What is the Duration of Bonds: Guide to Calculation?

The duration of bonds, or financial duration, is a concept with which we must necessarily get acquainted if we want to invest in bonds (and also in other instruments) with profit.

The duration is in fact a fundamental tool/calculation to calculate the convenience of a bond and also to compare it with other instruments that we could choose for the investment as an alternative.

The financial duration generally also indicates the date by which those who invested in the security will get back the money invested, also taking into account any coupons collected.

An introduction

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What kind of factors are summarized?

The duration is a fairly accurate indicator of the synthesis of four elements:

  • the duration of the title;
  • the frequency with which coupons are issued;
  • the type of reimbursement (if zero-coupon or with coupon);
  • the interest offered as a yield.

The calculation of the duration

Calculating the duration of a bond is relatively easy for fixed-rate bonds.

In fact, in this case, it is enough to calculate:  Sum (t) t (W) t,

where is it:

  • W (t) is FC x (1 + r) ^ – t / P;
  • FC = Cash flow;
  • r = rate of return to maturity;
  • P = price.
  • Duration of zero-coupon securities

It is worth remembering in this circumstance that zero-coupon bonds have a duration that is identical to the duration of the bond.

Duration as a summary of risk

The first use we can make of the calculated duration is the risk summary. In fact, all the data necessary to evaluate the risk inherent in a given bond ends up within this simple equation.

Unlike the rating that is disseminated by the main agencies, the duration expresses a mathematical value based on authentic and measurable data, as opposed to the philosophizing of agencies that are often directly involved in the bond market.

On securities with variable yield, the calculation is only “approximate”

Likewise, it is worth remembering that the duration calculation for variable yield securities is probabilistic only. In fact, we try to guess what the performance of a stock which, by its very nature, is variable may be.

The calculations often leave the time they find and cannot in any way be considered as reliable. Alternatively, it is also possible to “normalize” the floating rate, with the result, however, of having an extremely unreliable duration.

Modified Duration

The Modified Duration is another calculation that allows, starting from the Duration, to evaluate the change in the price of the security as the internal yield changes.

In this case, the calculation is very simple, provided you have already calculated the duration:

DM = D / (1 + r)

where r is the internal return and D the classic Duration.

How to interpret the duration?

Duration should be interpreted in this sense:

  • it decreases as the deadline approaches;
  • it increases when the frequency of the coupons decreases, that is when the coupons are disbursed at a greater distance.

The duration is directly proportional to the risk: the higher this is, the more the security must be considered as risky.

In fact, this index can also be understood as proven proof that very long-term securities, even when issued by states that we can consider reliable, are on average riskier unless of course, they have such high returns as to make us return the capital invested in a short time and definitely before the title expires.

Duration is one of the most reliable indices to value a bond

The duration is a very reliable index to assess the quality of a bond, although it is worth mentioning that it cannot consider other variables, such as the possibility that those who have to pay coupons and repay the principal is no longer able to do it.

It is therefore certainly an interesting method, which we will necessarily have to apply before evaluating the purchase of a bond, but once again not the only study we must do before investing money.

That said, if you really want to invest in bonds, I suggest you read my guide dedicated to the best bonds to buy: I always update the information on My Business.