 # Average life of MBS

People,

This is in reference to CFAI pg 343, Fixed Income. Says

Avg life = sigma(1to t) of t x proj principal received at t/ (12 x Tot principal)

So lets assume you plan on paying 1/12 every month, so proj principal/Tot equals 1/12. So then the formula is

Avg life = 1/ (12 x 12) sigma(1 to t) t

which becomes

Avg life = 1/(12 x 12) x t(t+1)/2

If you are paying 1/12the every month, t=12, so avg life is 0.54 yrs.

How do I make sense of the fact that 12 equal principal payments equals an avg life of 0.54?

Thanks,

P

Average life is use to estimate Duration.

if you pay 1/12 per month, it will take you 1 year to pay it back. average life of 0.54 make sens since duration it always under you term.

so you have about 0.54 sensitivity for a 1 year bond for a 1% shift in yield… let’s try it

pmt = 1/12

i = 5/12%

n = 12

PV = 0.97344

Now let’s shift it 1%

pmt = 1/12

i = 6/12%

n = 12

PV = 0.96824

you have 0.96824/0.97344 -1 = 0.534%

that is pretty damn close to a 0.54 duration.

Wow, nice insight ss182.

Thanks.