I understand that Treasury bills are sold at a discount and that the difference between the buying price and nominal value represents the return for the investor. However I am confused with the BEY formula ((Face value – Purchase price)/Purchase price * (365/ days to maturity)) particularly the ”multiplied by 365/d”. Why do we need to annualize the return? Can’t we simply quantify in percentage how much the investor wins (by, say, doing (F-P)/F * 100) ?
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Imagine two firms that both had a portfolio of one single bond. If both bonds had different maturities how would you compare these two firms when deciding who to give your money to? That’s why everything is annualized, so it can be compared.
BEY gives you an annualized return so you can compare it against yields from other discounted bonds.
Example. You buy a bond expiring in 6 months at 90 expecting 100 at maturity, your return is 11%. However since assets are compared by annual returns this value is kind of useless because it doesn’t help you make a decision.
By multiplying it by (365/180) or (360/180) depending on which country you’re in you get an annual figure this would be 11*2= 22%
Now if you do this for both the imaginary firms above you’ve found a way to standardize the metric that measures their relative performance
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