Investing in Portfolios

Portfolio PE

PE ratio of a company is the ratio of the share price of a company to its earnings per share. PE ratio allows one to infer how much investors are willing to pay for one Rupee of the company’s profit. More about the ratio can be read here.

Portfolio’s can also have PE ratio. Total net worth is the price of the portfolio or the numerator part of the PE ratio. Cumulative earnings of all the companies is the denominator part. You can read more about company’s financial statements and earnings here.

Stock	Number of shares held (A)	Current Price (B)	Net Worth (C = A * B)	Earnings Per Share (D)	Total Earnings (E = D * A)
SBI	33	158.8	5,238.80	23.50	774.20
PNB	122	71.0	8,662.00	18.00	2,198.40
BOB	53	131.9	6,990.70	17.30	918.50
BOI	85	83.30	7,080.50	26.30	2,232.10
ALBK	584	43.40	25,316.40	11.10	6,453.20
Total			53,288.40		12,576.40
PE Ratio			PE = C / D		4.2

One way of interpreting a portfolio PE is by comparing the same with the benchmark PE.

If a portfolio PE is higher than the benchmark PE, then one can interpret the portfolio as being overvalued when compared to the benchmark

One can also compare the current PE of the portfolio with its historical value to understand whether the portfolio is undervalued or overvalued.

If a portfolio has more companies growing at a fast pace, then PE ratio of the portfolio can be high as these companies usually are expensive compared to the rest of the market. If the portfolio companies have had weak total earnings, the total PE ratio could be inflated because of low denominator. Hence one has to closely inspect the portfolio companies before drawing any conclusion about portfolio PE ratio.

Importance of Portfolio Rebalancing

In this article, we invested Rs.50,000 in a portfolio of banking stocks. The total amount was allocated amongst the 5 stocks in equal proportion. However since fractional shares cannot be bought, the portfolio weight was a close approximation of the equal weighted portfolio that we wanted to create.

Suppose we revisit the portfolio after a year, the market value of each security within the portfolio will most likely be different, thereby affecting the weightage of the security within the portfolio.

Portfolio summary at the end of year 1:

Stock	Number of Shares	Day 0			End of Year 1
		Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks
SBI	61	164.70	10,043.70	20.10%	205.80	12,554.60	20.70%
PNB	131	76.20	9,975.70	19.90%	54.80	7,182.50	11.80%
BOB	72	139.60	10,051.20	20.10%	150.10	10,805.00	17.80%
BOI	114	87.40	9,963.60	19.90%	166.10	18,930.80	31.20%
ALBK	227	44.20	10,022.10	20.00%	49.40	11,224.70	18.50%
Total			50,056.20			60,697.60
Annual Returns						21.30%

In the case of our imaginary portfolio both PNB and BOI saw exaggerated price movements which resulted in drastic change in their weightage within the portfolio.

One option that we have in this case is to ignore the change in weightage and continue to hold the same number of shares. This strategy will allow an investor to earn good returns only if BOI continues to perform well and PNB continues to perform poorly.

Suppose the investor decides to retain the portfolio weights hoping that BOI and PNB will continue to perform in line with their historical performance. In case of the below example, share price of both BOI and PNB increased during the year. While share price increase is always good news, in this case the portfolio was less affected by the 40% increase in price of PNB and more affected by the only 5% increase in share price of BOI. This was because of the respective weights of the scrip’s within the portfolio.

Stock	Number of Shares	End of Year 1			End of Year 2
		Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks
SBI	61	205.80	12,554.60	20.70%	226.40	13,810.00	20.80%
PNB	131	54.80	7,182.50	11.80%	76.80	10,055.50	15.20%
BOB	72	150.10	10,805.00	17.80%	172.60	12,425.80	18.80%
BOI	114	166.10	18,930.80	31.20%	174.40	19,877.40	30.00%
ALBK	227	49.40	11,224.70	18.50%	44.50	10,102.20	15.20%
Total			60,697.60	100%		66,270.90	100%
Annual Returns			21.30%			9.2

Hence it is very important to rebalance.

Rebalancing is a form of risk management that will improve the investors risk-adjusted returns over time.

