Financial instruments futurum - applications for financial futures

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Applications for Financial Futures
Illustration 1 : Peoples Federal Savings Bank
1. Should Peoples Federal Savings (PFS) have hedged its September 1 savings
certificate rollover?
Strategi lindung nilai yang dilakukan oleh PFS menjadi pertanyaan bagi kami. Harus
diakui bahwa resiko yang berkaitan dengan tingkat bunga jangka pendek adalah satu
dari sekian resiko yang tampak jelas dalam pasar keuangan dan kontrak futures tingkat
bunga jangka pendek hadir atau keberadaannya untuk tujuan lindung nilai jenis resiko
ini, yang dihadapi sebagian besar oleh perusahaan-perusahaan yang bergerak di bidang
simpan-pinjam dan oleh bank-bank di mana mereka memperoleh pinjaman, memberikan
kredi dan terlibat dalam usaha intermediary di derivatif over-the-counter. Tetapi, dalam
kenyataan, penggunaan sesungguhnya dari futures tingkat bunga jangka pendek untuk
tujuan lindung nilai adalah relatif minimal. Di Amerika Serikat sendiri, kontrak futures
pada U.S. government Treasury Bills mempunyai volume perdagangan yang sangat
rendah. Eurodollar futures diperdagangkan secara luas tetapi jarang digunakan oleh
perusahaan-perusahaan untuk melakukan lindung nilai terhadap resiko tingkat bunga.
Perusahaan-perusahaan lebih menyukai penggunaan swap dan customized interest rate
Sukarnen
DILARANG MENG-COPY, MENYALIN,
ATAU MENDISTRIBUSIKAN
SEBAGIAN ATAU SELURUH TULISAN
INI TANPA PERSETUJUAN TERTULIS
DARI PENULIS
Untuk pertanyaan atau komentar bisa
diposting melalui website
www.futurumcorfinan.com

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derivatives untuk tujuan ini. Bank-bank adalah pengguna utama dari Eurodollar futures,
tetapi mereka menggunakan ini sebagian besar untuk melakukan lindung nilai terhadap
swap dan derivatif tingkat bunga lainnya yang digunakan dalam kegiatan mereka
sebagai dealer.
Di samping instrumen-instrumen lindung nilai yang dikenal seperti swap, FRA, bond
futures, Eurodollar futures dan derivatif tingkat bunga lainnya, pada umumnya, Asset-
Liability Management (ALM) dari perbankan juga memonitor eksposur mereka terhadap
tingkat bunga dengan seksama. Melakukan matching antara durasi aktiva dan
kewajiban adalah langkah pertama, tetapi hal ini tidak akan melindungi bank dari
nonparallel shift dalam yield curve. Pendekatan yang umum dikenal sebagai GAP
management.
Jadi mengacu pertanyaan di atas, sebaiknya PFS mempertimbangkan untuk
menggunakan instrumen-instrumen lindung nilai yang lebih sering digunakan oleh usaha
simpan-pinjam, seperti yang telah dijelaskan di atas.
2. What would you have advised Mr. Myers to do on August 6?
Karena sejak bulan Juli, tingkat bunga menunjukkan trend penurunan, Mr. Myers dapat
mempertimbangkan untuk tidak melanjutkan aktivitas lindung nilainya. Disebutkan dalam
cerita bahwa pada saat Mr. Myers akan mengambil cutinya pada tanggal 6 Agustus,
PFS telah melakukan pembayaran variation margin calls sebesar $690.000, dan Mr.
Rose berhasil meyakinkan Mr. Myers bahwa penurunan tingkat bunga bersifat temporer
dan PFS disarankan untuk mempertahankan posisi futures-nya.
Menurut kami, hal ini sudah tepat karena memang selalu ”tergoda” untuk melakukan
closing-out atas posisi futures, apalagi sesudah menderita kerugian yang besar dan
adanya permintaan margin call. Jika posisi futures di-closed out, ini berarti bahwa
lindung nilai sudah tidak berfungsi dan PFS akan ter-ekspos terhadap resiko di spot
market, yang beresiko lebih besar daripada resiko lindung nilai.
Sebagai alternatif, kalau memang PFS tetap mau menggunakan 90-day T-Bill futures
(lihat komentar kami dalam point 1 di atas), maka Mr. Myers dapat menggabungkan
strateginya dengan melakukan closing-out atas posisi futures dan membuka posisi baru.

