury effective annual spot rates are: 1-yr=2%; 2-yr=3%; 3-yr=3.5%; 4-yr=4.5%, the base forward rate for the loan before adding a risk premium is closest to: A. 4.5% B. 6.0% C. 9.0% d. 12.0%
1.045^4/1.03^2=1.124-1=12.4%. D the answer
ssdnola Wrote: ------------------------------------------------------- > 1.045^4/1.03^2=1.124-1=12.4%. D the answer you forgot to take square root -> B is the answer.
yeah, thats right. B the answer
maratikus Wrote: ------------------------------------------------------- > ssdnola Wrote: > -------------------------------------------------- > ----- > > 1.045^4/1.03^2=1.124-1=12.4%. D the answer > > you forgot to take square root -> B is the answer. So how did you get this 1.045^4/1.03^2? I was trying to use geometric mean formula and I was kind of being stuck there… (1+s4)^4 = (1+0f1)(1+0f2)(1+0f3)(1+0f4) and we need to calculate 0f2, right??? But I don’t know 0f1, 0f3 and 0f4, how would you utilize the given s1, s2 and s3? Could you show me more details? Thx.
(1+s2)^2*(1+2f2)^2=(1+s4)^4
remember this formula and your golden for these problems (1+r)^m+t=(1+r)^m * (1+r)^t where m= periods t=matrurity of bond not sure if this makes sense, but it works for me.
jut111 Wrote: ------------------------------------------------------- > remember this formula and your golden for these > problems > > (1+r)^m+t=(1+r)^m * (1+r)^t > > where m= periods t=matrurity of bond > > not sure if this makes sense, but it works for me. Thx, jut111. What you showed is quite easy to understand mathematically. However, it did not differentiate spot rate (s) and forward rate (f) and their relationship. I was trying to find a “one-fits-all” rule to solve spot rates vs forward rates problems. For now, the geometric mean formula is what I know to use but it does not seem to fit this case quite well…
maratikus Wrote: ------------------------------------------------------- > (1+s2)^2*(1+2f2)^2=(1+s4)^4 Hi, what’s your thinking process to conclude this? And what does 2f2 mean? The forward rate two years from now should be denoted as 0f2, am I wrong?
the forward rate is the last term, and what you are solving for here. so… (1.045)^4 = (1.03)^2 * (1.x)^2 so solving for x gets 1.193 = 1.0609 (1.x)^2 (1.x)^2 = 1.1245 x=.06
I like the appox method mentioned in the schweresr books for such problems. In this case, it would be (4.5*4 - 3.0*2)/2 = 6%
hyang Wrote: ------------------------------------------------------- > maratikus Wrote: > -------------------------------------------------- > ----- > > (1+s2)^2*(1+2f2)^2=(1+s4)^4 > > > Hi, what’s your thinking process to conclude this? > And what does 2f2 mean? The forward rate two years > from now should be denoted as 0f2, am I wrong? forward rate depends on two parameters: loan maturity term (2 years) and when it becomes effective (2 years). 2f2 means - forward rate effective in two years for a 2-year loan. Then using no-arbitrage principle you can calculate 2f2 from s2 and s4. It’s covered in CFAI materials and you should know the principle before you take Level I.
jut111 Wrote: ------------------------------------------------------- > the forward rate is the last term, and what you > are solving for here. so… > > (1.045)^4 = (1.03)^2 * (1.x)^2 > > so solving for x gets > > 1.193 = 1.0609 (1.x)^2 > > (1.x)^2 = 1.1245 > > x=.06 Thx, jut111. Actually your way is quite interesting… I’m going to test a few. If they work out well, then fairly easy to solve the similar problems. All else I’ll try to figure out later… 