What duration formulas do we need to know?

[Jones473]

It seems to me we only need to know effective duration. Is modified duration and Macaulay duration not a part of Level II curriculum?

[S2000magician]

The formula for modified duration is the same as the formula for effective duration; the difference is that modified duration assumes that the cash flows don’t change when the yield changes, while effective duration allows that the cash flows might change when the yield changes.

I haven’t seen Macaulay duration at Level II.

Alas.

[krokodilizm]

I hope to fully understand duration by the end of Level 3… That thing is a mystery to me.

[Flashback]

What is less easy to understand, it is more marketable (example - CDO).

[Jones473]

@S2000magician

The formula for modified duration is the same as the formula for effective duration; the difference is that modified duration assumes that the cash flows don’t change when the yield changes, while effective duration allows that the cash flows might change when the yield changes.

I haven’t seen Macaulay duration at Level II.

Alas.

Thanks. But how can the formula be the same, but only one allow for cash flow changes?

[S2000magician]

The formula is:

Dur = (P− − P+) / (2P0Δ_y_)

For modified duration, the values P− and P+ are computed assuming that the cash flows stay the same.

For effective duration, the values P− and P+ are computed allowing that the cash flows may change (e.g., that the bond may be called or put).

So the values for P− and P+ may be different for modified duration and effective duration, but the formula that uses those values is the same either way.

[jonta999]

@S2000magician

The formula is:

Dur = (P− − P+) / (2P0Δ_y_)

For modified duration, the values P− and P+ are computed assuming that the cash flows stay the same.

For effective duration, the values P− and P+ are computed allowing that the cash flows may change (e.g., that the bond may be called or put).

So the values for P− and P+ may be different for modified duration and effective duration, but the formula that uses those values is the same either way.

May I know whether there are different formulas to calculate convexity Tx

[S2000magician]

The formula for modified convexity is the same as the formula for effective convexity.

The difference is . . . you guessed it! . . . whether the cash flows are allowed to change. Modified convexity assumes no change in cash flows when the yield changes; effective convexity allows that they might change.

[jonta999]

Ok Thank you

Is this the formula for convexity ?

(P− + P+ -2P0 ) / (2 P0 Δ_y^2_)

[S2000magician]

@jonta999

Ok Thank you

Is this the formula for convexity?

(P− + P+ -2P0 ) / (2 P0 Δ_y^2_)

These days, they don’t put the “2” in the denominator; instead, they put a “½” in the formula to use convexity.

It’s a recent change.

I wrote an article on convexity that covers this: http://financialexamhelp123.com/convexity/

[jonta999]

Ok thank you

[S2000magician]

My pleasure.

[Jones473]

@S2000magician

The formula is:

Dur = (P− − P+) / (2P0Δ_y_)

For modified duration, the values P− and P+ are computed assuming that the cash flows stay the same.

For effective duration, the values P− and P+ are computed allowing that the cash flows may change (e.g., that the bond may be called or put).

So the values for P− and P+ may be different for modified duration and effective duration, but the formula that uses those values is the same either way.

Ok I thought it modified duration could also be calculated as Macaulay duration / [1+(YTM/n)] but that is perhaps the same?

[S2000magician]

@Jones473

@S2000magician

The formula is:

Dur = (P− − P+) / (2P0Δ_y_)

For modified duration, the values P− and P+ are computed assuming that the cash flows stay the same.

For effective duration, the values P− and P+ are computed allowing that the cash flows may change (e.g., that the bond may be called or put).

So the values for P− and P+ may be different for modified duration and effective duration, but the formula that uses those values is the same either way.

Ok I thought it modified duration could also be calculated as Macaulay duration / [1+(YTM/n)] but that is perhaps the same?

It’s exactly the same.

I wrote a article on duration that may be of some help here: http://financialexamhelp123.com/macaulay-duration-modified-duration-and-effective-duration/