Applications for financial futures

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Applications for Financial Futures

Catatan: Tulisan ini adalah pembahasan atas Study Case Harvard Business School No.

9-286-109 Rev. July 28, 1986 berjudul : “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

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



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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

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.


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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.

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, melakukan lindung nilai atas obligasi pemerintah dengan


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Treasury bond futures. Harga obligasi pemerintah dan perusahaan cenderung bergerak

bersama-sama, namun hubungannnya lebih lemah.

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 loans

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 a 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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Economy & Finance

Applications for financial futures