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) ?
In: 0
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
Because you should always annualize your yield if you want to compare
You’ve got options of three bonds
3 months that returns just 3%
1 year that returns 10%
5 year that returns 20%
If you look at just the absolute return then the answer seems to be the 5 year, but if you just bought the 1 year bond twice in a row you’d end up with more money in just 2 years, and the 3 month bond really returns 80% over the same time
If you look at annualized returns now you can compare them. The 3 month is 12.5%, the 1 year is still 10%, but the 5 year is just 3.7% making it obviously the worse investment. You can also use annualized yield to determine returns over a specific time period like 20 years
In nearly every financial metric, the measure is annualized. This makes it intuitive for comparison. In very roughly approximating the attractiveness of an investment, one would naturally compare it to prevailing circumstances like interest rates, inflation rates, yields on short terms bills etc etc which are all reported in annualized quantities.
We need to annualize the return because we calculate the annual return.
You can calculate return for any period you want. Only it’s norm in finance to calculate over 1 year period of time.
The (x/365) part in the formula is there because that bond cumulate the interest on daily basis.
Also, the bond is not quoted in yield but in price.
Latest Answers