This document analyzes various hedging strategies using futures contracts. It discusses using Eurodollar futures to hedge $70 million invested in equities, calculating that 6,667 contracts would be needed. It also examines a long/short portfolio hedging a $50 million investment in PRWCX using S&P 500 futures, determining a historical beta of 0.628. Leveraging this strategy at 150% with $100 million borrowed at 1% could yield a 4.54% return. However, future beta and market movements may differ from historical patterns. Additionally, the document proposes a spread trade betting on a rise in long-term vs. short-term interest rates using Eurodollar futures.

1. DERIVATIVE HEDGING
STRATEGIES
AN ANALYSIS OF FUTURES & VARIOUS
HEDGING STRATEGIES
OCTOBER 2014
Popov, Latchezar || Devletoglou, Nikolaos || Dadoun, Andrew || Schaible, Randall

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USING EURODOLLAR FUTURES TO HEDGE
In order to minimize transaction costs and maximize the ability to shift exposure quickly, we use
futures to allocate funds synthetically across the main asset classes. Using the S&P 500, Nasdaq 100 and
Eurodollar futures contracts that expire in December 2014 for the S&P 500 and Nasdaq 100 and in June
2017 for the Eurodollar we are able to determine the amount of contracts needed in the Eurodollar futures
in order to profit $5 million dollars if the implied interest rate rises 30 basis points. Furthermore, we are
investing $70 million dollar into equities - $50 million in the S&P 500 and $20 million in the Nasdaq 100.
Using price data as of the close price on October 17th, 2014 for each of these contracts, which can
be seen below, we calculated the following number of contracts needed for each:
The contract value for each of the futures is given in the description screen on Bloomberg of the
instruments. For SPZ4 the value is $250 * the index price while for the NDZ4 the value is $100 * the index
price. The number of contracts is then obtained by dividing our desired exposure for the S&P and Nasdaq
by the contact value. The position in the Eurodollars contract is determined by calculating the price change
in the contract for every basis point change in the interest rate. Then, we divide our desired profit of $5
million by the price change of the contract per every 30 basis point change in interest rates. The calculations
can be seen below.
The contract time to maturity or TTM is a quarter of a year or 0.25. The Eurodollar principle value
is $1,000,000 as seen in the contract description. Our desired profit, as mentioned previously is $5,000,000.
In essense, since one cannot buy or sell a fraction of a share, we would round up and sell 6,667 contract of
the Eurodollar futures.
Although it may appear at first that investing synthetically in equities is a great strategy, it raises
some key concerns from our end. Being able to have the equity market exposure through the index futures
allows you to invest your remaining funds in high yielding money market instruments, which as your
supervisor claims, seems to be a great strategy. However, when interest rates are high, we can expect future
contracts to reflect this high interest rate environment, through charging a premium for the future contracts.
The reason for this is when you price a future index contract, you take into consideration the current cost
of financing, which is the short-term interest rate, and the dividend yield. If the future contract does not
adjust it’s price for the high interest rates, then an arbitrage opportunity would exist. Therefore, it is our
belief, that the strategy above, is not a “great strategy” simply based on the fact that interest rates are high
since the futures instruments have the interest rates priced in.

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LONG SHORT PORTFOLIO HEDGE
We then looked at a long/short portfolio consisting of a long position in an ETF with a ticker
PRWCX which stands for T. Rowe Price Capital Appreciation Fund and a short position in the S&P 500
futures contract (SP1). The main objective was to determine how many shares we needed to short of the
SP1 futures in order to reduce volatility of a $50 million dollar investment in the PRWCX while still
capturing the relative performance of PRWCX. This in essence would give us returns that are uncorrelated
with the S&P returns.
We began by using historical data to calculating the historical beta of the PRWCX relative to the
S&P futures. This allowed us to determine the number of contracts we will need to buy in the SP1 if we
had initiated the strategy on January 2014 and held the position till September 30, 2014. Based on the
historical data, we obtained a historical beta of 0.628. This beta was obtained by taking the slope of PRWCX
returns against the slope of the SP1 returns or in essence regressing the two sets of returns against one
another. We would therefore want to short $31,392,132.33 dollars in the SP1 ($50 million * 0.628) on the
first trading day of January 2014. Based on this allocation, we obtained a returns on equity for the nine
month period of 2.01%, which can be seen on the excel sheet, and the volatilities for the individual
instruments as well as the portfolio which can be seen below.
Full formula for portfolio volatility:
In addition, here are the regression results from the two returns which can be found with the rest of the data
on our excel document. We can see that the beta based on the regression is 0.62785.

