DERIVATIVES TASK Harvard Case Solution & Analysis

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 dateEnd DateTime PeriodCumulativeRatesPresent value factor (Zi)Swap Fixed Rate
25/1/201625/4/2016

0.25

0.25

0.00431

0.998923186

0.11%

25/4/201625/7/2016

0.25

0.50

0.00460

0.997705278

0.23%

25/7/201624/10/2016

0.25

0.75

0.00529

0.996048179

0.40%

25/10/201624/1/2017

0.25

1.00

0.00583

0.994203792

0.58%

24/1/201724/4/2017

0.25

1.25

0.00594

0.992629724

0.74%

24/4/201724/7/2017

0.25

1.50

0.00439

0.993458079

0.65%

24/7/201724/10/2017

0.25

1.75

0.00466

0.991910966

0.81%

24/10/201724/1/2018

0.25

2.00

0.00514

0.989824603

1.02%

SWAP FIXED RATE

    

4.53%

b.

Start dateEnd DateTime PeriodCumulativeRatesPresent value factor (Zi)Swap Fixed Rate
25/1/201625/4/2016

0.25

0.25

0.0043

0.998923186

0.001076814

25/4/201625/7/2016

0.25

0.5

0.0046

0.997705278

0.002294722

25/7/201624/10/2016

0.25

0.75

0.0053

0.996048179

0.003951821

25/10/201624/1/2017

0.25

1

0.0058

0.994203792

0.005796208

SWAP FIXED RATE

    

1.31%

c.

Start dateEnd DateTime PeriodCumulativeRatesPresent value factor (Zi)Swap Fixed Rate
25/1/201625/7/2016

0.5

0.5

0.00891

0.995563817

0.004436183

25/7/201624/1/2017

0.5

1

0.01112

0.989002294

0.010997706

24/1/201724/7/2017

0.5

1.5

0.01033

0.984741432

0.015258568

24/7/201724/1/2018

0.5

2

0.00980

0.980776775

0.019223225

SWAP FIXED RATE

    

4.99%

d.

Start dateEnd DateTime PeriodCumulativeRatesPresent value factor (Zi)Swap Fixed Rate
24/1/201724/4/2017

0.25

0.25

0.00594

0.998517202

0.001482798

24/4/201724/7/2017

0.25

0.5

0.00439

0.997809807

0.002190193

24/7/201724/10/2017

0.25

0.75

0.00466

0.996517172

0.003482828

24/10/201724/1/2018

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 dateEnd DateRate at inceptionCurrent Forward RateTimeRate differenceCash Flow Difference
25/3/201625/4/2016

0.0052

0.0085

0.083

-0.0003

-0.055

25/4/201625/7/2016

0.0052

0.0085

0.25

-0.0008

-0.165

25/7/201624/10/2016

0.0052

0.0085

0.25

-0.0008

-0.165

25/10/201624/1/2017

0.0052

0.0085

0.25

-0.0008

-0.165

24/1/201724/4/2017

0.0052

0.0085

0.25

-0.0008

-0.165

24/4/201724/7/2017

0.0052

0.0085

0.25

-0.0008

-0.165

24/7/201724/10/2017

0.0052

0.0085

0.25

-0.0008

-0.165

24/10/201724/1/2018

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

 AppleWal-MartGoogleJohnson & JohnsonNovartisBank 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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