It involves buying and selling a portion of one’s portfolio in order to set the weight of each scrip back to its original state. If an investor fails to rebalance, the more volatile scrip’s in the portfolio will tend to take over and increase portfolio risk.

Assuming the investor chooses the smarter option of rebalancing at the end of year 1, he will have to buy or sell the shares in this order to ensure that the portfolio remains equal weighted.

Stock	Bought on Day 0	Position after rebalancing	Buy (/Sell)
SBI	61	59	-2
PNB	131	220	89
BOB	72	80	8
BOI	114	75	-39
ALBK	227	243	16

As can be seen the investor bought 89 shares of PNB to make up for the lost weightage and sold 39 shares of BOI to reduce its weightage within the portfolio. Minor adjustments were made in case of other shares as well.

Stock	Number of Shares	End of Year 1			End of Year 2
		Market Price	Net Worth	Weight of Stocks	Number of Shares	Market Price	Net Worth	Weight of Stocks
SBI	61	205.80	12,554.60	20.70%	59	226.40	13,357.20	19.70%
PNB	131	54.80	7,182.50	11.80%	220	76.80	16,887.00	24.90%
BOB	72	150.10	10,805.00	17.80%	80	172.60	13,806.40	20.30%
BOI	114	166.10	18,930.80	31.20%	75	174.40	13,077.20	19.20%
ALBK	227	49.40	11,224.70	18.50%	243	44.50	10,814.30	15.90%
Total			60,697.60	100%			67,942.20	100%
Annual Returns			21.30%				11.90%

Rebalancing allowed the investor to earn a return of 11.9% on his portfolio, a 2.7% (11.9 – 9.2) improvement compared to him when he had not rebalanced. This is because he now has more exposure to PNB whose prices increased significantly during the year and less exposure to BOI whose price moved by only 5%.

Nobody can predict with certainty the future returns of a security, past performance is almost never an indication of future performance.

By trimming back on winners and buying laggards, an investor is not only “buying low and selling high”, a sure shot way to make money, but also reaping the full benefit of diversification.

By giving up on past gainers the investor is accepting limited upside potential for greater investment security.

Now that we have learnt why portfolios should be rebalanced, lets look at when and how rebalancing should be done.

To understand the basics of benchmarking, please refer our article on the same here. The following article is written assuming that you have read this article. Once we have created our portfolio, the next step is to define a benchmark for the same. A good benchmark should have similar risk and return characteristics to our portfolio.

For the banking sector example which we have been using throughout this series, Bank Nifty would be a good Benchmark. Bank NIFTY is an index on National Stock Exchange of India comprising of the big banks in India. The index will also benefit from the recapitalization decision of government, which formed the basis of us creating this PSU banks portfolio. At the same time, the index faces the same set of risks faced by all banking stocks. We say this because the risks like rising interest rates and low loan demand are same for stocks in our portfolio, as well as stocks in Bank NIFTY.

Now, suppose in a period of 3 months, our portfolio generates a return of 10%. Generally, we would be very happy to know this. But if we get to know that Bank NIFTY generated a return of 15%, in the same time period, then what? In this case, our portfolio underperformed the benchmark by 5%. This means that our stock selection was not good, as the general sector (represented by Bank NIFTY) outperformed our portfolio. In an opposite case, if our portfolio generates a return of 18%, then we can confidently say that our stock selection was superior, as through our selection of banking stocks based on some criteria, we outperformed the broader banking sector. Thus, it is very important to use right benchmark in order to determine whether we are able to outperform the broader market through our stock selection.

Instead of banking stocks, if our portfolio had IT stocks, then CNX NIFTY IT would be a better Benchmark. Similarly, for Auto sector companies, CNX Auto will be a better benchmark. If our portfolio comprises of stocks from different sectors, then we can use Nifty as a benchmark. This would tell us whether we are able to beat the market through our portfolio selection or not.

Similar to our portfolio, we can create a custom index for benchmark also. Index creation process is exactly same for the benchmark and the portfolio. Assuming NIFTY as benchmark, below table summarizes the index values at different dates.

