Question #9 - Reading 25 The Term Structure and Interest Rate Dynamics

Reading: Reading 25 The Term Structure and Interest Rate Dynamics

PDF File: Reading 25 The Term Structure and Interest Rate Dynamics.pdf

Page: 4

Status: Correct

Correct Answer: A

Shared Context

of 79 Which theory explains the shape of the yield curve by considering the relative demands for various maturities? A) The pure expectations theory. B) The segmentation theory. C) The liquidity premium theory. Carol Stephens, CFA, oversees five portfolio managers who all manage fixed income portfolios for one institutional client. Stephens feels that interest rates will change over the next year but is uncertain about the extent and direction of this change. She is confident, however, that the yield curve will change in a nonparallel manner and that modified duration will not accurately measure the overall total portfolio's yield-curve risk exposure. To help her evaluate the risk of her client's total portfolio, she has assembled the table of rate durations shown below. Issue Value ($millions) 3 mo 2 yr 5 yr 10 yr 15 yr 20 yr 25 yr 30 yr Portfolio 1 100 0.03 0.14 0.49 1.35 1.71 1.59 1.47 4.62 Portfolio 2 200 0.02 0.13 1.47 0.00 0.00 0.00 0.00 0.00 Portfolio 3 150 0.03 0.14 0.51 1.40 1.78 1.64 2.34 2.83 Portfolio 4 250 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Portfolio 5 300 0.00 0.88 0.00 0.00 1.83 0.00 0.00 0.00 The value of the total portfolio is $1,000,000,000.

Question

For this question only, imagine that the original yield curve undergoes a parallel shift such that the rates at all key maturities increase by 50 basis points. The new value of the total portfolio will be closest to:

Answer Choices:

A. $980,537,500

B. $1,019,462,500

C. $961,075,000

Explanation

Key Rate Durations weight 3 mo 2 yr 5 yr 10 yr 15 yr 20 yr 25 yr 30 yr Effective Duration Portfolio 1 0.10 0.03 0.14 0.49 1.35 1.71 1.59 1.47 4.62 11.40 Portfolio 2 0.20 0.02 0.13 1.47 0.00 0.00 0.00 0.00 0.00 1.62 Portfolio 3 0.15 0.03 0.14 0.51 1.40 1.78 1.64 2.34 2.83 10.67 Portfolio 4 0.25 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 Portfolio 5 0.30 0.00 0.88 0.00 0.00 1.83 0.00 0.00 0.00 2.71 Total Portfolio 1.00 0.0265 0.3250 0.4195 0.3450 0.9870 0.4050 0.4980 0.8865 3.8925 Since the yield curve underwent a parallel shift, the impact on portfolio value can be computed directly using the portfolio's effective duration. There are two methods that can be used to calculate effective duration in this situation. Both methods use the market weight of the individual bonds in the portfolio. As shown in the second column of the table above, the total portfolio weight of each subportfolio equals: Bond value/Portfolio value, where the portfolio value is $1,000,000,000. Method 1) Effective duration of the portfolio is the sum of the weighted averages of the key rate durations for each issue. The 3-month key rate duration for the total portfolio can be calculated as follows: (0.10)(0.03) + (0.20)(0.02) + (0.15)(0.03) + (0.25)(0.06) + (0.30)(0) = 0.0265 This method can be used to generate the rest of the key rate duration shown in the bottom row of the table above and summed to yield an effective duration = 3.8925. Method 2) Effective duration of the portfolio is the weighted average of the effective durations for each issue. The effective duration of each issue is the sum of the individual rate durations for that issue. These values are shown in the right-hand column of the table above. Using this approach, the effective duration of the portfolio can be computed as: (0.10)(11.4) + (0.20)(1.62) + (0.15)(10.67) + (0.25)(0.06) + (0.30)(2.71) = 3.8925 Using an effective duration of 3.8925, the value of the portfolio following a parallel 50 basis point shift in the yield curve can be computed as follows: Percentage change = (50 basis points)(3.8925) = 1.9463% decrease. $1,000,000,000 × (1-0.0194625) = $980,537.500.

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