Key Rate Duration

Key rate duration refers to the change in a bond’s value based on the change in yield. This metric is used to measure the sensitivity of bond prices; it is expressed in terms of 100 basis points, or a 1% change in a bond's yield.

This metric is used to compare the fluctuation in bond prices. For investors, defining the probability of making a profit is paramount. Investors, therefore, study the difference between the duration values of two securities. Key duration affects the yield curve of a bond. In certain scenarios, the key duration and the yield curve are unparalleled.

• Key rate duration explains a bond's price sensitivity. It can be positive or negative. This metric determines the possible change in bond value from its yield.
• It can be applied to different debt securities but is most commonly applied to bonds with 100 basis points (1%) increase or decrease in yield.
• There are 11 US treasury maturity levels, and the duration for each level is measured by employing the formula.
• Interest rate and duration are directly proportional to each other. If the duration increases, the interest rate also increases. Also, the bond price decreases when there is a potential threat of high-interest rate risk.

Key rate duration is an important metric; it is used to assess the sensitivity of bond value. It compares bond price fluctuation—occurring after a specific maturity point. Alternatively, the fluctuation is studied about the bond’s yield. The assessment is expressed in 100 basis points, a 1% change in bond yield.

Therefore, every debt securities trader or investor keeps an eye on this metric. Investors get an idea of the projected profit expected from a particular bond—at various maturity dates. Options traders use a technique called key rate duration hedging. They shorten the duration of bonds and aim for a low duration compared to the actual duration of the portfolio. They achieve this by implying future derivatives. Unfortunately, this technique has a massive drawback; the trader encounters hedging costs, and the bond’s yield diminishes.

Regarding United States treasuries, the metric measures yield for 11 bond maturities. The key duration is calculated for each maturity level. Simultaneously, this method is used for comparing fixed-income investments.

It is especially useful for investors who hold a callable bond. In callable bonds, the investor can redeem the bond before maturity, but the investor can decide not to do so. Thus, investors use key duration to decide when to redeem callable bonds.

Investors who deal with mutual fund investments look for the underweight duration. Instead, fund managers announce that their portfolio is overweight. This implies that the funds’ duration is long (duration is higher than the benchmark). In contrast, a fund could be underweighted.

A key duration formula derives the difference between the price of a security before and after one percent yield changes. It is divided by the original security price. There can be a negative or positive key duration.

The key rate duration formula is as follows:

Key Duration = P_- + P₊ / 2 x 0.01 x P₀

Here,

• P_- = price of the bond after a 1% decline in yield.
• P+= price of the bond after a 1% increase in yield.
• P₀ = Original bond price.
  

Let us look at the key rate duration example.

The given bond was originally priced at $900. With a 1% increase in yield (at maturity), the bond's value declines to $891. Similarly, a 1% fall in yield would increase the bond's value by $909.

Let us apply the given values to the formula.

Key Duration = P_- + P₊ / 2 x 0.01 x P₀

Key Duration = 909 - 891 / 2 x 0.01 x 900

Key Duration = 18 / 2 x 0.01 x 900

Key Duration = 18 /18 = 1

Key duration can help predict the variance in a bond's price concerning the change in interest rates. There is a primary rule for key duration buckets; for every 1% hike or decline in interest rates, there will be a 1% fluctuation in the bond price every year (in the opposite direction).

For example, if a bond is of 4 years and interest rates hike by 1%, the bond's price will decline by approximately 4%. Alternatively, if the interest rates decrease by 1%, the bond's price will increase by 4%.

Let us look at key rate duration vs effective duration comparison to distinguish between the two.

• Key rate duration determines the variance in a bond’s value—based on yield rate. In contrast, the effective duration measures the impact of cash flows on bonds with embedded options. Here, the change in interest rates brings out the cash flow variance.  
• The former measures the entirety of the curve; It applies to debt securities and debt instrument portfolios. Whereas the latter only applies to parallel shifts in the yield curve.
• Due to its wide scope, the former is considered more reliable than the latter.
• The former is an improved calculation method over the latter. The former indicates that the anticipated bond value changes or yield curve shifts do not directly correlate with key rate maturities.

This has been a guide to what is Key Rate Duration. Here, we compare it with effective duration and explain its formula and calculation with an example. You can learn more about finance from the following articles -

• Floating Rate Note
• Interest Rate Cap
• Yield Spread Premium