Day	Portfolio Value	Portfolio Custom Index (A)	NIFTY Value	NIFTY Custom Index (B)	Outperformance (= A - B)
Day 0	50,056.15	100.00	7213.60	100.00	0.00
Day 1	52,108.65	104.10	7210.75	99.96	4.14
Day 2	51,105.87	102.10	7191.75	99.70	2.40
Day 3	53,500.12	106.88	7218.45	100.07	6.81
Day 4	54,100.11	108.08	7400.15	102.59	5.49
Day 5	54,800.14	109.48	7450.85	103.29	6.19
Day 6	55,321.15	110.52	7455.74	103.36	7.16
Day 7	58,659.75	117.19	7480.25	103.70	13.49
Day 8	59,457.87	118.78	7515.64	104.19	14.60
Day 9	57,458.78	114.79	7555.55	104.74	10.05
Day 10	57,300.12	114.47	7590.24	105.22	9.25

If we observe that on Day 9 the value of our portfolio is 57300.12 and the value of the NIFTY is 7590.24, its very difficult to conclude anything. But instead, if we are told that the index value of the portfolio is 114.79 and index value for NIFTY is 104.75, we can quickly conclude following things without any calculations:

• Portfolio has generated a return of 14.79%
• NIFTY has generated a return of 4.75% in the same period
• Portfolio has outperformed NIFTY by around 10%

In addition to above points, custom indices also helps in plotting meaningful graphs. In the first graph we have directly plotted the values of portfolio and NIFTY. In second graph, we have plotted index values of portfolio and NIFTY.

By looking at the first graph, we can’t say anything. But with the second graph, we can comfortably conclude how our portfolio has been performing, compared to Nifty. We can easily find out how our portfolio was performing to Nifty, on historical dates also.

Now we know the importance of benchmarking and custom indices and their role in making portfolio tracking simple, easy and efficient.

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.

Let’s take an example to understand different types of weighting schemes that can be used to construct portfolios. Suppose you are very impressed with government’s announcement regarding recapitalization (injecting more money) of public sector banks. You believe that this will lead to stocks of public sector banks performing well in the future and want to invest in the same. You have read smalltalk’s article on benefits of diversification and know that you need to invest in multiple banks, rather than just one banking stock, to avoid company specific risk. Thus, you decide to invest in the following 5 public sector banks

1. State Banks of India (SBI),
2. Punjab National Bank (PNB),
3. Bank of Baroda (BOB),
4. Bank of India (BOI) and
5. Allahabad Bank (ALBK).

In total, you want to invest a sum of INR 50,000 in these stocks. Now the question is how much should go into each stock? This is determined by weighting scheme. Generally, there are 3 different types of weighting schemes:

1. Equi-Weighted
2. Market-cap Weighted
3. Custom Weighted

Let’s look at the first two in detail

In this article, we will only be talking about equity portfolios. If you speak to any experienced equity investor, the first advice would be to always maintain a well-diversified portfolio. Before going into benefits of maintaining a well diversified portfolio, let’s understand the risks associated with equity investing and the meaning of diversification.

When you invest in any stock, there are two types of risks associated with this investment. First one is the company specific risk. This is the risk of something wrong happening specifically with the company you have invested in. For example, production stoppage due to a labour strike is a company specific risk, as it will only impact the stock price of the company experiencing it. Similarly, resignation of a CEO having successful track record is an example of company specific risk, as it will not have any impact on the prices of other stocks. The second type of risk is the broader market risk. This is not specific to any company in particular and affects the stock prices of all companies. For example, government not being able to pass important reforms in parliament is an example of market risk, as it will impact the whole economy and thus all the companies. Similarly, a natural calamity will impact all the companies equally and is an example of market risk. Thus, any risk impacting only the stock price of a particular company is company specific risk and the risks impacting stock prices of all the companies equally are market risks.

Having understood the risks associated with equity investing, let’s see how can we minimize them and protect ourselves. Suppose you have invested in Maruti and Tata Motors, and your friend has invested in Maruti and Sun Pharma. In such a scenario, if auto sales numbers start dropping in all probabilities you will experience more loss than your friend. Both the companies you have invested in belong to the auto sector and stock price of both will be impacted by this news. But in your friend might not experience any loss with his investment in Sun Pharma, as the auto sector news will not have any impact on a pharma stock. This is a very basic example of diversification. Diversification comes from investing in unrelated stocks and is the key to risk minimization. If your portfolio has 10 banking stocks and your friend has 10 stocks from 10 different sectors, obviously your losses will be very high, compared to your friend, if any bad news regarding banks hit the market. Your friend has protected himself by investing into different unrelated stocks providing protection against sector or company specific risk.

