Measuring Returns

Meaning of Return

The term 'return' can be defined as a certain extra amount that is received from initial investment amount. Mathematically, it can be expressed as:

Return = Terminal Wealth - Initial Wealth

Where, 

• Terminal Wealth = Maturity amount

• Initial wealth = Investment amount
  

Return on Investment (ROI) is the ratio of benefit and cost. It is also known as Return on Cost (ROC). Higher the ratio the greater the benefit and lower the ratio lower the benefit. It helps the investor whether to take or skip the investment opportunity by calculating ROI. 

Forms of Return

Basically, there are following types of returns that can be received from the company mentioned as bellows:

1. Capital Gain Return = Amount increment in unit price  i.e. P1-P0

2. Dividend Return = Extra amount received from the company as a Dividend i.e. D1

3. Interest Return = Certain fixed percentage gain on initial amount in a fixed period of time (Investment * Interest Rate)

4. Other Return: Ant other financial positive cash flows given by the company

5. Total Return = Capital Gain Return + Dividend Return + Interest Return + Other Return ((P1-P0) + D1+ I + O)/P0

Where, 

• P1 = Ending price of share
• P2 = Beginning price of share
• D1 = Dividend per share
• I  = Interest per rupee of investment
• O = Other positive cash flows

Concept of Yield

The above types of returns can be measured in terms of percentage is known as yield. Like:

• Capital Gain Yield = (P1-P0)/P0 * 100

• Dividend Yield = D1/P0 * 100

• Total Yield = (P1-P0+D1)/P0 * 100

Types of Return

The return can be calculated based on Absolute and Relative Basis. The absolute return is the return of the assets in the particular period of time whereas Relative return is the return of the assets as compared to benchmark or (market or index). 

There are various kinds of returns are taken into account due to investment holding period. Basically, the holding period may be classified into two types presented as bellows:

Fig: Natures of Holding Period

• Single Period Return: It is the return of up to one year or any specific period . It can be calculated as follows: 

Single Period HPR = (P2-P1)/P1

• Multiple Period Return: It is the return of more than a year or multiple any time periods. It is also known as Rolling Return. It can be calculated as follows: 

Multiple Period HPR = (P3-P1)/P1

• Annualized Return or CAGR: It is the return of more than a year that shows year on year rate of return on investment. It can be calculated as follows:
  

Annualized Return = [[(P3/P1) ^ (1/n)] – 1]*100

Where, n = no. of years, note if n is

• in year then (1/no. of years)
• in months then (12/no. of months)
• in weeks then (52/no. of weeks)
• in days then (365/no. of days)

Note 1: CAGR stands for Compounding Annual Growth Rate

Note 2: Annualized Return is also known as Annualized ROI.

• Internal Rate of Return (IRR): It is the return when the regularly payments are made. It can be calculated by using its formula under Capital Budgeting Techniques.  

• Extended Internal Rate of Return (XIRR): It is the return when the regularly payments are not made. It can be calculated by using Microsoft Excel.
  

Measuring Returns

Basically there are two returns that are measured for investment purpose mentioned as bellows:

1. Average rate of return (Expected Rate of Return): It is the average or mean returns of two or more periods of returns. Mathematically,
   

   In case of no probability is given,

   R Bar = Sum of all Returns / No. of Returns

   In case of probability is given,

   E [R] = Sum of [Investment Weight * Individual Stock Return] 
   

2. Required rate of return:  It is also known as risk adjusted rate of return. It can be measured by using the formula or equation of Security Market Line (SML). Mathematically,

Req-E[R] = Krf + Bi [E(Km) - Krf]

Where, Krf is the risk-free rate of return, Bi is the beta coefficient of a particular stock, Km is the expected market return and Req-E[R] is the required rate of return from a particular stock.

Decision Making for Investment 

The decision can be taken through following strategy from investor point of view provided as bellows:

1. If required rate of return is greater than expected rate of return then sell or short sell because it is the condition of overpriced.

2. If required rate of return is less than expected rate of return then buy because it is the condition of under-priced.

3. If required rate of return is equal to expected rate of return then not trade because it is the condition of correctly priced.

Conclusion

The term 'return' can be defined as a certain extra amount that is received from initial investment amount. The return could be in various forms such as capital gain, dividend, interest and other cash inflows etc. The returns can be measured in terms of percentage is known as yield. Basically there are two returns that are measured for investment purpose includes average rate of return (expected rate of return) and required rate of return. The investment decision can be taken by comparing the above two measures of return (average rate of return or expected rate of return and required rate of return). The return can be calculated based on Absolute and Relative Basis. There are various kinds of returns are taken into account due to investment holding period. Basically, the holding period may be classified into two types; Single Period Return is the return of up to one year where as the Multiple Period Return is the return of more than a year. The multiple periods HPR should convert in to annualized return or CAGR to know annual return of an investment. 

Come On, Tell Me What You Think!

Did I miss something?  Come on! Tell me what you think about this post on measuring return in the comments section.