Thanks S2000. So it’s simply time value of money. PV of coupons towards the end and principal makes up lower % of the PV as YTM increases.
Is there no reinvestment effect here? Since the YTM is only earned if coupons are reinvested at the same rate, I thought there’d be a connection between reinvestment rate and duration…
There are two views on IRR. One is that it’s a return on all of the money invested for the entirety of the investment term, and that’s the view that requires that the cash outflows be reinvested at the IRR. The other is that it’s a return only on the money that remains invested, and that cash outflows are no longer invested, so the reinvestment rate doesn’t matter. Because IRR (and YTM, which is nothing more nor less than an IRR) is a discount rate that equates the future cash flows to the present value, the second view makes more sense.
Thank you. I’ve always had this question. Could you please help me understand the “risk” other than credit risk in the second case, when no other market elements are considered as part of the duration metric here?
HIs conclusions would, but his reasons (“because . . . .”) would not.
Macaulay duration looks only at the cash flows from the bond – the coupon payments and the principal payment – not at the reinvestment of those cash flows.
It’s not so much a difference in risks between the two cases, per se, as a difference in viewpoint.
If you adopt the viewpoint that the YTM is a discount rate equating the (known) cash flows to today’s price, then there is no reinvestment risk _ in this investment _. The risk is in the _ next _ investment that you make with the cash flows that you receive.
If you adopt the viewpoint that the YTM measures the holding period return and that all proceeds will be removed only at the end, then the reinvestment risk is part of this investment.
So the reinvestment risk is the same, it’s simply a matter of which investment bears that risk: this one, or the next one.