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Proses ini dikenal sebagai rolling the hedge forward, dan meskipun strategi ini dapat
memberikan resiko tambahan namun dalam kasus ini mungkin cukup efektif.
3. How should Mr. Myers explain his futures losses to the board on August 27?
Perlu ditekankan bahwa perusahaan cenderung berpikir mengenai lindung nilai atas
dasar ex-post dan bukan ex-ante. Jika aktivitas lindung nilai menghasilkan keuntungan
pada posisi spot dan kerugian pada posisi futures, maka tampak jelas bahwa after the
fact, aktivitas lindung nilai seharusnya tidak dilakukan. Tetapi tentu saja hal ini tidak
dapat diketahui pada saat before the fact.
Coba kita melakukan analisa atas kegiatan lindung nilai PFS:
Peoples Federal Savings Banks
Total cumulative variation margin calls per contract
May 20 - August 18 (91 days) 6,300
Initial margin per contract 2,500
8,800
Total position : 400 contracts 3,520,000
Loss on futures contracts 3,520,000
Profit on spot contracts
Exposure 400,000,000
Interest rate down from 11.8% to 7.7%
Interest at 11.8% 11,800,000
Interest at 7.7% 7,700,000
Interest savings 4,100,000
Net gain 580,000
Dari analisa di atas, tampak bahwa, PFS masih mempunyai net gain sebesar $580,000.
Dan memang inilah tujuan (dan harga) dari aktivitas lindung nilai – yaitu forgoing gains
to limit losses.

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Illustration 2: Southeast Corporation
1. How many September 1984 T-Bond futures contracts should Lori Hiratani
sell short to hedge Southeast’s interest rate exposure?
Kita akan menggunakan Price Sensitivity Hedge Ratio untuk menentukan hedge ratio
(lihat Kolb, Robert W., and Raymond Chaing, “Improving Hedging Performance Using
Interest Rate Futures, ” Financial Management 10 (Fall 1981), : 72 - 79). Pada intinya
formula ini untuk menentukan nilai Nf yang mengakibatkan tidak adanya perubahan
pada nilai portofolio).
Nf = - (DURB/DURf) x (B/f) x ((1+yf)/(1+yB))
Nf = - (7.8/8.5) x (60,000,000/ (69 + (8/32)*1,000) x ((1+11.08%)/(1+12.88%))
Nf = - (DURB/DURf) x (B/f) x ((1+yf)/(1+yB))
DUR bond 7.80
DUR futures 8.50
Bond value 60,000,000.00
Futures value 69,250.00
Yield futures 11.80%
yield bond 12.88%
Number of futures contracts 787.47
2. What rate will Hiratani “lock in” by initiating this hedge?
The current Aa rate : 12.88%
3. Does this hedging strategy eliminate Southeast’s exposure? If not, what
risks remain?
Karena tidak ada corporate bond futures contract, maka Southeast memilih Treasury
Bond futures contract. Ini dikenal sebagai cross hedge dan tipe basis risk akan lebih
besar daripada, misalnya, malakukan lindung nilai atas obligasi pemerintah dengan
Treasury bond futures. Harga obligasi pemerintah dan perusahaan cenderung bergerak
bersama-sama, namun hubungannnya lebih lemah.

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Illustration 3: Alpha Investors
1. What futures position should Jim take to hedge his portfolio?
Alpha Investor
Portfolio beta 1.18
Value of S&P 500 Stock Index 191.85
Risk free interest rate T Bill rate
- 3 months 7.07%
- 6 months 7.41%
Dividends yield on index 4.16%
Current futures price
- Sept 193.65
- Dec 196.65
One futures contract is for delivery of 500 times index 500.00
Current value of portfolio 36,129,094.00
current value of stocks underlying one futures contract 95,925.00
N = Beta x (Current value of portfolio /current value of
stocks underlying one futures contract)
menggunakan minimum variance hedge ratio 444.43
Hedging strategi : Sell 444 contracts
2. What risks can Jim eliminate by shorting by shorting S&P 500 index futures
contracts? How effective do you expect his hedge to be? (Try to quantify the
effectiveness of Jim’s hedge using the methodology described in the Salomon
Brothers research report (Appendix 3).)
NOTE : Kami tidak mendapatkan Appendix 3 sehingga kami mencoba melakukan
tanpa data dari Appendix 3.
The objective of the hedge is to eliminate systematic risk. Clearly systematic risk is
reduced but not eliminated.

