What the hell is the “Duration”??
The Duration tells you how long, in years, it takes for the coupons to repay the price of a bond. It is the weighted average maturity of a bond’s cash flows or of any series of linked cash flows. The Macauley formula that gives a way to calculate the Duration goes like this:
Why is it important?
It is an important factor to know as it gives you a way to quantify the risk you bear in investing in bonds. Long term bonds have a higher Duration than short term bonds.
We’ll see later how Orange County’s treasurer lost 1.6 billion in 1994 in the bond market, leading the State to file for bankruptcy. You’ll better understand how to use the Duration to monitor your risk exposure
Are Zero-Coupon and Vanilla bonds equal in Duration?
No… The reason is simple: a zero-coupon bond doesn’t pay any coupon. As there is no cash flow over the life of the bond the returns are paid in full at maturity. That means that the Duration of a zero coupon bond equals its maturity.
For a normal bond that pays semi annual coupons (cash flows), its Duration is less that its maturity. These coupons can be discounted, manipulated, calculated…
Let’s see this in action in the following spreadsheet (Duration).
In the workbook “how it works” you have an explanation on how the Duration is calculated (using the “Macauley Duration”).
Please allow some time for the server to respond as it is pretty slow…
How could a Treasurer loose $1.6 Billion??
The recipe is fairly simple: Play the yield curve!
- Take all the money you can from your County: Schools, hospital, public services… (a mere $7.5 billion should be enough),
- Short the short term bond and ad a dash of leverage to your investment (turn $7.5 billion into $20.5 billion. For every dollar you have in your pocket you borrow 1.73 dollar),
- Buy the long term bonds,
- Wait for the Federal Reserve to increase the interest rates 6 times in a row. (Total variation was +3%…)
- Shake this explosive mix and see the results…
- Interest rates were 5% before the increase
The strategy would have worked out if only the rates had not increased…
So how to calculate the potential loss using the Duration?
In this case, Interest Rates were 5% and the Duration of the leveraged portfolio of bonds was 7.4.
A variation of 3% had the following impact on the portfolio value
The formula goes like this:
That is:
Portfolio Value = -7.4 x 7.5 x (0.03 / 1.05)
Portfolio Value = $-1.586 billion
Conclusion:
Thanks to the example in the spreadsheet you now know how to calculate the Duration of a bond. That can be used to compare 2 or more bonds and see their reaction to an interest rate hike.
From the experience of Orange County’s Treasurer we have learned that the Duration is very handy when it comes to calculate the risk exposure and can be a a good proxy to the VAR.
So: do you want to invest in bonds? 
