If we have HPY, EAY or MMY, we can use it to convert it to the other two.
Continuing with our previous example, let’s say the money market yield is 10.11% and the holding period is 90 days. This is the annualized yield from the asset on a 360-day year basis but it does not account for compounding. It uses simple interest.
First, let’s calculate the holding period return. This is the actual return earned by the investor. Since the investor held the asset for only 90 days, the HPY will be calculated as:
HPY = MMY*t/360 = 10.11%*90/360 = 2.53%
The effective annual yield (EAY) is the annualized yield on a 365-day basis that also incorporates compounding. We can use HPY to calculate EAY as follows:
EAY = 1.0253(365/90) = 10.66%
Bond Equivalent Yield
In the bond market the convention is to annualize the semi-annual yield by simply doubling it. So, if the semi-annual yield is 3%, the annual yield is calculated simply as 3% x 2 = 6%. The annual yield so calculated is called the bond-equivalent yield (BEY).
This convention doesn’t follow the time value of money rules where you would compound the semi-annual yield to calculate the effective annual yield. Instead the doubling convention is followed across the market.
A common question asked by students is ‘Why have such a convention and why not instead use effective annual yield?’ The answer to this question is that since it’s a convention everybody uses it and therefore yields are comparable. It doesn’t really affect performance or comparison between bonds because everyone would have used the convention to quote the yield. Conventions are usually made to make things simpler. In this case if someone tells you that the bond-equivalent yield is 6%, you instantly know that semi-annual yield is 3%, which you can use to perform any calculations or to calculate the effective annual yield if you require it.
If the convention was to use effective annual yield, it may have been better, but does it really matter? In fact there are many other limitations of YTM that far outweigh the problem of BEY convention. So, my suggestion to you would be to just follow the convention and don’t fret over it. It is important however, that you use the convention correctly.
Note: To calculate the bond equivalent yield, we first need the semi-annual yield. For a semi-annual coupon paying bond, we calculate this directly and double it to calculate the bond equivalent yield.
However, for an annual coupon paying bond or for any asset with a shorter maturity, we first convert the yield that we have into a semi-annual yield and then double it to calculate BEY.
For an annual-pay bond, BEY will be calculated as follows:
BEY = 2 x [(1+ yield on annual-pay bond) 0.5 -1]
For an instrument with a 3-month yield, BEY will be calculated as follows:
BEY = 2 x [(1+ yield on annual-pay bond)2 -1]