DERIVATIVES TASK Case Solution
Question 1
The Swap Fixed Rates are shown in the tables below and the calculations could be seen in the excel spreadsheet:
a.
| Start date | End Date | Time Period | Cumulative | Rates | Present value factor (Zi) | Swap Fixed Rate |
| 25/1/2016 | 25/4/2016 |
0.25 |
0.25 |
0.00431 |
0.998923186 |
0.11% |
| 25/4/2016 | 25/7/2016 |
0.25 |
0.50 |
0.00460 |
0.997705278 |
0.23% |
| 25/7/2016 | 24/10/2016 |
0.25 |
0.75 |
0.00529 |
0.996048179 |
0.40% |
| 25/10/2016 | 24/1/2017 |
0.25 |
1.00 |
0.00583 |
0.994203792 |
0.58% |
| 24/1/2017 | 24/4/2017 |
0.25 |
1.25 |
0.00594 |
0.992629724 |
0.74% |
| 24/4/2017 | 24/7/2017 |
0.25 |
1.50 |
0.00439 |
0.993458079 |
0.65% |
| 24/7/2017 | 24/10/2017 |
0.25 |
1.75 |
0.00466 |
0.991910966 |
0.81% |
| 24/10/2017 | 24/1/2018 |
0.25 |
2.00 |
0.00514 |
0.989824603 |
1.02% |
|
SWAP FIXED RATE |
4.53% |
|||||
b.
| Start date | End Date | Time Period | Cumulative | Rates | Present value factor (Zi) | Swap Fixed Rate |
| 25/1/2016 | 25/4/2016 |
0.25 |
0.25 |
0.0043 |
0.998923186 |
0.001076814 |
| 25/4/2016 | 25/7/2016 |
0.25 |
0.5 |
0.0046 |
0.997705278 |
0.002294722 |
| 25/7/2016 | 24/10/2016 |
0.25 |
0.75 |
0.0053 |
0.996048179 |
0.003951821 |
| 25/10/2016 | 24/1/2017 |
0.25 |
1 |
0.0058 |
0.994203792 |
0.005796208 |
|
SWAP FIXED RATE |
1.31% |
|||||
c.
| Start date | End Date | Time Period | Cumulative | Rates | Present value factor (Zi) | Swap Fixed Rate |
| 25/1/2016 | 25/7/2016 |
0.5 |
0.5 |
0.00891 |
0.995563817 |
0.004436183 |
| 25/7/2016 | 24/1/2017 |
0.5 |
1 |
0.01112 |
0.989002294 |
0.010997706 |
| 24/1/2017 | 24/7/2017 |
0.5 |
1.5 |
0.01033 |
0.984741432 |
0.015258568 |
| 24/7/2017 | 24/1/2018 |
0.5 |
2 |
0.00980 |
0.980776775 |
0.019223225 |
|
SWAP FIXED RATE |
4.99% |
|||||
d.
| Start date | End Date | Time Period | Cumulative | Rates | Present value factor (Zi) | Swap Fixed Rate |
| 24/1/2017 | 24/4/2017 |
0.25 |
0.25 |
0.00594 |
0.998517202 |
0.001482798 |
| 24/4/2017 | 24/7/2017 |
0.25 |
0.5 |
0.00439 |
0.997809807 |
0.002190193 |
| 24/7/2017 | 24/10/2017 |
0.25 |
0.75 |
0.00466 |
0.996517172 |
0.003482828 |
| 24/10/2017 | 24/1/2018 |
0.25 |
1 |
0.00514 |
0.994886284 |
0.005113716 |
|
SWAP FIXED RATE |
1.23% |
|||||
Question 2
The replacement cost of this Swap agreement is 1.21 million.
| Start date | End Date | Rate at inception | Current Forward Rate | Time | Rate difference | Cash Flow Difference |
| 25/3/2016 | 25/4/2016 |
0.0052 |
0.0085 |
0.083 |
-0.0003 |
-0.055 |
| 25/4/2016 | 25/7/2016 |
0.0052 |
0.0085 |
0.25 |
-0.0008 |
-0.165 |
| 25/7/2016 | 24/10/2016 |
0.0052 |
0.0085 |
0.25 |
-0.0008 |
-0.165 |
| 25/10/2016 | 24/1/2017 |
0.0052 |
0.0085 |
0.25 |
-0.0008 |
-0.165 |
| 24/1/2017 | 24/4/2017 |
0.0052 |
0.0085 |
0.25 |
-0.0008 |
-0.165 |
| 24/4/2017 | 24/7/2017 |
0.0052 |
0.0085 |
0.25 |
-0.0008 |
-0.165 |
| 24/7/2017 | 24/10/2017 |
0.0052 |
0.0085 |
0.25 |
-0.0008 |
-0.165 |
| 24/10/2017 | 24/1/2018 |
0.0052 |
0.0085 |
0.25 |
-0.0008 |
-0.165 |
| SWAP REPLACEMENT COST (Millions) |
-1.21 |
|||||
Question 3
a.
The risk minimization hedge ratios for each single stocks future contract is as follows:
|
HEDGE RATIOS |
||||||
| Apple | Wal-Mart | Johnson & Johnson | Novartis | Bank of America | ||
| Correlations (Spot, futures) |
0.994 |
0.962 |
-0.120 |
0.994 |
0.999 |
0.997 |
| Standard Deviation of Spot Prices |
197.4833335 |
4.687685781 |
209.3289583 |
10.15587714 |
12.6635403 |
1.999503678 |
| Standard Deviation of Future Prices |
189.4653444 |
5.184012485 |
156.69183 |
11.80671942 |
14.08993513 |
2.166356356 |
| Risk Minimizing Hedge Ratio |
104% |
87% |
-16% |
86% |
90% |
92% |
Looking at the above hedge ratios, the performance of Johnson & Johnson stock is better than all the other with a hedge ratio of 86%. After Johnson & Johnson, Wal-mart is the second least risky stock to invest in. Moreover, the most risky stocks are that of Google and Apple as seen by their respective hedge ratios.
b.
Most of the traders prefer to use one to one hedging strategy rather than the above risk minimization strategy for the futures. In one to one hedging strategy they analyze the stocks on the basis of a range of metrics such as Sharpe ratio, coefficient of variation etc. Looking at the performance of the stock on the basis of one to one hedging strategy it could be said that the results are much similar to that of the risk minimization strategy and again the most risky stocks are the Google stock and the Apple stock which should be hedged more. However, risk minimization strategy is more appropriate and easy strategy since in incorporates the correlation between the futures and the spot prices, so traders need to implement a risk minimization strategy......................
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