Calculation of price return and total return of an index

46.b: Calculation of price return and total return of an index

Calculating returns of an index

Index returns can be thought of as simple price return or total return. Price return is simply the change in index price level over time.

Value of Price return index = V_P = (1/D)*∑n_i P_i

where,

Price return = (VP₁-VP₀)/VP₀; where VP₁ is the current value of the index and VP₀ is the price of the index on the date from where the return is being calculated.

ni = the number of units of constituent security i held in the index portfolio,
N = the number of constituent securities in the index
Pi = the unit price of constituent security i,
D= Divisor

A divisor is a number chosen at the inception of the index to bring it to convenient value such as 100, 1000 etc.

Total return represents the price return as well as any dividend or reinvestments of income from the index. It is equal to or greater than the price return.

Portfolio return during measurement period = P_total= (1+P₁)*(1+P₂)*(1+P_n)-1 where, P₁, P₂ ... P_n represent returns during sub-period n.

Check your concepts:

(46.1) The price return and the total return of an equity index are equal. The dividend yield of the equity index is most likely to be:

(a) Positive
(b) Zero
(c) Negative

(46.2) What is the impact of a divisor on the annual total return of an index?

(a) Greater the divisor lower the annual total return
(b) Greater the divisor higher the annual total return
(c) No impact

Solutions:

(46.1) Correct Answer is B: If the price return and the total return are the same then the dividend yield will be zero because the total return equals price return plus the dividend yield.

(46.2) Correct Answer is C: There is no impact on the annual percentage return due to the choice of the divisor. The divisor only sets the value of the index.