SPOT RATE FROM FORWARD RATE

CFA Level I Fixed Income
#1

Assume the following six-month forward rates (presented on an annualized, bond-equivalent basis) were calculated from the yield curve.

Notation Forward Rate 1f0 0.50% 1f1 0.70% 1f2 1.00% 1f3 1.50% 1f4 2.20% 1f5 3.00% 1f6 4.00%

The 3-year spot rate is closest to:

Ans is 1.48%.

I cannot seem to get the ans using the APPROXIMATION method.

Can someone help me with this?

I did [(0.25%+0.35%+0.5%+0.75%+1.1%+1.5% +2%) / 6] x2 = 2.15

What is wrong with my working ???

I know the geometric mean method… so you don’t have to give me the working for that.

Thank you!

#2

Count the number of forward rates you added together.

#3

You don’t need to include the 2%… Just a check - 3 years is SIX six month periods - you have SEVEN (that shoudl have been a clue). You’d have included the 2% if you were calculating the 3 1/2 year spot.

#4

Spoiler!

#5

S2000 - yours wasn’t up when I posted. Sorry to harsh your mellow.

#6

wink

#7

w

here do those forward rate #'s come from in your calculation?

#8

The rates given are annual (BEY) rates, so he’s divided each by 2 to get semiannual (effective) rates. But, as busprof’s spoiler points out, he used 7 of them when he should have used only 6.

#9

Magician,

Can you pls clarify the ways we can tackle these questions on the exam? I just need a quick detailed refresher and yours are always great.

#10

Here’s an article I wrote (with colors and everything) on this:

http://financialexamhelp123.com/calculating-spot-rates-from-forward-rates/

At the bottom I give an example with BEYs. Let me know if it helps.