Finance Essentials: Understanding and Calculating Yields

To succeed in finance, one must understand the basics of rates/yields. Understanding and calculating yields allow the consumer or investor to capture the real rate of borrowing and/or lending. Below we would cover Effective Annual Rate, Bank Discount Yield, Holding Period Yield, Effective Annual Yield, Money Market Yield, and Bond Equivalent Yield.

1. Effective Annual Rate (EAR) is the real rate of interest due to compounding.
· Formula: (1 + APR/m) ^ m ) – 1.
· M in this case is the periodicity or number of compounding periods.

2. Bank Discount Yield is an annualized yield (T-bills are usually quoted using this yield). Keep in mind that that there are shortcomings for investors using this measure, which includes the yield is (i) based on the face value of the bond, not on its purchase price, (ii) annualized based on a 360 day year rather than a 365, and (iii) annualizes with simple interest, which ignores the opportunity to earn compound interest.
· Formula: (D/F) * (360/t).
· D is the dollar discount; F is the Face Value; t is the actual number of days remaining to maturity; and 360 is the bank’s convention of the number of days in a year.

3. Holding Period Yield (HPY) is the total return of holding an asset over a period of time. 
· Formula: ((Ending Value – Beginning Value) + Additional Income) / Beginning Value

4. Effective Annual Yield annualized the HPY to help ensure comparability. Somewhat similar to the EAR, the EAY substitutes the APR for HPY. This rate further helps account for the effect of compounding interest.
· Formula: [ (1 + HPY) ^ (365/t) ]  -1

5. Money Market Yield makes quoted yields on a T-bill comparable to quoted yields on interest-bearing money-market instruments that pay interest on a 360 day basis.
· Formula: (360 * Bank Discount Yield) / (360- (t * Bank Discount Yield)) or 
· Formula: HPY * (360/t)

6. Bond Equivalent Yield (BEY) annualizes the yield-to-maturity of the appropriate discount rate used for bonds; allows for comparing securities with different compounding periods.  
· Formula: ((1000-Purchase Price)/Purchase Price) *(365/t)