All REIT indexes are populated from the REITs available that fit the selection criteria of that index. Value-weighted and equal-weighted indexes are formed for each set of issues. Total return, capital appreciation, income returns, and corresponding index levels are calculated for each portfolio. The returns show the change in the total dollar value of the portfolio, over some period of time, per dollar in initial investment. The index levels show the cumulative value of the portfolio relative to a fixed starting date. All REIT index levels are set to $100 on December 30,1994.

The procedure for calculating each index involves three steps:

Calculating returns for individual securities

Calculating returns for indexes

Calculating index levels

Calculating Returns for Individual Securities

Returns are calculated for each individual security using the formula:

Where, for trading day t, t-1 is the previous trading day.

r(t) = security’s return for day t

p(t) = last sale or closing bid/ask for day t

f(t) = price adjustment factor for day t

d(t) = cash adjustment for day t

In the total returns, dividends, split factors, spin-offs,rights and all other distributions are compensated for or reinvested on the ex-distribution date. Total Returns include all cash distributions in the cash adjustment, while Returns without Dividends exclude ordinary cash dividends. The time series used prices are inputs to the returns for the REIT indexes.

Calculating Returns for Indexes

Returns for individual securities within an index are combined to create returns for the index. For a security to be eligible for index inclusion, Good Prices must be available for the previous period, but Good Prices, Soft Prices, or Delisting Prices can be used for the current period.

The sum of the weighted returns is divided by the sum of the securities’ weights to arrive at the return for the index:

Where, for trading day t, R(t) is the return for the index:

w_{n}(t) = weight of security n for day t

r_{n}(t) = security n’s return for day t

Index total returns use security total returns for the securities that fit the selection criteria of that index. Price appreciation uses security returns without dividends. Income returns use the difference betweenthe two. In an equal-weighted index, the weight of each security is one. In a value-weighted index, the weight assigned to each security is equal to its market capitalization at the end of the previous period, t-1.

Calculating Index Levels

The base year for the CRSP/Ziman REIT Indexes is12/30/1994^{1}. At that point in time the indexes are set to 100.

The Index level, l(t), is defined as:

If t = t_{0}, l(t) = 100

If t > t_{0}, l(t) = l(t-1)* (1+R(t))

If t < t_{0}, l(t) = l(t+1)/(1+R(t+1))

Where t_{0}= December 30, 1994:

l(t) = index level for day t

R(t) = total return for the index for day t

^{1}CRSP Market Indexes are set to 100 on 12/29/1972.

Summary Statistics and Quality Measures

Total Value, TOTVAL, in the CRSP/Ziman REIT Indexes is defined as the total market value of the eligible issues with a Good or Soft Price at the beginning of the period^{1}. The REIT Indexes also add new summary variables including Beginning Count, Add Count, Add Value, Drop Count, Drop Value, Observed Count, Observed Value, Concentration Ratio and the HHI – Herfindahl-Hirschman Index. See the Variable Table for descriptions.

^{1}CRSP Market Indexes use end of period market value calculated with observed trade or the average of observed closing bid and ask.

All REIT indexes are populated from the REITs available that fit the selection criteria of that index. Value-weighted and equal-weighted indexes are formed for each set of issues. Total return, capital appreciation, income returns, and corresponding index levels are calculated for each portfolio. The returns show the change in the total dollar value of the portfolio, over some period of time, per dollar in initial investment. The index levels show the cumulative value of the portfolio relative to a fixed starting date. All REIT index levels are set to $100 on December 30,1994.

The procedure for calculating each index involves three steps:

## Calculating Returns for Individual Securities

Returns are calculated for each individual security using the formula:

Where, for trading day t, t-1 is the previous trading day.

r(t) = security’s return for day t

p(t) = last sale or closing bid/ask for day t

f(t) = price adjustment factor for day t

d(t) = cash adjustment for day t

In the total returns, dividends, split factors, spin-offs,rights and all other distributions are compensated for or reinvested on the ex-distribution date. Total Returns include all cash distributions in the cash adjustment, while Returns without Dividends exclude ordinary cash dividends. The time series used prices are inputs to the returns for the REIT indexes.

## Calculating Returns for Indexes

Returns for individual securities within an index are combined to create returns for the index. For a security to be eligible for index inclusion, Good Prices must be available for the previous period, but Good Prices, Soft Prices, or Delisting Prices can be used for the current period.

The sum of the weighted returns is divided by the sum of the securities’ weights to arrive at the return for the index:

Where, for trading day t, R(t) is the return for the index:

w

_{n}(t) = weight of security n for day tr

_{n}(t) = security n’s return for day tIndex total returns use security total returns for the securities that fit the selection criteria of that index. Price appreciation uses security returns without dividends. Income returns use the difference betweenthe two. In an equal-weighted index, the weight of each security is one. In a value-weighted index, the weight assigned to each security is equal to its market capitalization at the end of the previous period, t-1.

## Calculating Index Levels

The base year for the CRSP/Ziman REIT Indexes is12/30/1994

^{1}. At that point in time the indexes are set to 100.The Index level, l(t), is defined as:

If t = t

_{0}, l(t) = 100If t > t

_{0}, l(t) = l(t-1)* (1+R(t))If t < t

_{0}, l(t) = l(t+1)/(1+R(t+1))Where t

_{0}= December 30, 1994:l(t) = index level for day t

R(t) = total return for the index for day t

^{1}CRSP Market Indexes are set to 100 on 12/29/1972.## Summary Statistics and Quality Measures

Total Value, TOTVAL, in the CRSP/Ziman REIT Indexes is defined as the total market value of the eligible issues with a Good or Soft Price at the beginning of the period

^{1}. The REIT Indexes also add new summary variables including Beginning Count, Add Count, Add Value, Drop Count, Drop Value, Observed Count, Observed Value, Concentration Ratio and the HHI – Herfindahl-Hirschman Index. See the Variable Table for descriptions.^{1}CRSP Market Indexes use end of period market value calculated with observed trade or the average of observed closing bid and ask.