# Measuring Historical Return

The total return on an investment for a given period is:

Total return = Cash payment received during the period + Price change over the period / Price of the investment at the beginning

All items are measured in rupees. The rupee cash payment received during the period may be positive or zero. The rupee price change over the period is simply the difference between the ending price and the beginning price. This can be positive (ending price exceeds the beginning price) or zero (ending price equals the beginning price) or negative (ending price is less the beginning price)

R = C + (PE+PB) / PB

Where R = total return over the period
C= Cash payment received during the period
PE = ending price of the investment
PB = beginning price

To illustrate consider the following information for an equity stock:

1) Price at the beginning of the year : Rs 60.00
2) Dividend paid at the end of the year: Rs 2.40
3) Price at the end of the year: Rs 69:00

The total return on this stock is calculated as follows:

2.40 + (69.00 – 60.00) / 60.00 = 0.19 p or 19 percent

It is helpful to split the total return into two components viz. current return and capital return as follows:

Cash payment + Ending price — beginning price
Beginning price Beginning price
Current return Capital return

The total return of 19 percent in our example may be broken down as follows:

2.40 / 60.00 + 69.00 – 60.00 / 60.00

= 4 percent / Current return + 5 percent / capital return

Thus, the total return concept is all inclusive (as it includes the current yield as well as the price change) and measures the total return per rupee of original investment. Hence it can be used for comparing investment returns over a specified period.

Return Relative:

Often it is necessary to measure returns in a lightly different manner. This is particularly true when a cumulative wealth index or a geometric mean has to be calculated, because in such calculations negative returns cannot be used. The concept of return relative is used in such cases. The return relative is defined as:

Return relative = C + PE / PB

Put differently

Return relative = 1 + Total return

In our example the return relative is: 1 + 0.19 = 1.19.

Note that even though the total return may be negative; the return relative cannot be negative. At worst it is zero.

Cumulative Wealth Index:

A return measure like total return reflects changes in the level of wealth. For some purposes it is more useful to measure the level of wealth (or price) rather than the change in the level of wealth. To do this, we must measure the cumulative effect of returns over time, given some stated init7ial amount, which is typically one rupee.

The cumulative wealth index captures cumulative effect of total returns. It is calculated as follows:

CWIn = WI0 (1 + R1) (1 + R2 ) …. (1 + Rn)

CWIn = cumulative wealth index at the end of n years
WI0 = the beginning index value which is typically one rupee
Ri =total return for year i (i= 1,….n)

To illustrate consider a stock which earns the following returns over a five year period: R1 = 0.14, R2 = 0.12, R3 = — 0.08, R4 = 0.25, and R5 =0.02

The cumulative wealth index at the need of the five year period, assuming a beginning index value of one rupee is:

CWI5 = 1 (1.14) (1.12) (0.92) (1.25) (1.02) = 1.498

Thus, one rupee invested at the beginning of year would be worth Re 1.498 at the end of year 5.

You can use the values for the cumulative index to obtain the total return for a given period, using the following equation:

R n = CWIn / CWI n – 1 – 1

Where

Rn = total return for period n

CWI = cumulative wealth index

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