Strategies for Changes in Market Level, Slope, or Curvature

Investors often hold individualized expectations about the yield curve that they generate from economic analysis, data mining exercises, following monetary policy and central bank actions, or other techniques. To the extent that investors position their portfolios based on these expectations, they are disagreeing with the forward expectations embedded in the yield curve. If their expectations turn out to be correct, they will earn superior returns. If their expectations are not met, however, they may suffer losses.

The primary strategies portfolio managers may use in anticipation of a change in the level of interest rates or in the slope or shape of the yield curve are duration management and buying convexity.

Duration Management

In its simplest form, duration management shortens portfolio duration in anticipation of rising interest rates (decreasing bond prices) and lengthens portfolio duration in anticipation of declining interest rates (increasing bond prices).

Modified duration, D, can be used to estimate the percentage change in a security’s price (or the portfolio’s value), P, given a change in rates.

P change ≈ –D × ΔY (in percentage points)  

Duration Management: A parallel shift in the curve portfolios with the same duration are expected to have the same percentage change in value.

  • If rates are expected to increase, decrease portfolio duration before this occurs to minimize the value lost.
  • If rates are expected to decrease, increase portfolio duration before this occurs to maximize the value gained.

Of course all changes in duration must be consistent with the portfolio constraints.

If a portfolio is fully invested, it is often easier to reduce duration than to increase it. Duration can be reduced by selling some securities and holding cash. To increase duration (without using derivatives), it is necessary to sell shorter-duration securities and simultaneously buy longer-duration securities. When altering duration through simultaneous purchases and sales of securities, the portfolio manager may find herself in a position of having to sell securities that she would have preferred to retain—securities that were hard to find or that have low liquidity and are costly to transact.

It is much easier to alter portfolio duration using interest rate derivatives. A derivatives overlay keeps the lengthening or shortening of duration separate from security selection, and it does not require a change in basic portfolio structure.

One way to adjust portfolio duration with derivatives is to use futures contracts. Fixed-income futures contracts are sensitive to changes in the price of the underlying bond. No cash outlay is required in futures contracts beyond posting and maintaining margin. There are two important concepts necessary to calculate the futures trade required to alter a portfolio’s duration—money duration and price value of a basis point (PVBP).

Interest rate swaps could also be used to achieve the increase in duration. Although swaps are not as liquid as futures, nor as flexible in the short term as using leverage, swaps can be created for virtually any maturity and are not limited to the standard maturities in note or bond futures. And, although the legal and liquidity considerations differ between swaps and either futures or leverage, theoretically they are hard to distinguish from one another. A receive-fixed position (receive fixed, pay floating) in a swap is essentially a long position in a bond and a short position in a short-term security, much like the long bond/short financing position of leverage, or the long bond/short repo position of a futures contract.

Buying Convexity

A portfolio manager may choose to alter portfolio convexity without changing duration in order to increase or decrease the portfolio’s sensitivity to an anticipated change in the yield curve.

Increase Portfolio Convexity: Greater convexity will:

  • Increase the value gained if rates decrease.
  • Decrease the value lost if rates increase.

Bullet and Barbell Structures

The basic concept is simple. First, determine the appropriate duration for the portfolio. Within that constraint of meeting, target total duration:

  • Increase exposure to those points on the curve where rates are expected to show a relative decrease in level.
  • Decrease exposure to those points on the curve where rates are expected to show a relative increase in level.

The simplest way to implement this strategy is selection of a bullet versus barbell portfolio.

  • The bullet portfolio concentrates exposure in the desired total portfolio duration point of the curve (denoted here as M for middle).
  • The barbell portfolio concentrates exposure at shorter and longer points of the curve to achieve the same desired total portfolio duration (denoted here as S and L for shorter and longer).
  • A laddered portfolio would distribute exposure more evenly along the curve between S and L.

 A bullet portfolio is made up of securities targeting a single segment of the curve. This structure is typically used to take advantage of a steepening yield curve—a bulleted portfolio will have little or no exposure at maturities longer or shorter than the targeted segment of the curve. If long rates rise (and the yield curve steepens), the bulleted portfolio will lose less than a portfolio of similar duration but composed of exposures distributed across the yield curve. If the yield curve steepens through a reduction in short rates, the bulleted portfolio has given up very little in profits given the small magnitude of price changes at the short end of the curve.

Barbells are portfolios combining securities concentrated in short and long maturities (and, consequently, owning less in the intermediate maturities) relative to the benchmark. They are typically used to take advantage of a flattening yield curve. If long rates fall more than short rates (and the yield curve flattens), the portfolio’s long-duration securities will capture the benefits of the falling rates in a way that the intermediate-duration securities cannot. If the yield curve flattens through rising short-term rates, portfolio losses are limited by the lower price sensitivity to the change in yields at the short end of the curve, whereas the (non-barbell) benchmark’s intermediate-duration securities will do poorly.

Key rate durations (KRDs) are often used to identify bullets and barbells. Also called partial durations, KRDs can be used to estimate a bond’s sensitivity to changes in the shape of the benchmark yield curve. KRDs measure durations of fixed-income instruments at key points on the yield curve such as 2-year, 5-year, 7-year, 10-year, and 30-year maturities.

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