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Lokicious wrote:
What I want is the measure for a bond fund that best approximates the actual holding period for a CD, T-bill, or other individual bond, so we can compare how much money we will have at the end of that period, under different circumstances. Duration, not average weighted maturity, seems to be the bond fund measure that best fits the bill. Another way of looking at it is duration is how long it takes to flush the average current bond holdings from the fund, which is analogous to your CD coming due.

I'm sorry, but the bolded text above has nothing to do with 'duration'.

'Duration' is an entirely artificial number whose only purpose is to give you a measure of the sensitivity of a bond (or bond fund) to interest rates. The fact that the number is expressed in years is only because the interest rate you are examining is an annual rate. There is no other significance of the years.

Duration is a weighted average of the times that interest payments and the final return of principal are received. The weights are the amounts of the payments discounted by the yield-to-maturity of the bond. The final sentence may be alternatively stated:
The weights are the present values of the payments, using the bond's yield-to-maturity as the discount rate.

To calculate the duration of a bond, you need to know its coupon, yield to maturity (YTM), and maturity. Here is an example:

Let's assume you own a single $10000 bond with 8% coupon that matures in 5 years and the YTM is 7%. How would you determine its duration?

The bond thus pays $800 a year from now, $800 in 2 years, $800 in 3 years, $800 in 4 years, $800 in 5 years and the $10,000 return of principal also in 5 years.

Now, to compute the weighted average of a set of numbers, you multiply the numbers (years) by the weights and add those products up. Then you divide that total by the sum of the weights.

In this case the weights are the present values $800/1.07^1, $800/1.07^2, $800/1.07^3, $800/1.07^4, $800/1.07^5, and $10,000/1.07^5, or $747.66, $698.75, $653.04, $610.32, $570.39, $7,129.86. The numbers being averaged are the times the payments are received, or 1 year, 2 years, 3 years, 4 years, 5 years, 5 years.

Thus, the numerator is: 1*$747.66 + 2*$698.75 + 3*$653.04 + 4*$610.32 + 5*$570.39 + 5*$7,129.86. This adds to $45,046.80

And the denominator is just the sum of the present values: $747.66 + $698.75 + $653.04 + $610.32 + $570.39 + $7,129.86. This total is $10,410.02

Now dividing those two 45046.80/1041.02 gives us a duration of 4.33 years.

This means that this bond has a duration of 4.33 years, which indicates that if we had a rise in interest rates of 1%, this bond would decrease in value by 4.33%. And, that is all that the duration tells us!

Some bonds actually have negative durations! Typically, a bond's duration will be positive. However, instruments such as IO mortgage backed securities have negative durations. You can also achieve a negative duration by shorting fixed income instruments or paying fixed for floating on an interest rate swap. Inverse floaters tend to have large positive durations. Their values change significantly for small changes in rates. Highly leveraged fixed-income portfolios tend to have very large (positive or negative) durations.

The duration and maturity are the same is with zero coupon bonds.

So, as you can see, you can't use the duration for anything other than as a means to determine a bond's sensitivity to interest rate changes. For anything related to time until a bond matures, you must use average maturity.

Russ
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