Creating a Custom Index

Custom Index Creation

We will continue with our example of banking sector stocks which we covered in last two articles. Let’s say we decide to go with the equi-weight scheme, then following would be our initial portfolio, as calculated in the first article on weighting schemes.

Stock	Weight	Investment	Shares	Current Market Price (B)
SBI	20.06%	10,043.65	61	164.65
PNB	19.93%	9,975.65	131	76.15
BOB	20.08%	10,051.20	72	139.60
BOI	19.90%	9,963.60	114	87.40
ALBK	20.02%	10,022.05	227	44.15
Total	100%	50,056.15

Suppose we make the above investment today and call it Day 0. At the end of Day 0, we will buy the above mentioned number of shares of each stock to build our portfolio. Next day (Day 1), no of shares will remain constant but the price of each stock will change. Value of each stock will be its market price multipl  ied by the no of shares. Total portfolio value will be the sum of individual stock values. Weight of a particular stock will be calculated by dividing its current value by the total portfolio value. Look at the table below, to understand how everything will be calculated on Day 1 when stock prices change

Stock	Shares (A)	Day 0			Day 1
		Current Market Price (B0)	Investment (C0 = B0 x A)	Weight (= C0 / sum[C0])	Current Market Price (B1)	Investment (C1 = B1 x A)	Weight (= C1 / sum[C1])
SBI	61	164.65	10,043.65	20.06%	167.00	10,187.00	19.55%
PNB	131	76.15	9,975.65	19.93%	78.20	10,244.20	19.66%
BOB	72	139.60	10,051.20	20.08%	145.50	10,476.00	20.10%
BOI	114	87.40	9,963.60	19.90%	90.10	10,271.40	19.71%
ALBK	227	44.15	10,022.05	20.02%	48.15	10,930.05	20.98%
Total			50,056.15	100%		52,108.65	100%

From the above table, it’s clear how weights and value of each stock changes on a daily basis. No of shares always remain constant, as we are not placing any new buy/sell trade on the exchange. Everything is calculated based on the existing no of shares and current market prices. The best way to track a portfolio and calculate its return is through creation of custom index. The initial amount on Day 0 is INR 50056.15. We can rebase this value to 100 and then calculate all future vales on this scale. Basic unitary mathematics say that if 50056.15 = 100, then 1 unit is equal to 100/50056.15. As calculated in the above example, the value next day is 52108.65. If 1 = 100/50056.15, then 52108.65 = [52108.65 * (100/50056.15)] = 104.1. Following table shows how custom index values will be calculated, assuming column B represents value of your portfolio on future dates.

Day	Portfolio Value	Calculation	Custom Index
Day 0	50056.15	50056.15 * (100/50056.15)	100
Day 1	52108.65	52108.65 * (100/50056.15)	104.10
Day 2	51105.87	51105.87 * (100/50056.15)	102.10
Day 3	53500.12	53500.12 * (100/50056.15)	106.88
Day 4	54100.11	54100.11 * (100/50056.15)	108.08
Day 5	54800.14	54800.14 * (100/50056.15)	109.48
Day 6	55321.15	55321.15 * (100/50056.15)	110.52
Day 7	58659.75	58659.75 * (100/50056.15)	117.19
Day 8	59457.87	59457.87 * (100/50056.15)	118.78
Day 9	57458.78	57458.78 * (100/50056.15)	114.79
Day 10	57300.12	57300.12 * (100/50056.15)	114.47

Let’s now understand the usefulness of custom index values in calculating portfolio returns & risks.

Returns for Custom Indices

Portfolio return calculations become very easy through custom indices. Let us continue with our example of banking sector stocks, discussed in previous articles, to understand this. From our last article, we know how to create a custom index for a portfolio by rebalancing it to 100 at the inception date. Following is the portfolio snapshot on inception date (Day 0) and 30 days after the inception date (Day 30).

Stock	Shares (A)	Day 0			Day 30
		Current Market Price (B0)	Investment (C0 = B0 x A)	Weight (= C0 / sum[C0])	Current Market Price (B1)	Investment (C1 = B1 x A)	Weight (= C1 / sum[C1])
SBI	61	164.65	10,043.65	20.06%	200.10	12,206.10	23.42%
PNB	131	76.15	9,975.65	19.93%	90.45	11,848.95	22.74%
BOB	72	139.60	10,051.20	20.08%	135.80	9,777.60	18.76%
BOI	114	87.40	9,963.60	19.90%	83.24	9849.36	18.21%
ALBK	227	44.15	10,022.05	20.02%	55.78	12,662.06	24.30%
Total			50,056.15	100%		55,984.07	100%

We can see that portfolio has grown from INR 50056.15 to INR 55984.07 in 30 days. As discussed in our article Portfolio Return Calculation, formula for returns generated by a portfolio is

Portfolio Return = (Current Networth – Initial Networth) / Initial Networth

By this formula, portfolio of banking stocks generate a return of 11.84% (5927.92/50056.15). Let’s see can we quickly get this number using custom index. We know that the value of the custom index on inception date is 100. So on Day 0 the value is 100. Thus, if 50056.15 = 100 then 55984.07 = [55984 * (100/50056.15)] = 111.84. If someone tells us that the custom index value of our portfolio on Day 30 is 111.84, we can quickly tell that portfolio is up +11.84% (111.84-100). Similarly if the index value after 75 days is 118.15%, we can quickly tell without any calculation that portfolio is up +18.15%. Suppose, the table below shows the custom index values on various dates:

Day	Custom Index	Portfolio Return
Day 0	100.00	0.00%
Day 30	110.00	10.00%
Day 75	111.84	11.84%
Day 100	118.15	18.15%
Day 150	124.75	24.75%
Day 200	127.45	27.45%
Day 250	120.48	20.48%
Day 300	131.45	31.45%
Day 350	135.48	35.48%

I can quickly say what is my portfolio return, without even knowing the total portfolio value. On day 250, if I tell you that the value of your portfolio is 60307.65, you can’t tell the return generated by your portfolio without any calculations. But if I say that the index value of your portfolio is 120.48, you can quickly conclude that your portfolio return is 20.48%. We can also use index values to calculate return generated between any two dates. From the above table, we know that the portfolio value on Day 150 is 124.75 and portfolio value on Day 300 is 131.45. With these values we can quickly tell that portfolio went up by 6.7% between day 150 and day 300. This means that on my initial investment on Day 0, I was earning 6.7% more on Day 300 compared to Day 150. We can also calculate the returns generated in this time period. The portfolio generated a return of 8.6% [(135.48-124.75)/127.75] between Day 150 and Day 300. This means that instead of Day 0, if we had invested on Day 150, we would have earned 8.6% by Day 300.

Let’s look at benchmarking and its benefits now.