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See analysis below:
Contract 444.0
times index 500.0
Dividends yield - index per annum 4.16%
Dividends yield - AIP per annum 1.35%
T-Bill rate 3 months per annum 7.07%
T-Bill rate 3 months per three month 1.77%
Beta portfolio 1.18
Value of portfolio 36,129,094
Value of index in three months 178.00 185.00 191.85 193.00 195.00
Futures price of index today (for Sept) 193.65 193.65 193.65 193.65 193.65
Futures price of index in three months 180.00 187.00 194.00 195.00 197.00
Gain (loss) on futures position 3,030,300.00 1,476,300.00 (77,700.00) (299,700.00) (743,700.00)
Return on market -6.18% -2.53% 1.04% 1.64% 2.68%
Expected return on portfolio
Results of regression
AIP = 0.13% + 1.18(S&P 500) -7.16% -2.86% 1.36% 2.06% 3.29%
if using CAPM:
Risk-free rate + Beta x (return on index -
risk-free rate) -7.61% -3.30% 0.91% 1.62% 2.85%
Expected portfolio value in three months
(including dividends) 33,379,820.12 34,935,339.10 36,457,525.53 36,713,075.08 37,157,509.07
Total expexted value of position in
three months 36,410,120.12 36,411,639.10 36,379,825.53 36,413,375.08 36,413,809.07
Performance of stock index hedge
3. What return can Jim expect to earn during the third quarter of 1985 assuming
he adopts your hedging strategy?
See analysis in No. 2 above. It can be seen that the total expected value of AIP’s
position in three months is almost INDEPENDENT of the value of the index.

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Illustration 4: Auto Star
Question : If you were Rob Rough, what advice would you give to Edith Cooper?
Edith was concerned that Auto Star’s extreme leverage and reliance on variable rate
financing exposed the company to an unacceptable level of financial risk. The concern is
more on the use of short-term interest rate futures. An interest rate futures contract fixes
the effective interest rate for borrowing at a specific date in the future.
As of December 30, 1981, Auto Star’s short-term notes payable totaling $18,565 was
exposed to short-term interest risk. As the data is not complete, we could for example,
assume that Auto Star decides to hedge his next roll-over of $18,565 three month loan
due on November 1. The loan is at spread of 0.5% above LIBOR, in this case, 9%. The
problem confronting Auto Star is to anticipate the likely net borrowing rate for June 20
and then to adopt a hedging strategy that will guarantee this rate. Anticipating that rates
may have arisen by then, the Company shorts a December $20,000 Eurodollar three
month futures contract. This enables the company to lock in currently available interest
rates, specifically 9%, for the three months beginning in December. Because the futures
quote is 100 minus the futures interest rate, Auto Star who is short, will gain when the
interest rates rise and will suffer loss from the spot/cash market.
Note : kami tidak mengutarakan lebih lanjut bagaimana penggunaan interest rate futures
karena dalam buku Options, Futures, and Other Derivatives oleh John C. Hull sudah
diberikan contoh yang jelas, namun demikian kami memberikan catatan di bawah.
However, as Auto Star hedges its variable-rate short-term notes payable with a futures
contract on a different underlying instrument, known as cross-hedging, this exposes
Auto Star to greater basis risk because there is less likelihood that interest rates on
different financial instruments will move exactly together. In general, Auto Star should
choose its liability using a futures contract which suggests the best correlation. Auto Star
should run a regression over prime vs T-Bill rates and prime vs 3-month CD rates, to
determine which one is most closely correlated with the prime rate. Nonetheless, it

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should be noted that correlation can change through time and past correlations may not
necessarily be good predictors of future correlation.
Illustration 5: Stock Index Futures Arbitrage
1. What is the theoretical price of the MMI March’86 futures contract?
Model for the stock index futures price:
Fo (T) = So e^(rc - q) T
rc = continuously compounded risk-free rate
q = continuously compounded dividend yield
Data:
So 311.74
rc 6.80%
q 0.99% (assuming dividends were paid on a quarterly basis)
T 0.07 February 26 - March 21 (satu tahun = 365 hari)
e 2.71828183
Fo (0.07) = 312.9327
2. Assume that Jim is subject to a $5,000,000 position limit. What position
should he take to exploit the mispricing of the March’86 MMI futures?
Since the March 86 MMI futures, which were to expire on March 21, were priced at
313.55 (higher than 312.9327), the futures is slightly overpriced. Profits can be made by
shorting futures contracts and buy the stocks in the MMI in the same proportions as in
the index at the spot price (i.e., for immediate delivery). At expiration, the futures price
would equal the spot price of the MMI. We then would sell the stocks. This transaction is
theoretically riskless and would earn a return in excess of the risk-free rate.
There are several problems in implementing this stock index arbitrage. Jim Lucey should
buy the stock index at 311.74. In reality, Jim as arbitrageur would have to purchase all
20 stocks in the appropriate proportions as the index and immediately execute all of the
trades. Although the New York Stock Exchange has established a computerized order

