Expected Real Interest Rate

finance a la shmoop what is the inverse relationship between interest rates and

bond values okay people think of Batman hanging [Batman hanging upside down]

upside down not with a date on a Saturday night but you know just as his

normal course of the business so yeah bonds have this same strange inverted

relationship with financial gravity when prevailing interest rates go up like [Bond is sucked up by hoover]

when the Fed makes the cost of renting money more expensive so it can fight

inflation and other bad guys then the principal values of bonds goes down [Bond values decreases]

think about it this way imagine you just paid a thousand dollars for a piece of

paper from the reputable corporation whoop-dee-doo the world's leading

manufacturer of whoopee cushions anyway whoopty-doo promises to pay you sixty [Whoopee cushions on a conveyor belt]

dollars a year for ten years and then pay you back a thousand bucks all right

a year later however the world's economies take off and a new president

commands that we fight inflation hard so that old people living on fixed incomes [President demanding to fight inflation]

don't get evicted from their homes and have to live in SUV's parked by the side

of the road yeah we don't like that and yeah that happens to old people they

can't afford to take the risk of owning stocks in the stock market so they

generally just own safe bonds and end up being subjected to inflation risk that

is when a government paper that they own is safe and pays bond interest of three

percent pre-tax and two percent after taxed with the world inflating at 3% a

year meaning old people then gradually see the buying power of their savings [Stack of cash disappears]

wither away to nothing and well that's why we fight inflation so the Fed the

thing that controls the price of renting money to banks who then rent the money

to borrowers the Fed then raises the price of renting that money hoping to

bring down inflation well that price hike then makes the cost of renting [example of renting money]

money for a corporation way higher that higher price of renting money is

collateral damage from the bonds the government is setting off to fight the [Explosion occurs in the distance]

war on inflation all right so back to whoopty-doo paper now with the federal

fund rate hikes the cost of renting money is more expensive, the company

thought they could get away with paying 6% rent on the money they wanted to

spend on their whoopee stamping Factory but now the cost of renting that money [Whoope cushion with 6% old cost of rent]

is 8% and those 2% difference points are a big deal on a

hundred million bucks two million a year is meaningful to a company with a

volatile product so now think about it from the perspective of all the

people who bought six percent corporate bonds of similar risk and duration as

the ones whoop-dee-doo was gonna sell ie apples to apples in all respects except [Girl holding two whoopee cushions]

the interest rate well almost overnight the rate of return on those bonds looks

anemic at best those old crappy six percent bonds now

need to yield a sexy eight percent to be competitive with the new or current

market environment well who would want to own those old six percent low

yielding bonds which should now yield eight percent answer nobody.. The six

percent paper sells off or sells down as people sell their bonds until that six

percent of yield equals eight percent a year yield more specifically previous [Old and New environment annual yield]

investors had paid a thousand bucks for 60 bucks a year in yield well now that

yield has to be $80 to match the new environment as set by the Fed and the

marketplace so the mathy question here is what price

must the bond be selling at the one which originally sold for $1000 par that

gave 6% yield so that that bond now gives 8 percent yield....

well the price has to go down so that the $60 of yield or something let's call

it cleverly...X equals $80 over a thousand or 8% so that's 60 over x equals .08[Maths formula for new bond price]

or 60 equals 0.08X or by dividing both sides by 0.08 you get 750

yeah which is the new price of the bond after the feds rate hike cost corporate

bond rates to go from 6% to 8% got it we following here people the yield on that [Man discussing bond rates]

old thousand-dollar par bond which was 6% when it was issued is now 8% because

the market price of a thousand bucks a unit that investors were paying for that

bond has fallen such that the bond at 750 a unit paying 60 bucks a year now

yields 8% so it should make sense that bond values would fall something

equivalent to that number it's like a teeter-totter so that when rates are [See-saw of rates and par value]

high par value of old bonds are low and vice versa that teeter-totter thing, everyone

uses that as an example we waited until this part in the the video to regale you with it..

and key self-awareness issue for you nervous Nellie investors you don't [Man is nervous and masked man points gun at him]

have to sell the bond at this price by the way you could just hold that six

percent formally yielding bond for the remaining nine years get your grand and [Man holding stack of dollars]

move on you still will have made six percent a year on your thousand dollar

investment which is good just not as good is that juicy eight percent you

could have gotten okay if all that hasn't confused you enough let's add one

more degree of difficulty here just keep the Bulgarian judge evaluating us happy [Bulgarian judge smiling]

because you know he lives in Bulgaria, so yeah well hidden in those numbers is the

fact that a buyer who would pay 750 bucks for your bond would also get the

250 bucks of appreciation on the bond over nine years to then get paid back

their principal so in real life the bond wouldn't fall fully to 750 there would

be some recognition of the roughly 250 divided by 9 which equals $28 ish a year

in extra financial return on top of the interest and oh by the way that

appreciation would be taxed each year as it appreciated in value so what happens [Man discussing bond value + recognition]

if things go the other way well yeah the bond yields continue to fall and that 60

bucks a year you paid a grand for has prevailing similar risk bond selling at

4% like what happens if inflation goes the other way while the value of your

fat yielding bond would go up right the markets only paying 40 bucks a year to

rent that brand and you have this awesome piece of paper that pays 60

bucks a year so the value of your paper would be bid up in that setting right [Man points to the ceiling]

60 over a thousand gave you 6% of your return when you

bought the bond but now the prevailing rates are 4% not six so the value of

your once $1000 value bond must change it becomes X unknown, mysterious yes like [Bond becomes X and Batman appears]

Batman so 60 over X must now equal 4% we multiply both sides by X to get it out

of the denominator and you have 60 equals 0.04X then you divide

both sides by 0.04 and 60 over 0.04 is 1500 so yes in that short window of

one year when interest rates fell from 6%to 4% your bonds value skyrocketed like [Bond value rocket launching into the air]

Manhattan Batman building from a grand to being

up 50% to 1500 bucks you know sorta remember that now this big premium

slowly fades away over time you're only gonna get back that original par value

thousand dollars when the bond matures it's over the next nine years that five

hundred bucks in premium will slowly decline at about fifty five bucks a year [Premium declining in value]

there abouts so in real life the bonds value wouldn't actually hit 1500

it would do well just not that well and yes what a roller coaster [Man sitting on a rollercoaster]

it's been riding that bond investment brought to the highest of heights when

interest rates go down only for the bond value to plummet back down and once [Bond value increasing and decreasing par value]

interest rates jump again so the lesson ...I'm not sure that's your job all we

know is in this poor shmucks case it'll be best to pick a ride with a you must

be too tall to enter sign [Man approaches rollercoaster and reads must be too tall to enter sign]