As discussed, through diversification (investing in unrelated stocks) we can protect ourselves against company/sector specific risk. But the market risk is non-diversifiable. Even if you invest in 10 different stocks from various sectors all will be negatively impacted with a news like higher taxes, instable government or large scale natural calamity. Thus, we cannot diversify away the market risk. But on the contrary all the company specific risk is diversifiable by investing in lots of unrelated stocks.

As we keep on increasing the number of stocks in the portfolio, company/sector specific risk keeps on decreasing.

As shown in the graph below, it is generally believed with 30 stocks you can completely diversify away the specific risk and only risk remaining in your portfolio would be market risk.

Let’s continue with the same example which we discussed in the last article. Five years back, Mr Trump had invested INR 50,000 in Reliance, INR 20,000 in Maruti and INR 25,000 in SBI. The current values of these investments in Reliance, Maruti and SBI are INR 35,000, INR 30,000 and INR 40,000, respectively. Thus, the total portfolio networth changed from INR 95,000 to INR 1,05,000.

The total cumulative value of Mr Trump’s investment increased by INR 10,000 (=1,05,000 – 95,000), in last 5 years. In last article we defined networth as the sum of values of all the investments. We can also define it as the amount that Mr Trump will receive, if he wants to liquidate his investments(sell whatever he owns). Suppose, today Mr Trump wants to take out all his money. He can sell shares of Reliance and get INR 35,000. Similarly, he can get INR 30,000 and INR 40,000, by selling all the shares of Maruti and SBI, respectively. The total money that he can generate by selling all his investments is INR 1,05,000 which is equal to the portfolio networth. We can say that Mr Trump will receive additional INR 10,000 on his investment of INR 95,000, if he decides to liquidate all investments. Thus, the current return generated by his portfolio is 10.53% (=10,000/95,000) or in other words, he can receive a return of 10.53%, if he sells off everything and liquidate his portfolio today.

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

Using the same logic, we can say that Reliance, Maruti and SBI generated a return of -30% (-15,000/50,000), 50%(10,000/20,000) and 60%(15,000/25,000), respectively. In our last article, we mentioned that by looking at the above two pie charts we can easily conclude that Reliance has generated less returns than SBI and Maruti. The calculations that we just did also proves the same thing, but there is also an intuitive way of deducing this result. We defined weight of an instrument as the portion of total portfolio value represented by the instrument. Reliance’s weight in the portfolio dropped from 53% to 33%, which means that value of portfolio represented by Reliance dropped by 20%. This can happen only if the value represented by SBI and Maruti increases by 20%. Maruti now represents 29% (8% more than the initial composition) and SBI represents 38% ( 12% more than the initial composition). Thus, SBI experienced the highest growth, followed by Maruti and then Reliance. One look at the above charts and we can clearly see that blue portion represented by Reliance shrunk while the green and Red portion represented by SBI and Maruti grew. Thus, growth in value of the investment in Reliance would be definitely less than SBI and Maruti.

A portfolio is a collection of financial instruments

Your portfolio is a selection of financial instruments in which you have invested your money. By financial instruments we mean various investment options like Shares, Mutual Funds, Real Estate, Banks Fixed Deposits and Bonds.

Let’s taken an example to understand this. Suppose, five years back Mr Trump made 3 different investments. He put INR 20,000 in stocks, INR 15,000 in mutual funds and INR 10,000 in Bank FD. The total initial portfolio value of Mr Trump was INR 45,000, as represented in the first pie chart below. This total portfolio value is called networth. Today, the same investments have grown and the value of the stocks that Mr Trump bought is INR 30,000, value of the mutual funds is INR 20,000 and amount in Bank FD is INR 12,000. So the current total portfolio networth of Mr Trump is INR 62,000, as shown in the second pie chart.

