### Bonds:Interest Rate Sensibility

The price of bonds can vary, but not every bond is affected in the same way when circumstances change. If the typical market interest rate drops, market price will fall for all bonds, but not at the same rate. We will look at the reasons for this, while taking a look at the duration of bonds, which will show us the remaining average lifetime of a bond. The point of this is to be able to compare different bonds with each other.

## Elasticity

Elasticity is a statistical concept, but is widespread in economics, and we will now take a look at it in this context. We can determine the interest elasticity of the market price using the following:

The numerator is the current price change in percentage, and the denominator is the interest rate change in percentage. The result will be in percentage format and the way we interpret it is (if E=4,5) that: If the interest rate changes by 1% that will induce a 4,5% change in the current price.

Elasticity is not actually used in finance because it only gives a rough estimate and is not a good base for comparison. What we use in reality is duration and modified duration.

## Duration

Duration was first developed by Frederick Macaulay in 1938, and is used widely since 1952 when F.M Reddington alerted financial corporations of its importance. This just shows how recent some concepts are in finance.
Duration is officially the measure of the average (cash-weighted) term-to-maturity of a bond. Practically it means how much an investor has to wait for his investment to break even (on average). It has a large formula, but do not be swayed, it is not difficult.

The numerator is really the maturity of the cash-flows weighed with the present value of the respective cash-flows. The denominator is actually the current price of the bond (the present value of the cash flows).

We can observe some important laws about duration:

• Every bond which has any other cash flows than the repayment of the face value has a smaller duration than the time to maturity.
• If two bonds have the same time to maturity the one with the larger duration has a lower coupon rate.
• If two bonds have the same coupon rate, the one with the longer time to maturity will have a higher duration. So with longer maturity time comes growing duration, although this growth is a slowing growth, a bond with a ten year maturity will not have twice the duration of a five year bond.
• If two bonds have equal time to maturity and coupon rates the one with the lower yield expected by investors will have a higher duration.
• Zero coupon bond's duration equals their time to maturity

## Modified duration

To determine how prices react to interest changes we use modified duration. It will show us exactly what elasticity has showed us, but more precisely.

Information is for educational and informational purposes only and is not be interpreted as financial or legal advice. This does not represent a recommendation to buy, sell, or hold any security. Please consult your financial advisor.