# Return Calculation Methodology

Each smallcase’s return is calculated from its Index value. To understand how index values are calculated and used to derive smallcase returns, please refer to following sections

## What is an index value?

An index value allows the user to measure the change in the value of a portfolio relative to its value on a historical date. For example, let's assume that portfolio A was created on 1st Jan 2020. The index value of A on that day was 100. Suppose the index value of the portfolio on 31st March 2021 was 127. We can calculate the absolute return of A between the above-mentioned dates as (127/100)-1 * 100 = 27%.

## How are smallcase index values calculated?

Lets understand this with an example. Portfolio FAME was created on 1st Jan 2014. The creator of the portfolio will rebalance FAME once in 3 months.

Let's call the first version of FAME as FAME 1.0. The stocks and weights in FAME 1.0 portfolio are as below:

StocksWeights
A30%
B20%
C15%
D35%

To calculate the index values, the portfolio creation date, constituents of the portfolio and their respective weights are required. On the date of creation of the smallcase, the index value is set to 100. This can also be understood as a hypothetical Rs.100 investment in FAME 1.0. The calculation on 1st Jan 2014 is as below:

Index value: 100

DateWeightClosing priceNo. of sharesIndex Value
ABCDABCDABCD
1-Jan-1430%20%15%35%176.5101.4105.952.10.170.200.140.67100.00
2-Jan-1430%20%15%35%174.3105.8103.351.50.170.200.140.6799.67
3-Jan-1430%20%15%35%172.0104.2100.950.90.170.200.140.6798.22
4-Jan-1430%20%15%35%172.0104.2100.950.90.170.200.140.6798.22
5-Jan-1430%20%15%35%172.0104.2100.950.90.170.200.140.6798.22
6-Jan-1430%20%15%35%168.8103.9101.251.10.170.200.140.6797.86
On 1st Jan 2014, the portfolio contained 4 stocks A, B, C and D. The weights of these stocks were 30%, 20%, 15% and 35% respectively. The closing prices of the stocks on that day is used to calculate the hypothetical number of shares that can be bought, assuming Rs.100 is invested in the portfolio. “100 * weight of the stock” will give the amount of money that can be invested in a specific stock. This number is divided by the closing price of the stock to derive the number of shares of that stock. Finally, by multiplying the number of shares of each stock with the stock’s closing price and adding the output for all the stocks, the index value is derived. Of course on the first day, the index value is the same as the amount invested, i.e 100.The number of shares of each stock will remain the same till the next rebalance date. Each trading day, the closing stock prices are multiplied by the number of shares. The sum of these data points will be the index value for that specific date.

## How does rebalance affect the index value?

Rebalancing is the process of reviewing the stocks and their respective weights to ensure that it remains true to the theme or strategy of the smallcase.

Continuing with the same example, let's assume The FAME portfolio gets rebalanced on 31st March 2014. The index values leading upto the rebalance date were as below:

DateWeightClosing priceNo. of sharesIndex Value
ABCDABCDABCD
26-Mar-1430%20%15%35%176.8100.788.065.80.170.200.140.67106.54
27-Mar-1430%20%15%35%183.7100.189.567.50.170.200.140.67108.97
28-Mar-1430%20%15%35%190.2100.392.768.80.170.200.140.67111.39
29-Mar-1430%20%15%35%190.2100.392.768.80.170.200.140.67111.39
30-Mar-1430%20%15%35%190.2100.392.768.80.170.200.140.67111.39
31-Mar-1430%20%15%35%191.8100.391.870.40.170.200.140.67112.65
In the rebalance, the weights of both A and D were reduced and a new stock E was added to the portfolio. Let’s call this new portfolio FAME 2.0. Post rebalance, the stocks and their corresponding weights were as below:
StocksWeights
A20%
B20%
C15%
D30%
E15%
On 31st March, the Rs.100 that was initially invested in the portfolio had grown to Rs.112.65. The latter amount is the one that should be reinvested.A simple of way calculating the new number of shares is by multiplying 112.65 * weight of stocks in the rebalanced portfolio and dividing the output by closing price of the individual stocks. Continuing the earlier process, these new numbers of shares can be multiplied by the daily close price of respective stocks and their summation could be the new index value. The index values calculated using this method will be as below:

Index value: 112.65

DateWeightClosing priceNo. of sharesIndex Value
ABCDEABCDEABCDE
31-Mar-1420%20%15%30%15%191.8100.391.870.4373.60.120.220.180.480.05112.65
1-Apr-1420%20%15%30%15%189.4105.793.468.5368.20.120.220.180.480.05112.72
2-Apr-1420%20%15%30%15%193.5116.494.169.2365.10.120.220.180.480.05115.94
3-Apr-1420%20%15%30%15%189.6114.194.268.4363.60.120.220.180.480.05114.51
4-Apr-1420%20%15%30%15%190.3118.992.270.4361.90.120.220.180.480.05116.18
5-Apr-1420%20%15%30%15%190.3118.992.270.4361.90.120.220.180.480.05116.18

However this methodology has limitations. Investors will be able to execute the trade only after the market opens the next day. It is unlikely that these trades will be executed at the previous day's close price. If the price of securities that the investor is buying goes up and the price of securities that the investor is selling goes down, then the investor's portfolio will underperform the manager's smallcase. If the scenario is reversed and the investor is able to buy at a lower price and sell at a higher price, then his/her portfolio will outperform the manager's portfolio. In order to lessen the impact of this issue and ensure that the investor's returns are in line with that of the manager's portfolio, we use the following methodology.