As you can see in the above pie charts, weight of stocks in Mr Trump’s portfolio increased from 45% to 49%. Weight of any instrument is current value of the instrument divided by the portfolio networth. It shows the portion of total networth represented by a particular instrument. Initially the value of the stocks was INR 20,000, so the initial weight was 22% (20,000/45,000). After five years, the value of the stocks is INR 30,000 and total networth is INR 62,000. Thus, the current weight is 49% (30,000/62,000).

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Instead of investing in different types of financial instruments, one can invest in different financial instruments of the same type. For example, you can buy 3 different stocks. In this example, the instrument type is Equities (shares) for all the investments. Let’s take the same example again. This time instead of three different types of instruments, Mr Trump bought 3 different stocks – Reliance, Maruti and SBI. He put INR 50,000 in Reliance, INR 20,000 in Maruti and INR 25,000 in SBI. After 5 years, current value of these investments in Reliance, Maruti and SBI are INR 35,000, INR 30,000 and INR 40,000. These pie charts show what happened with Mr Trump’s portfolio in last 5 yrs.

By looking at above charts, we can easily conclude that Reliance generated less returns compared to Maruti and SBI, in last 5 years.

 

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.

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:

Stock	Investment	Weight
SBI	10,000	20%
PNB	10,000	20%
BOB	10,000	20%
BOI	10,000	20%
ALBK	10,000	20%
Total	50,000	100%

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:

Stock	Investment	Weight	Current Market Price	Shares
SBI	10,000	20%	164.65	60.73
PNB	10,000	20%	76.15	131.32
BOB	10,000	20%	139.60	71.63
BOI	10,000	20%	87.40	114.42
ALBK	10,000	20%	44.15	226.50
Total	50,000	100%

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.

Stock	Investment (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])
SBI	10,000	20%	164.65	60.73	61	10043.65	20.06%
PNB	10,000	20%	76.15	131.32	131	9975.65	19.93%
BOB	10,000	20%	139.60	71.63	72	10051.20	20.08%
BOI	10,000	20%	87.40	114.42	114	9963.6	19.90%
ALBK	10,000	20%	44.15	226.50	227	10022.05	20.02%
Total	50,000	100%				50056.15	100%

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.

Portfolio Dividend Yield

A stock’s dividend yield measures its annual dividends as a percentage of its price. More about the ratio can be read here.

A portfolio’s dividend yield represents the total annual dividend income from the portfolio as a percentage of the current net worth of the portfolio

A high dividend yield number is good as it indicates that the investor received more dividends from the companies in his / her portfolio.

So how does one know whether the dividend yield he / she has earned is high or low? Obviously either by comparing the portfolio dividend yield with the benchmark dividend yield or by comparing the current dividend yield of the portfolio with its’ historical numbers.

However one has to be careful before drawing broad conclusions about the dividend yield of a portfolio. A portfolio might earn low dividends due to a number of reasons. Companies growing at a fast pace conserve cash and do not pay out dividends. Companies making losses continuously might also not have spare cash to pay dividends. If the investor’s portfolio has a lot of fast growing companies or a lot of loss making entities, dividend yield will be low. However the first case is good for the investor because share prices of fast growing companies also grow fast, thereby earning good return on investment. Low dividend yield because the portfolio has a lot of loss making companies will affect the investor 2 ways. He/ she does not earn dividend income and at the same time company’s share prices might also drop resulting in loss on investment.

Hence investor should understand the portfolio companies better before interpreting the dividend yield number.

When & How to Rebalance?

There are 3 basic strategies one can adopt to decide when to rebalance a portfolio:

1. Time-only rebalancing strategy : In this case, portfolio is rebalanced at regular intervals like quarterly, semi-annually or yearly. Regardless of how much or how little weights of constituents within a portfolio drift from their target, rebalancing will be done only at a pre determined time. Determining the frequency of rebalancing depends mainly on how much risk an investor wants to take, an investor who wants to avoid risk will rebalance more and vice versa.
2. Threshold-only strategy : This strategy involves rebalancing the weights of the portfolio only if they drift away from the weights set on day 0 by a predetermined margin, like 2%, 5% or 10%. The frequency of rebalancing is irrelevant and might happen as regularly as once every month or once every 3 years.
3. Time and threshold : Portfolio will be rebalanced on a scheduled basis (monthly, quarterly or annually) only if its weight has drifted away from the weight set on day 0 by a predetermined minimum rebalancing margin, such as 2%, 5%, or 10%. If at the time of rebalancing, the portfolio’s weights have deviated by less than the predetermined margin the portfolio will not be rebalanced. If the portfolio’s weights drifts by more than the minimum margin at an intermediate time period, the portfolio will then not be rebalanced.

