Formulas for Return of Securities

To compute the Holding period return, holding period yield, expected rate of return, annual HPR, arithmatic mean, geometric mean, standard deviation for historical returns as well as future returns we have extracted some formulas from Reilly/Brown's "Investment Analysis and Portfolio Management". These formulas are as follows -

1. Holding period return (HPR) for single period of a security -

OR,

OR, Dividend Yield + Capital Gain Yield

2. Holding period return (HPR) for "N"th period, where "N" is the amount of years -

OR, HPR =

  

3. Holding period yield = HPR - 1

OR, HPY =

 

4. If the HPR is hold on Annual basis then it will be -

Annual HPR =

5. Average rate of return on the basis of Arithmatic mean -

OR,

 

OR,

 

6. Average rate of return on the basis of Geometric mean -

Here, "" is the product of HPR.

7. Expected rate of return of a security - 

 

OR,

   

Here, 

Ri = Return for securities in "i"th situation for alternatives

Pi = Probability for occuring each outcome.

8. Standard Deviation "" for "Historical Returns" - 

 

 

Here,

=> If it is a "Sample Distribution" then there will be = N-1

=> If it is a "Population Distribution" then there will be = N

9. Standard Deviation "" for "Future Returns" -

 

10. Real Risk Free Rate of return - 

11.Nominal Risk Free Rate of return -