### CFA Practice Question

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### CFA Practice Question

A 5.25% coupon Treasury security with one year left to maturity is selling for 101.75 and a two-year 5.45% coupon Treasury security is selling at a discount of 0.40% from par. Assume annual discounting. The spot rate for the second year is ______.
A. 5.67%
B. 5.45%
C. 5.73%
Explanation: The first year spot rate is computed first from the one-year bond. FV = 105.25; N = 1; PV = -101.75; CPT I/Y = 3.44%

It is then used in the valuation of the two-year bond, without the forward rate. 99.60 = 5.45/(1.0344) + 105.45/(1 + s2)2

s2 = [105.45 / (99.60 - 5.45/1.0344)]1/2 - 1= 0.0573, or 5.73%

User Comment
george2006 The spot rate for 2nd year == the spot rate from t=0 to t=2.

Don't confuse it with the expected future spot rate == forward rate from t=1 to t=2.

Spot rate is always for the rate at time zero.
tanyak where do they get 1o5.25 and 3.44% in the same calculation?
Shelton clear explanation S=5.7293%
Janey I think the 105.25 came from the one year treasury \$100 principal plus the \$5.25 for the coupon payment
ehc0791 The coupon treasury should make coupon payment every 6 month, not every year, right ? I don't get this question.
rkrazib "assume annual discounting" has been mentioned here.
tonytough shelton,i agree with janey, since spot rate is ytm for zero coupon bond, for 1yr coupn pmt conviniently coincides with maturitry (hence principal of no interim pymts b4 maturity upheld).
mountaingoat i don't understand why s1 was used in calculation and not just solve using s2. afterall only C2 coupon was used in association with first cashflow. any insight?
LordHux is there an easier way to do this?
shann680 folks it doesn't matter if you use fv=105=25 or fv=100 and pmt=5.25. you still get the i/y.
michaeloa3 This doesn't make sense to me. Isn't the YTM on the 2 year treasury they mention the spot rate?