Now let’s understand the process of how a portfolio should be rebalanced.

STEP 1: Recording target portfolio mix and target rebalancing schedule

When purchasing the scrip’s, record the total cost of each security and the total cost of the portfolio. Number of shares bought will be contingent on the desired portfolio weight of each security. First decide on the rebalancing strategy to be adopted, time and threshold strategy is comprehensive and is the recommended strategy. For illustration purpose let’s assume a margin of 10%, i.e if the weights change by more than 10% portfolio will be rebalanced. The period of rebalance will be quarterly. So if the weights change by more than 10% during a quarter, the weights will be rebalanced at the end of the quarter.

Here’s a sample equi-weighted portfolio:

Stock	Day 0
	Number of shares	Market Price	Net Worth	Weight of Stocks
SBI	61	164.70	10,043.70	20.10%
PNB	131	76.20	9,975.70	19.90%
BOB	72	139.60	10,051.20	20.10%
BOI	114	87.40	9,963.60	19.9%
ALBK	227	44.20	10,022.10	20.0%
Total			50,056.20	100%

STEP 2: Compare the actual weight with the target weight after 3 months

Stock	Day 0				End of Q1			Target Weights
	Number of shares	Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks	Low Limit	High Limit	Rebalancing Required?
SBI	61	164.70	10,043.70	20.10%	214.0	13,056.70	24.9%	10.1%	30.1%	No
PNB	131	76.20	9,975.70	19.90%	72.3	9,476.90	18.1%	9.9%	29.9%	No
BOB	72	139.60	10,051.20	20.10%	148.0	10,654.30	20.3%	10.1%	30.1%	No
BOI	114	87.40	9,963.60	19.9%	97.9	11,159.20	21.3%	9.9%	29.9%	No
ALBK	227	44.20	10,022.10	20.0%	35.3	8,017.60	15.3%	10.0%	30.0%	No
Total			50,056.20	100%		52364.80	100%

At the end of 1st quarter no rebalancing action is required, though weights of shares have moved, they are within the margin.

Lets analyze the same portfolio 3 months later:

Stock	Day 0				End of Q2			Target Weights
	Number of shares	Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks	Low Limit	High Limit
SBI	61	164.70	10,043.70	20.10%	312.80	19,082.90	30.8%	10.1%	30.1%
PNB	131	76.20	9,975.70	19.90%	83.80	10,973.20	17.7%	9.9%	29.9%
BOB	72	139.60	10,051.20	20.10%	195.40	14,071.70	22.7%	10.1%	30.1%
BOI	114	87.40	9,963.60	19.9%	120.60	13,749.80	22.2%	9.9%	29.9%
ALBK	227	44.20	10,022.10	20.0%	17.70	4,008.80	6.5%	10.0%	30.0%
Total			50,056.20	100%		52364.80	100%

We can see that SBI and Allahabad Bank have breached the 10% margin and hence the portfolio will have to be rebalanced.

STEP 3: Buy and/or sell shares to rebalance

The number of shares to be bought or sold is as below:

Stock	Bought on Day 0	Position after rebalancing	Buy (/Sell)
SBI	61	33	-28
PNB	131	122	-9
BOB	72	53	-19
BOI	114	85	-29
ALBK	227	584	357

Rebalancing allows us to reap the full benefit of diversification and hence should be carried out regularly.

 

Market-Cap Weighted

Here we want to give stock weights in proportion to their market capitalization. To understand the meaning of market capitalization, read our article What is an Index. To calculate the weight of each stock, we divide stock market cap by the total market cap of all stocks in the portfolio, as explained in the table below. Also, we know weight of an instrument is the portion of total portfolio value represented by that particular instrument. So the investment into each stock will be its weight multiplied by the total portfolio investment of INR 50,000.

