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Friday, March 27, 2009

bond duration - learning notes

I like the official definition in http://en.wikipedia.org/wiki/Bond_duration#Definition. Each payout has a payout-date and therefore a 'distance' from valuation-date. (Example: 47 months from now). Weighted average of all these "distances" is the Mac Duration.

* eg: zeros aka STRIPS -- one payout-date only. If distance is 4.5 years then Mac Duration is the same. Zeros have the longest duration[1]
* eg: low coupon bond maturing in 4.5 years -- Weighted average means Mac duration is dominated by the principal repayment's distance of 4.5 years. Duration is slightly shorter than that that last distance.
* eg: high coupon bond with that same maturity of 4.5. Duration is much shorter than the last distance.

[1] among bonds of the same maturity date.

"distance" is a more visual word than the "time-to-maturity" or "term-to-maturity" technical jargon. I also like the TTL or time-to-live phrase.

Now, if we receive \$50 coupons five times and then \$1000, we get total \$1250 [2]. Q: what's a reasonable "average-payout-date" of this \$1250? Answer is the Duration.

[2] actual formula uses present value of each payout.

Now let's see why the zero is most volatile, i.e. "this bond's current price swings wildly with interest rate"

Key assumption: yield is roughly correlated to benchmark interest rates (such as the overnight FedFund rate), an indication of market sentiment.

For a high-yielder, larger portions (half?) of the total PresentValue come early and suffer minimal discount (discount factor close to 100%) . Remember DF and yield are subject to semi-annual compound. STRIPS have no early payouts, so the final payout must be discounted deeply due to compounding. Impact of yield change is deep.

Remember yield of 7% is always semi-annually compounded to derive DiscountFactor. See posts on DF and yield.