# OAS and Valuation

Similar bonds with high OAS are considered undervalued and similar bonds with low OAS are considered overvalued.

Not really understanding the intuition behind that very well they don’t really explain why.

Also, not really grasping the understanding behind why increasing the interest rate volatility will decrease the OAS.

Can anyone explain?

If two bonds are similar in their aspects, they should theoretically have the same OAS. That being said, if one of those 2 similar bonds has a higher OAS than the other, it will be undervalued RELATIVE to the other bond since you are using a higher discount rate (Due to the added OAS) in the PV calculation.

Simple Random Example:

Bond 1: 3 Year bond with 6% coupon and 6% interest rate with an OAS of 2%

Bond 2: 3 Year bond with 6% coupon and 6% interest rate with an OAS of 3%

(Using TVM)

Value of Bond 1: \$94.845

Value of Bond 2: \$92.406

Even though the bonds are identical, Bond 2 is relatively undervalued (In respect to Bond 1) due to the higher OAS.

The opposite applies for a lower relative OAS for similar bonds. You are using a lower discount rate for one bond which will make it seem overvalued relative to the other one.

i’ll simplify this for you…

OAS is an adjustment made for riskier bonds. If a different OAS is applied to 2 identical risky bonds then one is going to be overvalued the other undervalued:

• a lower OAS means you’re discounting less than you should and the value of the bond will be higher (overvalued)

• a higher OAS means you’re discounting more than you should and the value of the bond will be lower (undervalued)

Now as for volatility of interest rates, you need to keep few things in mind:

1. a change in level of interest rate is different than the change in volatility of interest rate (keep this mind)

2. Options thrive with volatility

3. So when interest rate volatility is high --> Value of the call will increase

Vcallable bond = Vstraight bond - Vcall option

==> if value of the call will increase --> this means Value of the callable bond will decrease --> which means you need lower adjustment and as a result lower OAS

i’ll add to make things clearer:

and why options do well with volatility ? because the more the volatility the more likely the option will be exercised and the higher the value of the option.