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Index Level

Index Level is the value of an investment relative to its value at one fixed point in time. Index Levels allow convenient comparison of the relative performance of the different portfolios or asset classes. Differences arise between the daily Index Levels and the Index Levels of other frequencies due to compounding; therefore, these series are not directly comparable.

The initial date and value are set arbitrarily, but must be consistent if comparing multiple indices. The Index Level for any series at any time after the initial point indicates the value at that time of the initial value invested at the initial point. The Index Level of a series is set to zero prior to available data. Let:

i_t = Index Level for any series at time t
r_t = return for the period t - 1 to t
t₀ = the time of the first non-missing return of the series
D₀ = initialization date. An arbitrary date where the level is set to the initial value
V₀ = initialization value. An arbitrary value the level is set to on the initialization date

then

if t = D₀ then i_t = V₀
if t > D₀ then i_t = i_t-1(1+r_t)
if t < D₀ and t₀-1 then i_t = i_t+1 / (1+r_t+1)
if t < t₀ then i_t = 0

Defined CRSP indices use the following initial dates and levels:

CRSP Stock File Indices

initial level: 100.00
initial date: December 29, 1972

CRSP Cap-Based Portfolios

initial level: 1.00
initial date: December 31, 1925

CRSP US Government Treasury and Inflation Indices

initial level: 100.00
initial date: December 29, 1972

Publicly available indices such as for the S&P 500 Composite and NASDAQ Composite have initial values set by their creators of those indices and do not match the CRSP initializations.