1019I
ExpertverifiedReturn to Table 10.1 and calculate both the real and nominal rates of return on the TIPS bond in the second and third years.
Time  Inflation in Year just ended  Par Value  Coupon Payment  Coupon Payment + Principal payment  Total Payment 
0  $ 1000 .00  
1  2  $ 1020.00  $ 40.80  0  $ 40.80 
2  3  $ 1050. 60  $ 42.02  0  $ 42.02 
3  1  $ 1061.11  $ 42.44  $ 1061.11  1103.54 
Second year = 7.12% and 4.00%
Third year = 5.04% and 4.00 %
The formulae for Nominal Return = Interest + Price Appreciation / Initial Price
= $ 42.20 + $ 30.60 / $ 1020.00
= 0.071196
= 7.12%
The formula for real return = 1 + Nominal return / 1 + Inflation rate – 1
= (1 + 0.071196) / (1 + 0.03) – 1
= 1.071196 / 1. 03 – 1
= 1.0400 – 1
= 4.00 %
The formulae for Nominal Return = Interest + Price Appreciation / Initial Price
= $ 42.44 + $ 10.51 / $ 1050.60
= 0.050400
= 5.04%
The formula for real return = 1 + Nominal return / 1 + Inflation rate – 1
= (1 + 0.050400) / (1 + 0.01) – 1
= 1.050400 / 1. 01 – 1
= 1.0400 – 1
= 4.00 %
Sandra Kapple presents Maria Van Husen with a description, given in the following exhibit, of the bond portfolio held by the Star Hospital Pension Plan. All securities in the bond portfolio are noncallable U.S. Treasury securities.
STAR HOSPITAL PENSION PLAN BOND PORTFOLIO
Par value (in US $)  Treasury security  Market value (in US $)  Current Price  Up 100 basis points  Down 100 basis points  Effective duration 
$48,000,000  2.375% due 2010  $48,667,680  $101.391  99.245  103.595  2.15 
50,000,000  4.75% due 2035  50,000,000  100.000  86.372  116.887 

98,000,000  Total bond portfolio  98,667,680         
a. Calculate the effective duration of each of the following:
i. The 4.75% Treasury security due 2035
ii. The total bond portfolio
b. Van Husen remarks to Kapple, “If you changed the maturity structure of the bond portfolio to result in a portfolio duration of 5.25, the price sensitivity of that portfolio would be identical to the price sensitivity of a single, noncallable Treasury security that has a duration of 5.25.” In what circumstance would Van Husen’s remark be correct?
Question: The following table contains spot rates and forward rates for three years. However, the labels got mixed up. Can you identify which row of the interest rates represents spot rates and which one the forward rates?
Year  1  2  3  
Spot rate of Forward rates?  10.00%  12.00%  14.00%  
Spot rate of Forward rates?  10.00%  14.0364%  18.1078% 
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