T0 : Rebalance date, 31st March 2014 in this instance

T1 : Calendar day after rebalance date, 1st April 2014

V0 : smallcase version before rebalance, FAME 1.0

V1 : smallcase version after rebalance, FAME 2.0

OHLC average : Average of Open, High, Low and Close price of the stock on a particular trading day

1. ### Calculating intermediate index value on T1

Intermediate index value = Sum of (No. of shares of each stock in V0 * OHLC average of the respective stock on T1)

DateWeightOHLC average priceNo. of sharesIndex Value
ABCDABCDABCD
1-Apr-1430%20%15%35%190.6104.092.869.50.170.200.140.67112.68
2. ### Calculating the new number of shares for stocks in V1

New no. of shares = (Intermediate index value * weight of the individual stock in V1) / OHLC average of the respective stock on T1

Index value: 112.68

DateWeightOHLC average priceNo. of shares
ABCDEABCDEABCDE
1-Apr-1420%20%15%30%15%190.6104.092.869.5371.10.120.220.180.490.05
3. ### Calculating the final index value on T1

Final index value = Sum of (No. of shares of each stock in V1 * Closing price of the respective stock on T1)

Again, the number of shares of each stock will remain the same till the next rebalance date. As earlier, each trading day the closing stock prices are multiplied by the number of shares. The sum of these data points will be the index value for that specific date.

The index values calculated using the improved method will be as below:

DateWeightClosing priceNo. of sharesIndex Value
ABCDEABCDEABCDE
31-Mar-1430%20%15%35%-191.8100.391.870.4373.60.170.200.140.67-112.65
1-Apr-1420%20%15%30%15%189.4105.793.468.5368.20.120.220.180.490.05112.41
2-Apr-1420%20%15%30%15%193.5116.494.169.2365.10.120.220.180.490.05115.56
3-Apr-1420%20%15%30%15%189.6114.194.268.4363.60.120.220.180.490.05114.13
4-Apr-1420%20%15%30%15%190.3118.992.270.4361.90.120.220.180.490.05115.79
5-Apr-1420%20%15%30%15%190.3118.992.270.4361.90.120.220.180.490.05115.79

Please note that smallcase returns were impacted when the above updated methodology wrt to calculating impact of rebalance on index values was implemented on 25th Apr’22. Returns were adjusted to reflect the impact of updated methodology on all the historical rebalances of the smallcase since launch.

## Calculating returns using index values

As clarified earlier, index values are used to calculate smallcase returns. Index values of the smallcase and the corresponding category performance are available on the platform.

The “Download” button on the rebalance timeline feature in the stocks and weights section of the smallcase page can be used to download the index value of the smallcase and historical components.

To calculate the 1-month return of a smallcase, first decide on the base date and historical date. Suppose the base date is 1st Jan 2015, the historical date is 1st Dec 2014. Let's suppose the index values on these dates are 470.2 and 482.6 respectively. Then the 1 month return is (470.2/482.6)-1 = 2.58%. The absolute returns between any 2 dates can be calculated similarly.

## Calculating returns when manager has not prescribed any weights

Equal weights are used to calculate the returns, for smallcases where manager has just prescribed a list of stocks/ETFs, but has not prescribed any weights. So if there are 5 stocks/ETFs in the smallcase, each would be considered to have 20% weight while using the above-mentioned methodology for returns calculation. Similarly, if there are 10 stocks/ETFs in the smallcase, each would be considered to have 10% weight while using the above-mentioned methodology for returns calculation.

## Does smallcase performance include the impact of transaction fees?

No, transaction fees and other related costs are not included to calculate the index value and performance of the smallcases. No actual money was invested or trades were executed while calculating smallcase performances. Returns are based on end of day prices of stocks in a smallcase.

## Does smallcase performance include historical rebalances?

Yes, smallcase performance accounts for all the rebalances. smallcases are reviewed and rebalanced as per a schedule depending on the smallcase. As a result of this review process, some stocks may be added, some may be removed and some may undergo weight changes. smallcase returns reflect all these changes.

## Does smallcase returns include any backtested data?

No, smallcase returns do not include any backtested data. Interested users can separately checkout the backtest performance through the factsheet of a smallcase.

## Does smallcase performance include the adjustment for stocks which users are not able to buy/sell in rebalances due to stocks hitting the upper/lower circuits?

Yes, at the end of every month, we identify all the smallcases which experienced following events :

• Manager added or removed the stocks which were in the upper/lower circuit on the day when users received the rebalance update for execution (next market open day after the Manager added the rebalance)
• Manager reduced or increased the weights of the stocks which were in the upper/lower circuit on the day users received the rebalance update for execution
For such smallcases, we recalculate the index value for the last month in a manner that ensures :
• Circuit stocks are not removed/added from the Manager’s smallcase for the period in which they remained in the circuit. This will ensure that Manager smallcase returns are in line with the user smallcase returns, as users would also not be able to buy/sell these stocks for the same period.
Recalculated index value is used to calculate all the ratios like CAGR, volatility labels, etc