Volatility Smile

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