Stock	Market Cap in INR cr (C)	Weight (C/sum[C])	Investment in INR
SBI	1,25,330	68.76%	34,378.81
PNB	14,952	8.20%	4,101.43
BOB	32,253	17.69%	8,847.20
BOI	7,092	3.89%	1,945.38
ALBK	2,651	1.45%	727.19
Total	1,82,278	100.00%	50,000

We will follow the same steps when we used the equi-weighted scheme.

The next step is to calculate shares of every stock, based on the investments that we calculated in the above step. Number of shares would be equal to investment in the stock divided by its current market price. We know that the share calculated in the last step might be fractional and thus non-executable on the exchange. For this reason, we change the fractional number of shares to nearest whole number. Once we have no of shares, actual investment amount is equal to no. of shares multiplied by current market price and final weight would be total actual investment divided by individual stock investment.

Stock	Weight (A)	Investment in INR (B=A x 50,000)	Current Market Price (C)	Shares (D = B/C)	Rounded Shares	Actual Investment in INR (E = D1*C)	Final Weight (E/sum[E])
SBI	68.76%	34,378.81	164.65	208.80	209	34411.85	68.90%
PNB	8.20%	4,101.43	76.15	53.86	54	4112.10	8.23%
BOB	17.69%	8,847.20	139.6	63.38	63	8794.80	17.61%
BOI	3.89%	1,945.38	87.4	22.26	22	1922.80	3.85%
ALBK	1.45%	727.19	44.15	16.47	16	706.40	1.41%
Total	100.00%	50,000				49947.95	100.00%

In the market cap scheme, SBI has a weight of 68.09%, compared to 20.06% that we calculated in the equal weight scheme. Thus, market cap portfolio will be more exposed and sensitive to movement’s in SBI stock price, compared to equal-weight. This is happening because majority of your money is still concentrated in one particular stock and company specific risk is very high in the absence of proper diversification.

The third type of weighting scheme which we mentioned in our last post is Custom. In the eual-weight scheme the investment was divided equally among all the stocks. In the Market-cap scheme, it was divided based on the market capitalization of individual stocks. In Custom scheme, there is no set patter to derive this amount. Here the decision could be based on some exclusive information or investor’s gut feeling. For example, you might believe that PNB is expected to perform better than other stocks, then you can give a higher weight to PNB, compared to others. Once weighting scheme is decided, rest of the steps are similar to market-cap and equal-weight schemes.

Read the next post to learn how to calculate portfolio risk and return based on a custom index.

Portfolio Beta

Beta is a measure of market risk. If the beta of a stock is more than 1, it means stock moves along with the market in the same direction and is more volatile than the market. If the beta is less than 1, it means that stock is less volatile and not related to the market.  Read more about beta here.

Similar to stock beta, a portfolio beta represents the volatility of the portfolio. In one of the earlier chapters we understood the benefit of diversification and how it allows us to protect ourselves against company/sector specific risk. However market risk – risk that is not specific to any single company and affects all the companies in the market – is not diversifiable. A portfolio beta represents market risk.

Portfolio beta helps us understand the direction of the portfolio movement and the strength of the portfolio movement in comparison to the market

If the beta of the portfolio is more than 1, it means that the portfolio moves in the same direction as the market and at a faster pace than the market. Similarly if beta is less than 1 it means portfolio does not move in tandem with the market. So let’s assume imaginary portfolio X has a beta of 1.3. Suppose the market is expected to increase by 1% on a particular day, portfolio X can be expected to increase by 1.3% (1% * 1.3). Similarly if imaginary portfolio Y has a beta of -0.8, then on a day market is expected to increase by 1%, portfolio Y can be expected to decrease by 0.8% (1% * -0.8).

Portfolio beta is the weighted average beta’s of the individual stocks of the portfolio. Proportion of company’s weight in the portfolio can be used as the weight when calculating portfolio beta. So portfolio beta can be altered by changing stocks in the portfolio. If the investor expects the market to go up over the next 1 year, then he can add high beta companies to his portfolio to enhance portfolio returns. On the contrary if the markets are expected to drop over the next 1 year, the investor can load up his portfolio with low/ negative beta stocks thereby protecting portfolio returns.