Spot Rates

CFA Level I
#1

Is there an easier way to calculate this using the BA II Plus calculator? This Question took me almost 4.5min to answer

Given the following forward rates, the value of a 4-year, 11% annual pay, $1,000 par bond, is closest to:

Year Rate 1 7.00% 2 8.15% 3 10.30% 4 12.00%

Note that the year 1 rate is the current rate (or spot rate) on a 1-year security.

A) $1,052.63. B) $984.25. C) $1,060.36.

correct answer C) $1,060.36.

Spot Rates: Year 1 = 7%. Year 2 = [(1.07)(1.0815)]1/2 – 1 = 7.57%. Year 3 = [(1.07)(1.0815)(1.103)]1/3 – 1 = 8.48%. Year 4 = [(1.07)(1.0815)(1.103)(1.120)]1/4 – 1 = 9.35%.

Bond Value: N = 1; FV = 110; I/Y = 7; CPT → PV = 102.80 N = 2; FV = 110; I/Y = 7.57; CPT → PV = 95.06 N = 3; FV = 110; I/Y = 8.48; CPT → PV = 86.17 N = 4; FV = 1,110; I/Y = 9.35; CPT → PV = 776.33

102.80 + 95.06 + 86.17 + 776.33 = 1,060.36

#2

Not sure…good question though.

#3

Work the bond backwards:

Discount the Year 4 cash flow ($1,000 + $110) by one period using the Year 4 rate:

$1,100/1.12 = whatever result you get, add $110

Now, discount the total by the Year 3 rate, i.e. ((1,110/1.12) + 110)/1.103 = whatever result you get, add $110 … and so on.

Effectively, you are performing the following computation:

(((((((1,110/1.12) + 110)/1.103) + 110)/1.0815) + 110)/1.07)

You will arrive at the same bond value and it should take less than 1 minute.

#4

good one!!!