ShmoopTube

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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anemic at best those old crappy six percent bonds now

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

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

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

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

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

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

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

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marketplace so the mathy question here is what price

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Manhattan Batman building from a grand to being

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

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

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

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

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

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

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

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

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

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

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

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