Bond X is a BBB rated corporate bond with an embedded call option.
Benchmark:Treasury Market
Nominal spread based on Treasury yield curve:165bp Zero-volatility spread based on Treasury spot rate curve: 155bp
OAS based on Treasury spot rate curve:115 bp
OAS indicates that bond is trading at a spread < nominal spread of otherwise comparable option-free bonds i.e. 115 bp< 165 bp. Hence, Bond X is overvalued relative to Treasury market.
How is Bond X overvalued? I can’t understand this. Please help.
There isn’t enough information given to deduce that the bond is overvalued. (Do you mean overpriced, perhaps?)
The OAS tells us that the bondholder is getting 115bp for the risks inherent in this BBB bond, and the Z-spread tells us that the bondholder is getting an extra 40bp for the call option. Without another bond to which to compare it, those numbers don’t in and of themselves sound unreasonable.
Nominal spread is the difference in YTM between the risky bond and a risk-free bond (usually a Treasury) of the same maturity; it is a spread added to one point on the Treasury par curve. Thus, the nominal spread ignores the term structure of interest rates; it uses only one point, not the entire yield curve.
The Z-spread is added to every point on the (zero-volatility) spot curve; it uses the entire yield curve, not just one point.
The OAS is added to every point on the (nonzero-volatility) spot curve; it uses the entire yield curve, not just one point.
The difference between the Z-spread and the OAS is that the Z-spread includes the spread for any embedded options (along with the spread for all other risks associated with the bond), whereas the OAS removes the spread for the embedded options, leaving only the spread for all other risks associated with the bond. The Z-spread minus the OAS is the price of the empedded option(s), measured in bp of return (instead of being measured in price difference).
I’ve been looking for a succinct answer to this very question - it’s a concept I just really struggle with. Thought I’d add my thanks too! Great explanation S2000…
One thing that wasn’t made clear in the readings is from whose perspective these assumptions are made? The investor/bond holder or the bond issuer? Above when you’re saying the Z-Spread minus the OAS equals the price of the embedded option…
It says that as interest rate volatility goes down the value of an embeded call goes down…to me this sounds like its from the perspective of the bond issuer?
In other areas there are formulas stating that the value of a callable bond = value of option free bond - the value of the embedded call option…to me this sounds like its from the perspective of the bond investor?
I’m right in assuming that the value of a call option (for example) is just as valuable to a bond issuer as it is “unvaluable” to the bond holder/investor right? All else constant (volatility, etc.)
If the price of a Bugatti Veyron increases by $100,000, do you ask, “From whose perspective?”? No. The price goes up. Absolutely. No matter whether you’re buying a Veyron or selling one.
Whether you’re better off or worse off because of the price increase depends on who you are: Veyron sellers are better off and buyers are worse off when the price increases, but the price increase doesn’t depend on who’s looking at it.
Same thing with options embedded in bonds. If interest rate volatility increases, the price/value of a call option goes up and the price/value of a put option goes up. From everybody’s perspective. Issuers of callable bonds are better off and buyers of callable bonds are worse off. Issuers of putable bonds are worse off and buyers of putable bonds are better off. But the value of both options increases, no matter who you are.
Before answering that question, i will first explain to you what the question is trying to ask. The second to the last paragraph is telling you to imagine another benchmarek(say) which has a nominal spread which exceeds the OAS of the bond with embedded options. And this benchmark is option free meaning the nominal spread=the z spread= the oas.
With this in mind, if the nominal(or OAS) spread of the benchmark bond exceed that of the option free bond, it mean the option free bond is over valued.
What i think this writer of this question intended to say was z spread and not nominal spread, but however, i understand what his reasoning is. The nominal spread normaly compensates for option risk, liquidity risk and credit risk. for a bond without an option, it will compensate for liquidity and credit risk. An OAS also compensates for liquidity and credit risk.
Unless the benchmark is risk-free – so that nominal spread = Z-spread = OAS = _ 0 _ – it is not true (in general) that nominal spread = Z-spread; that will happen only when the yield curve is flat.