Effective Duration
Categories: Bonds
When you buy a bond, it will have a duration. Bonds are like loans, and the duration represents the amount of time it takes to pay the money back.
So you might purchase a bond with a 5% interest rate and a duration of five years. That means you'll get a 5% return per year for each of the next five years. At the end of five years, the money is paid back and the bond expires.
Some bonds have a clause that lets them get retired early. It's like a parachute for the bond issuer. If they don't need the money anymore, or think they can get a better deal somewhere else, they can "call" the bond, basically buying it back at a set price.
Effective duration measures how this option impacts the price for callable bonds.
You buy a bond with a 10-year duration. But if it's callable after three years, you might not get to hold it for the full decade.
That circumstance is bad for you, because it means you won't get those sweet interest payments for as long. If you've got your 10-year bond and it gets called after four years, that's six years of interest you missed out on.
Because of these factors, the price of the callable bond is heavily impacted by movements in interest rates. If prevailing rates are sitting at 7% and you have a bond paying out at 5%, it's not going to get called. The company has a pretty good deal. If it were to call the bond and issue a new set, instead of paying 5%, it would have to pay 7%. Calling would be a mistake.
But say interest rates plunge to 4%. It might be worth it to call in the 5% bonds and issue a new set paying out 4%. The company would save money with the lower interest rate. It just becomes a question of whether it would be worth the effort.
Effective duration is a mathematical equation that takes all this into account, using the callable bond interest rate and current prevailing rates to describe the impact on the bond's price.
Related or Semi-related Video
Finance: How does duration affect bonds ...2 Views
And finance Allah Shmoop How does duration affect bonds Okay
people It's a tale of two bond babies They're both
incubating in this well giant bond Womb Meet Harry Harry
the homunculus He's a bond He's almost ready to come
out and say hey to the world He'll turn right
into cash when he you know exits He carries in
his heart a short term bond with life We know
a ton about him We could see his excellent facial
features here in his strong arms here and his you
know excellent job They're incubating Harry Well Harry is a
short term bond We have only a very short period
of time until he matures and then is on his
own at least not directly You know swimming in our
bond Cool little ambiguity with tons of doctors looking in
on him Little risk that his AIPO are rather retirement
from incubating doesn't go well Short term bond Short duration
until maturity Not very volatile because well we can see
so much already and have clarity that he's healthy Like
the payments supporting him are right there We can identify
him No risk no worries Bond pays off And everyone
moves on Now Meet Justin fertilized a tiny dot ages
until he's born or matures We have no idea what
he'll look like how he'll perform in the incubation process
whether the womb will continue to be a healthy pool
to swim in or well frankly whether or not he'll
even make it Justin is a long term bond or
a bond with long duration like when a given company
sells one hundred million dollars worth of their bonds promising
to pay five percent a year in interest and then
pay back the principal in thirty years That's a long
bond Thirty years from now is eternity For a lot
of companies we'll think about what the world looked like
thirty years ago Yahoo was just coming into prominence Is
one of the largest companies in the world Well guess
what it died Nokia not Apple was the largest market
cap company in the world or most highly valued company
in the world It died Facebook and Google really weren't
even formed so long Duration bonds have extreme sensitivity to
very small inputs Early in there Jess Station Disney has
a hundred year bond Siri's that are about two decades
into their maturity Is there no risk that Disney will
be gone in eighty years Like Well could ABC Television
no longer exist because producers just stream their own TV
shows on the Web and they don't need a network
Is it possible ESPN is gone Because the NFL and
others just want to go direct to customers They don't
need ESPN anymore Could roaming gangs have taken over Disneyland
and Disney World and the other Disney thing He's making
it you know not the happiest place on Earth You
know like the Pirates of the Caribbean weren't menacing enough
So it's not like one in a million shot that
Disney joins Yahoo in Nokia in the next eighty years
When bonds have long durations tons of exogenous risk I
risk you can't imagine fathom believe or accept comes into
play And one other big element hits long duration bonds
Very hard That is prevailing interest rates like let's imagine
that when Justin was you know planted the world's economies
were fragile needing a boost from low interest rates Teo
Turbo charge things and help get the world's economies going
again So at that time for say a rated you
know best quality bond paper Well rates were four percent
But then a dozen years later inflation in a globally
heated mesh of economies started to be a real thing
and central banks around the world began raising rates So
twelve years later that prevailing rate was seven percent instead
of four And Justin was yielding just four Like his
yield doesn't change year after year or rather his coupon
or that four percent he's paying doesn't change Year after
year the price of the bond might go down and
it does so now for eighteen freaking more years until
that thirty year maturity bond of just and matures and
then pays cash well Justin will be paying three percent
per year less than his brethren who are being seven
percent essentially costing his parental investors in him One point
Oh three to the eighteenth power there That's how we
do the bond math on how much that cost them
Or set another way Investors in a seven percent yield
ER versus the four percent or in Justin would get
almost seventy percent more money by the time Justin pops
out of the oven then sticking with Justin So think
about this in extreme short case situations like let's say
you have Harry and Justin both yielding four percent Harry
is doing a year Justin is due in thirty years
If tomorrow rates suddenly jumped to seven percent overnight well
then Harry loses one year's worth of opportunity Cost meaning
Harry only yields four percent instead of the prevailing seven
percent right Yeah he could have been a seven percent
or he could have been somebody instead of a bum
So Harry loses three percent for one year Not great
but not a disaster either So if that rate hike
suddenly happened well what would Harry likely trade at one
year before his cash conversion in principle payoff Well if
Harry was a thousand dollar bond and he'd pay forty
bucks over that year the four percent there But the
new rates were paying seventy bucks over that year Wealth
Then you'd ask How does Harry's forty dollars in interest
payments and just so that they now pay seventy dollars
or set another way and ignoring some time value of
money things here for simplicity If Harry dropped in price
to nine hundred seventy dollars well then in the course
of a year He'd appreciate thirty bucks for the principal
while still paying the forty and interest And he deliver
seventy bucks in total return like thirty and appreciation in
forty and interest to his parental investors and match the
seven percent prevailing rates Okay so that's Harry in one
year What happens to just think about it He's got
only four percent a year yield That's got to adjust
to the new world reality of seven percent a year
RO rates that kind of class of a bond Well
his thousand dollars par value That market price drops a
lot In fact it dropped by one point Oh three
to the eighteenth power Or rather that becomes the denominator
in the new calculation So the thousand dollar bond value
drops to a thousand invited by one point seven ish
or about five hundred eighty five dollars and then slowly
slowly slowly over eighteen years It then crawls back tto
par assuming the parent company that issued Justin Will survives
the entire time And then finally mercifully eighteen years later
the emerges at par as a Philadelphia On paying off
in cash he goes out into the rial adult bond
world and it does you no adult bond things But
hopefully he makes good decisions and doesn't get too heavily 00:06:37.933 --> [endTime] into you know bondage Oh my