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If we had decided to leverage this strategy by borrowing $100 million at 1% annual rate to create
a long position in the PRWCX of $150 million we would get a return on equity of 4.54%. This calculation
can be seen in the table below.
The “EndingPortValue” is the value of the portfolio at the end of the nine month period which
comes out to $153,019,186.37. The “PrincipalEquity” is the $150 million dollars that we allocated to the
position. You take the difference between those two and subtract the interest paid on the borrowing of
$750,000, then divide it by the “InvestorEquity” value which is the $50 million that we started out with of
investor funds.
Based on historical data, this strategy obviously seems logical and profitable. However, going
forward there are many aspects that may change from the historical data that would make this strategy risky
and much less appealing. As noted, historical data is not a predictor of the future. The main aspect that may
change and effect your position is the future beta which can vary greatly from the historical beta due to
potential unexpected events that can have an impact on the ETF’s price. Therefore, an adjustment to beta
may be needed in order to stay market neutral. Furthermore, we do not believe that a nine month period of
either the PRWCX or the SP1 reflects the true behavior of either instrument. A larger historical data range
may produce a different beta and give us better results. Lastly, there is always a risk or possibility of huge
unpredicted movements of both instruments in the opposite direction that was not observed from the
historical data. In this case, if the market continues higher due to good economic data but the PRWCX falls
and continues to fall then significant losses will be realized.
Nevertheless, there are clear benefits to utilizing a long/short portfolio strategy. These include the
reduction of the volatility of an instrument which still capturing the relative performance of the instrument,
in addition to generating returns independent of market direction. As stated in a report by Deutsche Bank,
“a higher correlation to equity markets in rising markets and lower correlation in falling markets (sometimes
referred to as an “asymmetrical” risk/return profile)”. In addition, “assets under management by long/short
equity hedge funds have grown more than 20% annually”. Note however that this report was generated in
2004 (Lamm, McFall).
EURODOLLAR FUTURES BET ON FED FUNDS RATE
Based on our analysis, we would need to go long 2000 EDM5 contracts and short 2000 EDM7
contracts. By doing so we are betting that the long term interest rates are going to rise more than the short
rates. We would effectively be putting a bear spread trade on the interest rates. If the spread does not change
regardless of the movement in interest rates, we do not lose or gain anything in the trade.
Excel snapshot A shows the strategy we have implemented.

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For the spread to move in our favor by 20 basis points (bps), we would need the EDM7 rate to
increase by 20 bps more than the EDM5. To test that our portfolio requirements hold we imagined a scenario
in which the EDM7 rate increased by 20 basis points while the EDM5 rate stays constant. The excel
snapshot below shows the result of such an occurrence.
Since the value per 1 basis point is $25/contract, we would perceive an increase of $500/contract.
By holding 2000 contracts short, we achieve our desired profit of $1,000,000.
On the other hand, an unfavorable change in the spread by 20 basis points, we would have the
EDM5 rate increase by 20 bps more than the EDM7 rate. To test that our portfolio requirements hold we
imagined a scenario in which the EDM5 rate increased by 20 bps while the EDM7 rate remained constant.
The excel snapshot believe summarizes this occurrence.
Again sine the value per 1 basis point is $25/contract; we would perceive a loss of $500/contract.
By holding 2000 contracts long, we make a $1,000,000 loss.

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WORK CITED
R. McFall Lamm, Jr. (Ph.D.), Chief Investment Strategist; The Role of Long/Short Equity Hedge Funds
in Investment Portfolios;” Deutsche Bank – DB Absolute Return Strategies. (2004)
http://www.trendfollowing.com/whitepaper/long_short.pdf
Bloomberg L.P. Futures contracts SPZ4, NDZ4, EDM7, SP1, PRWCX (October 17th, 2014).
Bloomberg database. Bentley University Terminal.