# Equi-Weighted

In this weighting scheme, we want to give equal weights to all the stocks. We earlier defined weight of a particular instrument as the portion of total portfolio value represented by it. In this case instruments are the stocks and total portfolio value at the time of investing should be 50,000. We want each stock to represent equal portion of the total portfolio value. This can happen only if total value is dividend equally amount all the stocks, so each stock should have a value of INR 10,000. Thus, the initial investment going into each stock would be INR 10,000 (50,000/5) and weight of each stock would be 20% (10,000/50,000). This would be the portfolio composition:

StockInvestmentWeight
SBI10,00020%
PNB10,00020%
BOB10,00020%
BOI10,00020%
ALBK10,00020%
Total50,000100%

Now in order to execute this strategy in market, we have to buy shares of each stock worth INR 10,000. No. of shares of each stock is calculated by dividing the investment in the stock by its current market price. So, we will have to buy the following number of shares:

StockInvestmentWeightCurrent Market PriceShares
SBI10,00020%164.6560.73
PNB10,00020%76.15131.32
BOB10,00020%139.6071.63
BOI10,00020%87.40114.42
ALBK10,00020%44.15226.50
Total50,000100%

As you can see in the above table, when we divide the investment amount by current market price we get fractional shares. It is not possible to buy fractional shares in the market. For example, you cannot buy 1.6 shares of SBI or 2.2 shares of PNB. For SBI, you will have to either buy 1 or 2 shares and similarly, for PNB either 2 or 3 shares. In order to meet this requirement of non-fractional shares we change the above calculated no of shares to nearest integer. Once we have the no of shares of each stock, investment can be recalculates as shares multiplied by current market price. Final weights would be calculated by dividing the new investment for non-fractional shares by total investment, as shown.

StockInvestment (A)Weight (B = A/sum[A])Current Market Price (C)Shares (D = A/C)Rounded Shares (D1)Actual Investment (E = D1 x C)Final Weight (= E/sum[E])
SBI10,00020%164.6560.736110043.6520.06%
PNB10,00020%76.15131.321319975.6519.93%
BOB10,00020%139.6071.637210051.2020.08%
BOI10,00020%87.40114.421149963.619.90%
ALBK10,00020%44.15226.5022710022.0520.02%
Total50,000100%50056.15100%

In the above example, we wanted to achieve an equi-weighted portfolio where each stock has a weight of 20% but as shares can be bought only in whole numbers, we end up with a close approximation.

Read on to understand what happens when we try to build the same portfolio with Market-Cap or Custom weighting scheme.