INVESTMENT MANAGEMENT Case Solution
DURATIONS
Q2a, b and c COMPUTE THE MODIFIED DURATION FOR EACH OF THE TREASURY BONDS. COMPUTE THE EFFECTIVE DURATION FOR EACH OF THE TREASURY BONDS. PLOT THE MODIFIED AND EFFECTIVE DURATIONS TOGETHER WITH MATURITY ON THE HORIZONTAL AXIS AND EXPLAIN THE DIFFERENCES IN THE TWO DURATIONS.
The modified duration and effective duration of different bonds with different terms to maturity and yield rates are calculated; the Macaulay duration was calculated in order to calculate the modified duration of different bonds, the effective duration is increasing with the increase in term to maturity.Thisis evident below in the table.
Maturity | Bonds | MacAulay duration | Modified duration | Effective duration |
Â | GSBK16 | 1.08 | 1.06 | 0.49 |
1 | GSBC17 | 1.04 | 1.03 | 0.57 |
Â | GSBM17 | 0.96 | 0.96 | 0.59 |
2 | GSBA18 | 0.95 | 0.94 | 0.68 |
Â | GSBS18 | 0.91 | 0.92 | 0.72 |
3 | GSBE19 | 0.94 | 0.94 | 0.85 |
Â | GSBS19 | 0.82 | 0.83 | 0.74 |
4 | GSBG20 | 0.87 | 0.87 | 0.91 |
Â | GSBU20 | 0.72 | 0.72 | 0.67 |
5 | GSBI21 | 0.80 | 0.80 | 0.91 |
Â | GSBM22 | 1.16 | 1.16 | 2.04 |
6 | GSBG23 | 1.18 | 1.18 | 2.30 |
Â | GSBG24 | 1.04 | 1.04 | 1.89 |
7 | GSBG25 | 1.09 | 1.09 | 2.20 |
Â | GSBG26 | 1.14 | 1.14 | 2.58 |
8 | GSBG27 | 1.16 | 1.16 | 2.82 |
Â | GSBU27 | 1.03 | 1.03 | 2.31 |
9 | GSBG29 | 1.05 | 1.05 | 2.54 |
Â | GSBG33 | 1.15 | 1.16 | 3.23 |
10 | GSBK35 | 0.98 | 0.98 | 2.44 |
Â | GSBG37 | 1.06 | 1.06 | 2.97 |
11 | GSBK39 | 1.02 | 1.02 | 2.85 |
HEDGING INTEREST RATE RISK
Q3a USE THE CURRENT YIELD CURVE TO DETERMINE THE PRESENT VALUE AND ALSO THE EFFECTIVE DURATION OF THE LIABILITY.
The present value of liability is computed using the yield of 11 years of maturity, the liability is discounted back to present value in order to ascertain the value of liability in the present terms. This can be seen below in the table.
Net present value of Liability | Â | 83835.92 | ||
Duration | 0.84 | |||
100000 | Â | |||
22 | payments within 11 years | |||
4545.455 | Payment after 6 months | |||
The two bonds are being selected with higher yield rated and the dollar amount is identified, which should be invested to hedge the liability of $100000.The bonds with higher yields and higher maturity are being selected for this purpose.
Â | Bond A | Bond B | Yield Bond A | Yield Bond B |
Â | ||||
Â | 106.0856 | 101.7522 | 3.01% | 3.06% |
Amount Invested | 34480.89 | 51721.34 | 40% | 60.00% |
Â | Weight |
Q3c NOW SUPPOSE THE ENTIRE YIELD CURVE SHIFTS DOWN BY 50 BASIS POINTS. CALCULATE THE PERCENTAGE CHANGE IN THE PRESENT VALUE OF THE LIABILITY IN PART (A) AND ALSO OF THE VALUE OF THE BOND PORTFOLIO IN PART (B). COMMENT ON THE ELECTIVENESS OF THE HEDGE.
The yield curve of 3.6 was taken as 2.56 after deducting 0.005 basis and then gained liability present value was calculated in present value terms with the lower yield.It has been seen that the value of liability in present value terms increased as well as the value of the portfolio, such that the weight of investment in two bonds stayed same but the overall amount in the bonds increased with their respective percentages. This can be seen below.
Net present value of Liability | Â | Â | Â | 86202.2352 | |
Duration | 0.862022352 | ||||
Â | Bond A | Bond B | Yield Bond A | Yield Bond B | |
Â | |||||
Â | 106.0856 | 101.7522 | 3.01% | 3.06% | |
Amount Invested | 34480.89 | 51721.34 | 40% | 60.00% | |
Â | Weight | ||||
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