I have read a definition about credit spread that credit spread should be considered as the difference between yield to maturity on a zero coupon (and not coupon paying) corporate bond (corporate spot rate) and the yield to maturity on a zero coupon government bond (government spot rate) of the same maturity .the justification behind using zero coupon bonds and not coupon paying bonds to calculate spread is that arbitrage arguments hold with spot rates, not with yield to maturity. Since a riskless coupon- paying bond can always be expressed as a portfolio of zeros, spot rates are the rates that must be used to discount cash flows on riskless coupon-paying debt to prevent arbitrage. The same is not true for yield to maturity.I wasn't able to understand this argument. Can anyone explain it to me?Thx

It's not that arbitrage arguments don't apply to yield to maturity, it's that you can't use arbitrage arguments with instruments with different promised cash flows. Two zero coupon bonds delivered on the same date have the same promised cash flows. Two bonds with different coupons but the same maturity have different promised cash flows.Take a simple example. If a riskless one year zero sells at a log yield of 2% and a risky one year zero sells at a log yield of 1.99%, you have an arbitrage. Buy $1,000,000 of the riskless bond for $980,199 and short $1,000,000 of the risky bond for $980,297. You pocket $98 today and might make $1,000,000 in one year if the risky bond defaults.Now suppose the riskless bond is actually a 2.0075% coupon, semi-annual pay bond selling at par (the coupon rate has to be slightly higher than 2% because that is the log yield, but the interest in paid semi-annually instead of continuously). Now the yield to maturity of the one-year riskless (coupon) bond is higher than the yield of the one year (zero) risky bond, but there is no arbitrage. If I buy $1,010,037.5 par of the risky bond for $990,136, I match the one-year payment I must make if I short $1,000,000 par of the riskless bond. That puts $9,864 in my pocket today, out of which I must fund a $10,037.5 payment in six months. Not only can't I guarantee that will happen, it requires investing at 3.5% for six months, when the implied six month riskless interest rate is only 1.5%. So I will almost certainly lose money on this position unless the risky bond defaults.