Reinvestment Risk (Coupon) vs. Interest Rate Risk (Zero-Coupon)

[hsuwang]

Hello David,
I really liked your illustration of reinvestment risk versus interest rate risk in the video tutorial. \

For further clarification, zero-coupon bonds have duration equals to its time to maturity, if I bought a 10 year zero-coupon bond at a 10-year spot rate of say 10%, I'll pay $385.6 today to receive $1000 in 10 years, so can you please explain what interest rate risk refers to in this context? Does interest rate risk equals the risk that the 10 year spot rate would either increase or decrease in the future? If this is the case, how would this affect the value of my bond that will pay $1000 regardless of the fluctuation in the interest rates? (or is interest rate risk referring to the difference between the price I paid ($385.6), and the future price of the same bond in the future (that may or may not be cheaper than $385.6 depending on the future spot rates?)

I think this is simple but I can't get my thoughts through for some reason.. Thanks!

 

[David Harper CFA FRM]

Hi Jack,

Thanks, really appreciate that...there are some interesting sub-issues here but Tuckman's point (which i merely parrot) is: let's say you purchase your 10-year zero today. The Macaualy duration (the duration that uses time as units, being a weighted average *time* to receipt of cash flows, where here only one cash flow is received in ten years) is 10. The modified duration (the % sensitivy measure) is less, but it's another topic...

The high "interest rate risk" is reflected in the 10 which tells you (if we temporarily round off the difference between the Mod and Mac duration, maybe the Mod duratoin is 9.5, so ignore the difference): if the rate goes up by 1%, the price of your bond goes down by almost 10%. So we can use duration as a proxy for interest rate risk, hardly the only measure, just the most popular single-factor risk. In fact, for FRM purposes, this is exactly how i would define interest rate risk: the single-factor Macaulay/modified duration.

We can say it less technically: if you buy a zero, you get a single cash flow far into the future, such that the present value of your zero is highly dependent on the discount rate (interest rate).

Compared to me, say, let's say i buy a high-coupon bond: my bond has coupons that arrive sooner. Lower duration, some cash flows that are (in relative terms) less senstive to the discount rate (interest rate). And, if you focus on the comparison between our choices (this gets to another Tuckman point), we can invest the same amount of money today, both facing the same term structure of spot rates. Now go foward six months: I "pull a coupon" out of my investment. Am I doing better or worse than you? We don't know today, all we know today is that you have more interest rate risk and i have more reinvestment risk. In six months, if rates are lower, I am worse b/c i need to reinvest the coupon at a lower rate. You avoided that reinvestment risk but you are loaded up on interest rate risk (high duration). For any given voliatility of interest rate changes, your bond price will fluctuate more than mine as it has higher duration. I sweat the coupon reinvestment but you have more of a valuation roller coaster ride. Hope that helps...

David