**"interest payments"**

## Hedge Fund Strategies (8) – Basis Trading

*by Eric Bank on June 5, 2011 · No Comments · in Documenting the Search for Alpha*

Basis trading is a form of fixed-income arbitrage that seeks to benefit from a change in the spread between a spot bond price and an adjusted futures price.

In preparation for resuming our exploration of hedge fund trading strategies, we took a detour last time out to learn about ** bond futures** and

**, which are used in**

*conversion factors***. Basis trading is a form of fixed-income arbitrage that seeks to benefit from a change in the spread between a spot bond price and an adjusted futures price. The formula for the**

*basis trading***is:**

*basis*B = SP – (FP x CF)

where:

B is basis

SP is spot price of bond (clean)

FP is futures contract price (clean)

CF is conversion factor

** Clean prices** are ones in which the present value of future cash flows, such as interest payments, are not included in the price. Normally, one purchases a bond at the

**, which includes such cash flows.**

*dirty price*A bond basis trade is the simultaneous purchase and sale of a bond and a bond futures contract to capture a non-zero basis as profit. It is also known as a ** cash-and-carry** trade. (There is an alternative method of achieving the same result using

**(EFP) which we’ll not discuss in this article).**

*exchange of futures for physicals*The conversion factor is the key to a basis trade. Here’s how it works:

- If the basis is negative, the bond spot price is less than the adjusted futures price. In this case, you would “buy the basis” by buying cash bonds and selling futures contracts. Say that the conversion factor on the 8 ¾ T-Bonds of 5/15/2017 is equal to 1.077. To buy $100M of the basis, you purchase $100M face value of the bonds and simultaneously sell 1,077 (= $100M * (1.077 / $100K) of bond futures.
- If the basis is positive, the bond spot price is greater than the adjusted futures price. Here you would “sell the basis” by selling cash bonds and buying futures contracts. For instance, if the conversion factor on the 7 5/8 T-Bonds of 2/15/2005 equals .0960, then selling $10M of the basis would require selling $10M face of the bonds and buying 96 futures contracts.

To close out the trade, you need to purchase your short position and sell your long position. If you compare the opening spread with the closing one, the difference is the change in basis during the holding period. A narrowing spread favors the short position; a widening spread benefits the long.

If you think the spreads will narrow over time, you benefit from selling the expensive bonds and buying the cheap futures contracts if your prediction is correct. The change in basis over time is the cash part of the trade. The carry portion consists of coupon payments less financing costs (at the ** repo rate**) for the bond (including accrued interest). You realize a profit if the sum of the cash and carry portions are positive.

Every 1/32 of a basis point is worth $31.25; on a position of $10M face, this equals $3,125. Therefore, if a basis narrows by 2.6 basis points, the short position profits on the cash portion of the $10M face trade by 2.6 * $3,125 = $8,125. As long as the short’s carry costs do not exceed $8,125, he/she will pocket a profit.

The risk in a basis trade is that the basis will move in an unfriendly direction due to a change in the yield curve, and/or the repo rate will change to your disadvantage. These changes are important because of the following reasons:

1) If the repo rate decreases, or if the yield curve steepens, carry and basis increases

2) A decrease in the bond’s yield relative to other deliverable bonds will increase the basis

3) Bond duration can affect a bonds response to yield changes: the basis of a low-duration bond will tend to rise with bond yields, whereas the basis of a high-duration bond increases when bond yields fall.

4) Volatility affects technical considerations involving the short’s strategic delivery options. A rise in volatility would tend to lower the futures price and raise bond basis.

*There is extensive literature on basis trading, and interesting parties are urged to seek it out before embarking on any trading activity.*

Our next topic will be ** asset swap trades**.

## Yield Curve – Theories

*by Eric Bank on May 11, 2011 · No Comments · in Documenting the Search for Alpha*

Recall that yield curves (also known as the term structure of interest rates) plot debt maturities (the independent variable) against interest rates (the dependent variable).

Recall that yield curves (also known as the ** term structure of interest rates**) plot

**(the independent variable) against**

*debt maturities***(the dependent variable). Debt maturities indicate the length of the borrowing period for a debt instrument. We spoke last time on how a yield curve is shaped; today we’ll look at a few theories that attempt to explain yield curve behavior.**

*interest rates***Pure Expectations Theory (PET)**

In this theory, it is assumed that any maturity of debt can substitute for any other through the miracle of compounding. For instance, if you have a view as to what the one-year interest rate will be one year from now (the ** forward rate**), then you can determine the current two-year interest rate as the compounded sum of the current one-year rate and the one-year forward.

This generalizes to the ** geometric mean **of short-term yields as the determinant of long-term yields. A geometric mean differs from an average in the it is calculated by taking the

*n*th root of the product of

*n*terms. For example, if you have two terms, say 4 and 16, the average is of course 10, but the geometric mean is the 2

^{nd}root – the square root – of their product (64), or 8.

The Pure Expectations Theory accounts for the fact that yields tend to change together over time, but doesn’t explain the fine details of the shape of the yield curve. It posits that forward rates are perfect predictors of future rates, which they are not. It thus ignores interest rate risk and also reinvestment risk. The latter is the risk that one cannot reinvest interest payments at an expected rate. The theory also assumes that the ability to arbitrage among different maturity bonds is minimal.

**Liquidity Preference Theory (LPT)**

This is a variant of the Pure Expectations Theory. It basically adds a premium to the PET-calculated yield for long-term debt to account for investor preference for short-term bonds over long-term ones. This premium is called the term premium or the liquidity premium. It acknowledges the risks involved in holding long-term debt, which is more likely to experience catastrophic events and price uncertainty than is short-term debt. A second premium is also included in LPT, for default risk, which is more likely when holding a bond for a long period of time, once again due to uncertainty.

**Market Segmentation Theory (MST)**

This theory acknowledges that different maturities of debt cannot be substituted for each other. This results in separate demand-supply relationships for short-term and long-term debt. Since investors (assumed to be risk-adverse) prefer the less risky short-term maturities, the demand for short-term debt is higher than that for long-term debt, and thus prices of the former are higher, driving down their yields. This helps to explain the normal shape of the yield curve, but not the fact that long and short term rates tend to change in unison, since they are supposed to be two separate and independent markets.

**Preferred Habitat Theory (PHT)**

Preferred Habitat Theory is an extension of MST which posits maturity preferences, or habitats, for debt investors: some investors like 3-year bonds, some prefer 6-year maturities, etc. If you want to sell an investor a bond outside the investor’s preferred investment horizon, you must offer the investor a premium. Since it is assumed that more investors have short-term habitats, it explains the higher yields on long-term debt, and is consistent with the tendency of short- and long-term debt yield curve segments to retain their shape when overall yields change.

Now that we have a good understanding of yields and the yield curve, we can resume our review of hedge fund strategies. Next time: * fixed-income arbitrage*.

## Termination of Interest Rate Swaps

*by Eric Bank on January 14, 2011 · No Comments · in Financial topics*

Though there are several types of interest rate swaps (IRS), the most familiar type is known as fixed-for-floating. A notional amount of principle is used to calculate periodic fixed and floating interest payments.

Though there are several types of interest rate swaps (IRS), the most familiar type is known as fixed-for-floating. A notional amount of principle is used to calculate periodic fixed and floating interest payments. One of the counterparties receives fixed interest payments and pays out floating-rate interest to the other counterparty, who reciprocates by paying fixed and receiving floating. The floating rate can be pegged to three-month the U.S. Treasury bills, London Interbank Offer Rate (LIBOR), or any other well-established rate index. Continue reading “Termination of Interest Rate Swaps” »

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