Yield Curve Risks And Economic Factors

Managing Yield Curve Risks

Yield curve risk refers to risk to the value of a bond portfolio due to unexpected changes in the yield curve.

To counter yield curve risk, we first identify our portfolio’s sensitivity to yield curve changes using one or more measures. Yield curve sensitivity can be generally measured by effective duration, or more precisely using key rate duration, or a three factor model that decomposes changes in the yield curve into changes in level, steepness, and curvature.

Effective Duration

Effective duration measures price sensitivity to small parallel shifts in the yield curve. It is important to note that effective duration is not an accurate measure of interest rate sensitivity to non parallel shifts in the yield curve like those described by shaping risk. Shaping risk refers to changes in portfolio value due to changes in the shape of the benchmark yield curve.

(Note, however, that parallel shifts explain more than 75% of the variation in bond portfolio returns.)

Key Rate Duration

A more precise method used to quantify bond price sensitivity to interest rates is key rate duration. Compared to effective duration, key rate duration is superior for measuring the impact of nonparallel yield curve shifts.

Key rate duration is the sensitivity of the value of a security (or a bond portfolio) to changes in a single par rate, holding all other par rates constant. In other words, key rate duration isolates price sensitivity to a change in the yield at a particular maturity only.

Numerically, key rate duration is defined as the approximate percentage change in the value of a bond portfolio in response to a 100 basis point change in the corresponding key par rate, holding all other par rates constant. Conceptually, we could determine the key rate duration for the five year segment of the yield curve by changing only the five year par rate and observing the change in value of the portfolio. Keep in mind that every security or portfolio has a set of key rate durations, one for each key rate.

For example, a bond portfolio has interest rate risk exposure to only three maturity points on the par rate curve: the 1 year, 5 year, and 25 year maturities, with key rate durations represented by $D_1$ = 0.7, $D_5$ = 3.5, and $D_{25}$ = 9.5, respectively. The sum total of these key rate durations is the effective duration of the portfolio.

The model for yield curve risk using these key rate durations would be:

Sensitivity to Parallel, Steepness, and Curvature Movements

An alternative to decomposing yield curve risk into sensitivity to changes at various maturities (key rate duration) is to decompose the risk into sensitivity to the following three categories of yield curve movements:

Level ($\Delta x_L$). A parallel increase or decrease of interest rates.

Steepness ($\Delta x_S$). Long term interest rates increase while short term rates decrease.

Curvature ($\Delta x_C$). Increasing curvature means short and long term interest rates increase while intermediate rates do not change.

It has been found that all yield curve movements can be described using a combination of one or more of these movements.

We can then model the change in the value of our portfolio as follows:

where $D_L$, $D_S$, and $D_C$ are respectively the portfolio’s sensitivities to changes in the yield curve’s level, steepness, and curvature.

For example, for a particular portfolio, yield curve risk can be described as:

If the following changes in the yield curve occurred: $\Delta x_L$ = −0.004, $\Delta x_S$ = 0.001, and $\Delta x_C$ = 0.002, then the percentage change in portfolio value could be calculated as:

This predicts a +0.5% increase in the portfolio value resulting from the yield curve movements.

Maturity Structure of Yield Curve Volatilities

Interest rate volatility is a key concern for bond managers because interest rate volatility drives price volatility in a fixed income portfolio. Interest rate volatility becomes particularly important when securities have embedded options, which are especially sensitive to volatility.

The term structure of interest rate volatility is the graph of yield volatility versus maturity.

Figure 23.4 shows a typical term structure of interest rate volatility. Note that, as shown here, short term interest rates are generally more volatile than are long term rates.

Figure 23.4: Historical Volatility Term Structure: U.S. Treasuries, August 2005−

December 2007

Volatility at the long maturity end is thought to be associated with uncertainty regarding the real economy and inflation, while volatility at the short maturity end reflects risks regarding monetary policy.

Interest rate volatility at time t for a security with maturity of T is denoted as σ(t,T). This variable measures the annualized standard deviation of the change in bond yield.

Macroeconomic factors that affect bond yields include inflation forecasts, GDP growth, and monetary policy. Two thirds of the variation in short and intermediate term yields is explained by monetary policy, and the remaining is explained by the other factors. In contrast, inflation explains two thirds of the variation in long term yields, with the remaining mostly explained by monetary policy.

Bond risk premium is the excess return (over the one year risk free rate) earned by investors for investing in long term government bonds. Bond risk premium (also known as the term premium or duration premium) is a forward looking expectation. For example, suppose that the expected one year holding period return on a 5 year government bond is 4%, while the one year risk free rate is 1%.

The 5 year bond risk premium in this example would be 4% − 1% = 3%.

Monetary policy influences the shape of the yield curve. During economic expansions, to combat rising inflation, central banks may raise short term rates, leading to a bearish flattening of the yield curve. During recessionary times, central banks may reduce short term rates, leading to a bullish steepening.

The U.S. Federal Reserve has dramatically expanded its balance sheet in recent years, purchasing U.S. Treasuries and mortgage backed and municipal securities, reducing long term bond yields.

Other factors affecting bond prices include the following:

Fiscal policy. Expansionary (restrictive) fiscal policies increase (decrease) yields. Maturity structure.

The government’s choice of maturity when issuing new securities affects the supply (and yield) of bonds in those maturity segments. An increase in offerings in a specific segment of the market increases the supply and increases the yield in that segment (the market segmentation theory). Investor demand.

Domestic and foreign investor demand and preferences for specific maturity segments affect the yield in that segment. For example, pension plans and insurance companies may prefer longer maturity bonds, driving down longer term yields. During periods of market turmoil, a flight to safety may reduce long term government bond yields, resulting in a bullish flattening of the yield curve.

Figure 23.5: Categories of Shifts in the Yield Curve

Investor Actions

In expectation of a rise (fall) in rates, investors will lower (extend) the duration of their bond portfolios. Expectations of a steepening of the yield curve may lead to investors going long short term bonds and short longer term bonds. Trades may be designed to be duration neutral so that a change in the level of interest rates does not affect the value of the portfolio.

Investors with long only mandates may rotate between a bullet portfolio (a portfolio concentrated in a single maturity) and a barbell portfolio (a portfolio with short and long maturities). An investor that expects a bullish flattening of the yield curve may rotate out of a bullet portfolio and into a barbell portfolio.

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