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processing system, called the Designated Order Turnaround, or DOT, that expedites
trades, it is still difficult to get all the trades in before the price of any single stock
changes. Thus, most arbitrageurs do not duplicate the index but use a smaller subset of
the stocks. Naturally, this introduces some risk into what is supposed to be a riskless
transaction.
For example, we assume that the trades can be executed simultaneously (or in the case,
it was said that Jim believed that transactions in the 20 large-capitalization stock
included in the MMI could be executed with less than 0.25% market impact). Jim has
$5,000,000 to use. Then Jim will buy the appropriately weighted 20 stocks of MMI with
that amount. Because of the $250 multiplier on the futures, the MMI is actually priced at
311.74 (250) = $77,935, so Jim will need to buy $5,000,000/$77,935 = 64.16 futures
contracts. Because Jim can not buy fractional contracts, the transaction will not be
weighted precisely.
In addition, there are transaction costs. However, in this case, it was said that Jim would
incur no commission expenses.
In addition, there are problems involved in simultaneously selling all of the stocks in the
MMI at expiration. These transactions must be executed such that the portfolio will be
liquidated at the closing values of each stock. This is very difficult to do and frequently
causes unusual stock price movements at expiration.
3. What rate of return can Jim expect to earn on his position?
Fo (T) = So e^(rc - q) T
Assuming that futures price is equal to its theoritical fair price, then we could
solve this equation for the implied interest rate
Implied rc = ln (fo(T)/So) divided by T plus q
Fo (T) actual 313.55
Implied rc = 9.80%

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If this transaction were undertaken, it would provide a risk-free return of 9.80%. With the
risk-free rate at 6.8%, the transaction is an attractive opportunity. Also, if Jim Lucey
could not borrow at 6.8%, but could borrow at any rate less than 9.80% (in the case, it
was said that his firm’s cost of borrowing was approximately 8%), the transaction would
still be worth doing.
4. Who, in addition to securities dealers, would you expect to engage in index-
futures arbitrage?
No, see some practical considerations detailed in no. 2 above. This type of arbitrage
transaction is mostly executed by many large financial institutions, which trade large
blocks of stock simultaneously or a relatively small representative sample of stocks
whose movements closely mirror those of the index, implemented through program
trading. In addition, a small retail trader faces enormous transaction costs in attempting
to engage in index arbitrage.
5. Why do index futures often trade at a premium or discount to their theoretical
values?
Four different types of market imperfections could affect the pricing of futures contracts.
Those market imperfections are : direct transaction costs, unequal borrowing and
lending rates, margins and restrictions on short selling, and limitations to storage. The
effect of these market imperfections is to create a band of no-arbitrage prices within
which the futures price must fall.
Direct transaction costs affect stock index futures trading to a considerable extent.
Relative to many goods, transaction costs for stocks are low in percentage terms.
Nonetheless, stock traders face commissions, exchange fees, and a bid-asked spread.
In general, these costs may be about one-half of 1% for stock market transactions. Even
with such modest transaction costs, we can not expect the cost-of-carry model to hold as
an exact equality. Instead, these transaction costs will lead to an no-arbitrage band of
permissible stock index futures prices.

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However, a highly competitive trading environment and low transaction costs keep this
no-arbitrage band quite tight around the perfect markets theoretical fair value of the
above equation.
6. How do you expect the pricing efficiency of broader market index futures, like
the S&P 500, to compare to the pricing of MMI futures?
A highly competitive trading environment and low transaction costs keep this no-
arbitrage band quite tight around the perfect markets theoretical fair value of the above
equation, which means that the broader market index futures, like the S&P 500, will tend
to have more pricing efficiency compared to the pricing of MMI futures. In addition, since
the stocks of the S&P 500 are so widely held by financial institutions with low transaction
costs, quasi-arbitrage is a dominant feature of stock index futures trading. The quasi-
arbitrage opportunities enjoyed by financial institutions ensure that no individual could
ever engage in index arbitrage.
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