# Delta Hedging at Dayton Manufacturing Harvard Case Solution & Analysis Problem Diagnosis

The treasury manager of Dayton Manufacturing, Scout Finch has been evaluating and analyzing the use of one of the new foreign exchange hedging strategy in the year 2005. The company is basically a manufacturer in US. A number of losses had been incurred by the management of the company in the past 90 days as a result of the long positions in European Euro and British pounds as a result of purchasing the put options. Therefore, the consultant of the company has now used a hedging technique known as the delta hedging which makes the use of the forward contracts. However, this delta hedging strategy is slightly different and dynamic and under this strategy the hedging position of the company is frequently updated over the entire life of the exposure with respect to the changing spot rates and thus results in a risk free portfolio. Thus, this case attempts to perform an analysis of the delta hedging strategy and determines its risks and rewards for Dayton Manufacturing,

Analysis

Hedge Updates, Valuations & Forward Contract Valuations

The hedge updates or the inputs for the delta hedging could be seen in the following table as follows:

INPUTS/ASSUMPTIONS
Spot rate 1.3309 per Euro
Strike price (same units as Spot) 1.335 per Euro
volatility (annualized) 10%
domestic Interest rate (annualized) 3%
foreign Interest rate (annualized) 2%
time to maturity in days 92
Put option value 0.0265 per Euro
Euro Exposure 1000000 Euro
Initial Forward Rate 1.3353 per Euro

The formula which has been used in order to calculate the put delta is as follows:

This formula has been in the handbook called as the Financial Risk Manager which has been illustrated by Jorian(2009). The N (d1) in the above formula has been calculated as follows:

Where,
So: Spot rate, X: Strike rate, r: domestic rate, q: foreign exchange rate, Sigma, volatility and t: time to maturity.
The put delta calculations could be seen in the excel spreadsheet. The put delta value is al; negative which prove the fact that this is a put delta. Based upon these negative put delta values, the forward contracts have been bought in order to perform proportionate hedging. However, there is still some portion which is uncovered. For each new time to maturity and spot price the delta is recalculated and in this way the realignment of the portfolio is performed. This process is repeated each week. The values of the forwards that are sold and bought are shown in the excel spreadsheet for each of the updates values of the delta. The results of the delta hedge are shown in the table below:

DELTA HEDGE RESULTS

Net proceeds from forwards 1960672.5
Proceeds from uncovered' 7243181.1
Total dollar proceeds 9203853.6

After obtaining the results for the data hedging, the comparison of delta hedging is made with respect to other strategies that had been previously used at Dayton Manufacturing. The blue figures indicate that money is made whereas; the red figures that the money is lost. The comparison of all the strategies is done under four different scenarios and then the ranking has also been performed for each of the hedging strategies as shown in the tables below:

DOLLAR MOVEMENR SCENARIOS

Domestic interest rates 0.06 0.06 0.033 0.033
Foreign interest rates 0.08 0.08 0.04 0.02
Forward rate range 1.754 1.7612 1.754 1.7371 1.905 1.8286 1.3353 1.2239
Spot Rate Range 1.764 1.7618 1.764 1.735 1.9111 1.8311 1.3309 1.22
Remained uncovered 1761800 2792 1735000 -10522 1831100 -41577 1220000 -88790
Forward covered 1754000 5008 1754000 8478 1904960 32283.33 1335300 26510.1
Put Option Cover 1734625 -24383 1734635 -10887 1863818 -8859 1308500 -289.5
Delta Hedge 175900 0 1741211.7 0 1866626 0 9203853.6 0.....................

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