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if interest rates are lower than coupon rate, then you would be expecting the bondholder to call and refinance. I.e. the call is very valuable to the bond issuer.

if interest rates rise then the value of the call will drop. so the issuer loses and the holder gains.

if interest rates are lower than coupon rate, then you would be expecting the bondholder to call and refinance. I.e. the call is very valuable to the bond issuer.

if interest rates rise then the value of the call will drop. so the issuer loses and the holder gains.

If we break down a MBS, its position is basically the combination of two things:

An option free bond that pays interest like an annuity, spread evenly over the life of the security

A short call option (Remember, if volatility up, the option value goes up, and the MBS Price goes down)

The option is what gives an MBS negative convexity. What that downward slope shows is that as interest rates decrease people “exercise” their prepayment option and refinance their mortgages at lower rates..

As a holder of an MBS, this prepayment of mortgages means that you are now receiving cash flows earlier. Furthermore, you have high reinvestment risk because interest rates are suddenly lower just as you have cash on hand. When the option is out of the money the MBS will have positive convexity. The level of convexity, or the rate at which prepayments will occur, depends on the current level of interest rates relative to the coupon on the MBS.

To summarize:

If rates are high: Prepayments decrease, Duration increases, and MBS Price decreases lessthan a non-callable bond

If Rates are low: Prepayment increases (the option is in the money), duration decreases, and the MBS Price increases less thana non-callable bond

If we break down a MBS, its position is basically the combination of two things:

An option free bond that pays interest like an annuity, spread evenly over the life of the security

A short call option (Remember, if volatility up, the option value goes up, and the MBS Price goes down)

The option is what gives an MBS negative convexity. What that downward slope shows is that as interest rates decrease people “exercise” their prepayment option and refinance their mortgages at lower rates..

As a holder of an MBS, this prepayment of mortgages means that you are now receiving cash flows earlier. Furthermore, you have high reinvestment risk because interest rates are suddenly lower just as you have cash on hand. When the option is out of the money the MBS will have positive convexity. The level of convexity, or the rate at which prepayments will occur, depends on the current level of interest rates relative to the coupon on the MBS.

To summarize:

If rates are high: Prepayments decrease, Duration increases, and MBS Price decreases lessthan a non-callable bond

If Rates are low: Prepayment increases (the option is in the money), duration decreases, and the MBS Price increases less thana non-callable bond

When interest rate is in the historical low below coupon rate, and expected to rise, why callable bond will outperform the non-callable bond?

Because the callable bond has a lower effective duration than the non-callable bond.

Sorry to check, other than the lower effective duration of the callable bond, does the negative convexity comes into picture which explains the smaller decrease in price as interest rate increase ?

When interest rate is in the historical low below coupon rate, and expected to rise, why callable bond will outperform the non-callable bond?

Because the callable bond has a lower effective duration than the non-callable bond.

Sorry to check, other than the lower effective duration of the callable bond, does the negative convexity comes into picture which explains the smaller decrease in price as interest rate increase?

No.

If two bonds have the same effective duration, then the one with the lower convexity will underperform the one with the higher convexity. Here, the MBS has a lower effective duration, which explains its outperformance; its negative convexity, in fact, works against that.

Simplify the complicated side; don't complify the simplicated side.

If rates are high: Prepayments decrease, Duration increasesdecreases, and MBS Price decreases lessthanabout the same amount as a non-callable bond

This isn’t true.

When rates are high, (effective) duration is low, and gets lower as the YTM increases. Furthermore, an MBS has much the same effective duration as a straight bond when rates are high. (To be fair, its effective (or modified, or, for that matter, Macaulay) duration will be slightly lower than that of a similar noncallable bullet bond because it pays monthly rather than semiannually and because it is an amortizing bond rather than a bullet bond, but those differences are slight.)

When rates are low, (effective) duration is low, and gets higher (to a point) as the YTM increases.

Simplify the complicated side; don't complify the simplicated side.

When interest rate is in the historical low below coupon rate, and expected to rise, why callable bond will outperform the non-callable bond?

Because the callable bond has a lower effective duration than the non-callable bond.

When rates decrease, a callable bond’s price increases less than a non-callable bond’s price. This makes sense to me. But why does a rate increase cause less of a drop in callable bond’s pice than in a non-callable bond’s price?

If you're the first out the door, that's not called panicking

if interest rates are lower than coupon rate, then you would be expecting the bondholder to call and refinance. I.e. the call is very valuable to the bond issuer.

if interest rates rise then the value of the call will drop. so the issuer loses and the holder gains.

(seems like a L2 question?)

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It shows up in the Scheweser Practice Problems.

Thank you！

Because the callable bond has a lower effective duration than the non-callable bond.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

http://financialexamhelp123.com/

If we break down a MBS, its position is basically the combination of two things:

The option is what gives an MBS negative convexity. What that downward slope shows is that as interest rates decrease people “exercise” their prepayment option and refinance their mortgages at lower rates..

As a holder of an MBS, this prepayment of mortgages means that you are now receiving cash flows earlier. Furthermore, you have high reinvestment risk because interest rates are suddenly lower just as you have cash on hand. When the option is out of the money the MBS will have positive convexity. The level of convexity, or the rate at which prepayments will occur, depends on the current level of interest rates

relative tothe coupon on the MBS.To summarize:

If rates are high:Prepayments decrease, Duration increases, and MBS Pricethan a non-callable bonddecreases lessIf Rates are low: Prepayment increases (the option is in the money), duration decreases, and the MBS Pricea non-callable bondincreases less thanStudying With

Thanks a lot!

Sorry to check, other than the lower effective duration of the callable bond, does the negative convexity comes into picture which explains the smaller decrease in price as interest rate increase ?

No.

If two bonds have the same effective duration, then the one with the lower convexity will

the one with the higher convexity. Here, the MBS has a lower effective duration, which explains its outperformance; its negative convexity, in fact, works against that.underperformSimplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

http://financialexamhelp123.com/

This isn’t true.

When rates are high, (effective) duration is low, and gets lower as the YTM increases. Furthermore, an MBS has much the same effective duration as a straight bond when rates are high. (To be fair, its effective (or modified, or, for that matter, Macaulay) duration will be slightly lower than that of a similar noncallable bullet bond because it pays monthly rather than semiannually and because it is an amortizing bond rather than a bullet bond, but those differences are slight.)

When rates are low, (effective) duration is low, and gets higher (to a point) as the YTM increases.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

http://financialexamhelp123.com/

When rates decrease, a callable bond’s price increases less than a non-callable bond’s price. This makes sense to me. But why does a rate increase cause less of a drop in callable bond’s pice than in a non-callable bond’s price?

If you're the first out the door, that's not called panicking

Because the starting price is lower.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

http://financialexamhelp123.com/

thanks once again!

If you're the first out the door, that's not called panicking