# 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
* 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.

 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 . Q: what’s a reasonable “average-payout-date” of this \$1250? Answer is the Duration.

 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.