Arbitrage-Free Valuation Approach

[paul_ledin]

Ok so I understand the method, but I’m not sure that I’m buying the assumption or rather its logical conclusion. If a zero coupon bond is by definition more valuable than an otherwise identical coupon bond shouldn’t coupon bonds be entirely replaced by synthetic strips since an arbitrage opportunity exists? Or is it just that it’s at one of the limits to arbitrage?

 

[JoeyDVivre]

“If a zero coupon bond is by definition more valuable than an otherwise identical coupon bond ”
I dunno about by definition, however, I will absolutely trade you one zero coupon bond for an otherwise identical coupon bond anyday. You can even choose the coupon.

 

[paul_ledin]

Alright so by definition is a little too strong a phrase, but that’s what I’m saying. If there’s such a bias towards avoiding reinvestment risk with a coupon paying bond than one would think that somebody would be happy to make a spread by stripping coupon bonds. And if the bias is as strong as you suggest then why would anyone buy a coupon bond except for the purpose of stripping it.

 

[bchad]

Zeros don’t always exist at all maturities; there’s much more variety in coupon bonds…
Stripping does involve transaction costs which may be a limit to arbitrage. I’d have to see some numbers to know whether that’s a real limit or not.
Zero coupon bonds have no reinvestment risk, but you can also be paid for taking on reinvestment risk through a spread. If you think that interest rates will rise and the duration is low, you can actually benefit from being exposed to reinvestment risk. Maybe you want to have it.
If you have default risk, you can reduce some of your default risk by having some cash flows (coupons) up front earlier. (this is why a lot of people want to have a bond paying coupons… it forces the company to ensure continuously that there are enough cash flows to cover interest)
If you have income needs, it may be easier to construct them with a sequence of reliable coupons than have to hunt for zeros that mature at just the right time.

 

[JoeyDVivre]

My point was that if I have a zero maturing in 2015 and a coupon bond maturing in 2015, the coupon bond is worth more (ceteris paribus) because the coupon bond is just the zero + a bunch of coupons. We like the coupon bond more.
To add to bchadwick’s post - remember that zeros are tax disadvantaged because you have to pay taxes on accrued discounts and you don’t have any cash from the bond to do it.