Investment Problem

[superprismatic]

Once in a while, one sees a column with a mathematical bent in a newspaper. More often than not, there's

something that doesn't seem quite right about it. In the Chicago Tribune column found here,

a claim is made that you could have purchased 10-year bonds with a 3% rate at the beginning of 2011,

sold them at the end of 2011 (when similar 10-year bonds had a 2% rate), and made a profit of around

16% on your original investment. Can anyone offer any mathematical justification for this claim?

[dyalDragon]

I can get a 15.4% profit, but I'm not sure I'm attacking the problem right.... I'm a H&W actuary, not Investment

[curr3nt]

$1000 at 3% for 10 years comes out to about $1344

$1000 at 2% for 10 years comes out to about $1219

Instead of waiting 10 years for the $1344 you could sell it (to someone willing to wait) for $1160 after 1 year. There is a 16% gain.

But $1160 at 2% is about $1386 at 9 years (removing one year since the 3% has 9 years left) which is $42 more than what you would get for buying the bond at 3%.

Unless I totally do not understand (which is quite possible) it seems to be a loss. Then again I'm sure if you sold it right you could find a sucker willing to believe buying the 3% bond is a good thing.

[dyalDragon]

a $10,000 10 year bond at 3% would cost roughly$7,441 initially. A year later you have received one 3% coupon for $223. You can sell the bond for the same price as a 9 year $10,000 bond at 2%, which is worth roughly $8,368. The profit would be $927 That makes your total profit $1,150, which is 15.45% of the original investment.

It's been awhile since I have had to value a bond, though, so likely my memory of how to handle the situation has been muddled....

[plasmid]

I think curr3nt and dD are essentially right, they're just omitting a bit of a fudge factor in the article -- it mentions bonds at the beginning of the year selling for "a little over 3 percent" and at the end of the year "just under 2 percent", and they may very well be rounding the return up to 16% from an actual value just over 15.5%.

And all of that makes much more sense than the real estate market around here.