 # Vol risk, MBS

On reading 31 page 172 CFAI states “because OAS compensates the investor for selling the prepayment option to the homeowner, OAS tends to widen when expected vol increases and narrow when expected vol decrease”. Can somebody explain? I thought it would be the opposite since OAS=Z-spread - Opt Cost. Also, what happens to duration of MBS when interest rates rise? It decreases? In other words, does an MBS exhibit positive or negative convexity when rates rise? Thanks

When vol rises , it is more likely that prepayments also rise ( because the level that will induce prepayment is more likely to be hit). So spreads widen. The equation you wrote down implies a steady state ( vol is steady ) , but the prepayment model results would change at increased volatility. MBS displays +ve convexity at increased interest rates.

A mortgage security exhibits both positive and negative convexity negative convexity when yields fall positive convesity when yields rise look at the graph on page 164 in volume 4

Thanks guys, I get the positive/negative convexity. I get that when vol rises,the value of the prepmt option rises, but I don’t get why spread widens from that point. Can you show me mathematically (formula please?).

It is not complicated . The spread is what the investor expects to earn before committing to purchase a security . So he EXPECTS to earn a larger spread when vol rises and the option of prepayment looks attractive to a borrower. Don’t confuse a forward anticipation or EXPECTATION from a realization of profit or loss , after the security is purchased. For example : If the prepayment option is priced in on the expectation that vol will be large , the borrower gets less because the option is attractive to him.Subsequently if vol is not large or rates actually rise versus expectation , then the option becomes less attractive to the borrower who is now tied in into a loan. The investor is now happier because the security is now more valuable. If the reverse happens and the investor sees vol even larger or rates declining more than anticipated then the investor is unhappy and the borrower is happier. This is the realized part ( p&l)

OK, but looking at this equation OAS= Zspread - Option Cost, if vol increases, option cost increases and OAS narrows. This is true for callable bonds which exhibit negative convexity just like MBS when rates decrease. So why is that for callable bonds, OAS narrow and for MBS widens when int rate vol increases? Sorry for the questions but I need to get this concept, so thanks in advance,

this was already discussed in other threads. I also googled something regarding this, and the logic is that due to increased uncertainty of future rates (higher volatility) the spreads go up. My understanding is that the option value would be more sensitive to vol. change than the sensitivity of OAS, but did not research this further. so, higher vol will cause that investors will require higher option price (that they sell) and higher OAS as well. Nominal spread will go up due to both components

OAS= Zspread - Option Cost This is not an explanation…only a way to think it through. When interest rate volatility increases, Option cost icreases, but Z-spread might increase even faster. Consider an option-free bond, the z-spread will increase when the interest rate is more volatile…(kind of strange to me since z-spread is static spread – but z-spread is actually affected by the interest rate volatility.:D). Although it might be hard to prove why OAS widen when the vol increases, we can still find some factors which can contribute to the widened spread. OAS is the spread over the benchmark yield minus the embedded option cost…Yes, the option cost is more sensitive to the vol, but OAS also reflects other risks(such as credit risk, liquidity risk, model risk), which could be less significant in the options.

Yes it was discussed before but was still not very clear. So int rates vol increases, value of prepmt option increases, value of MBS decreases and OAS spread widens. Correct? What about for callable bonds. Is it the same thing?

IMHO, this is an exception when the partial derivative doesn’t apply.

I think the CFAI curriculum is a bit contradictory or not very clear on this argument

“z-spread is actually affected by the interest rate volatility” - to avoid confusion, it shall be: z-spread tends to widen when the interest rate volatility increases.

I think that my confusion rest in the formula of OAS=Zspread - Option Cost. The equation states that if int rate vol rises, option cost rises and OAS narrows. But that assumes no volatiulity in int rates (as Zspread is a static spread). In reality, OAS widens because the increase in spread over treasuries is greater than the increase in option cost.

That’s not what the CFAI text says. It does not say the spread over treasuries widens due to higher volatility.

The widening of OAS is perhaps more based on empirical results than based on the theories. z-spread is a zero-volatility spread, and it assume zero volatilty to calculate it. But I do have a question: Will the z-spread change when the [expected] interest rate volatility change?

janakisri Wrote: ------------------------------------------------------- > That’s not what the CFAI text says. It does not > say the spread over treasuries widens due to > higher volatility. Then the OAS should narrow, like I was saying, because the z-spread (no volatility spread) is reduced by higher option cost. If OAS widens, it MUST be because spread over treasuries is increases more than option cost.

deriv108 Wrote: ------------------------------------------------------- > The widening of OAS is perhaps more based on > empirical results than based on the theories. > > z-spread is a zero-volatility spread, and it > assume zero volatilty to calculate it. But I do > have a question: > > Will the z-spread change when the interest rate > volatility change? Z spread is based on a single expected flow of coupon payments, as vol changed, the investor’s expectation of this stream of coupons will change, hence the z spread can change.

mik82, don’t confuse us. “Then the OAS should narrow, like I was saying, because the z-spread (no volatility spread) is reduced by higher option cost.” – The z-spread widens in this case.

Sorry that wasn’t my intention. But I am confused because I think that CFAI curriculum is not clear on this matter. Level 3, for MBS OAS, widens when int rate vol increases Level 2, for Callable bonds, OAS narrows when int rate vol increases But MBS and callable bonds have the same characteristics (convexity), so why OAS reacts differently? When is OAS=Zspread-option cost formula used?