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Although this is off-topic, a little digression doesn't hurt anyone. This chapter will be the most special of all the ones I've written in Varsity. It is not because of the topic I will be discussing. It's because of where I am sitting now, and the fact that I am writing this for you. It is 6:15 am. 360 degrees surround me are misty mountains. The landscape can't get better. Only one small shack is there, with a little music player playing Bob Marley's Redemption Song. It doesn't get much better. For me, it's not enough.
But, it's back to school
In the previous chapter, we discussed Portfolio Variance. If we don't put this information to good use, it would be futile to crunch all the numbers in order to determine the portfolio's variance. In the next two chapters, we will accomplish exactly this.
In the next two chapters, we'll try to do the following:
This chapter continues the discussion that was panned out in previous chapters. This chapter is contextualized. If you're reading this chapter and don't know what happened in the previous chapters, I suggest that you read those chapters first.
This will allow us to create an equity curve for our 5 stock portfolio. A typical equity curve allows you to visualize the portfolio's performance on a 100-point normalized scale. It will show you how Rs.100/invested in this portfolio would perform over the specified period. This can be used to compare the portfolio's performance with its benchmark, such as Nifty 50 or BSE Sensex.
To gain deeper insight into the portfolio, there are some attributes that can be extracted from the equity curve. We'll get there in a second.
Let's build an equity curve to represent the five stock portfolios. To create our portfolio, we used the following stocks. We also gave random weights to each stock. These are the stock names and weightages.
| Stock Name | Investment Weight |
|---|---|
| Cipla | 7% |
| Idea Cellular Ltd | 16% |
| Wonderla | 25% |
| PVR | 30% |
| Alkem | 22% |
What does "Investment weight" mean? It is the amount of your corpus that has been invested in the stock. So, for example, of Rs.100,000.00, Rs.7000/- was invested in Cipla, and Rs.22,000/– in Alkem Lab. And so on.
Normalizing the portfolio to Rs.100 is a common practice when developing an equity curve. This allows us to see how an investment of Rs.100/in this portfolio performed over the investment period. This information has been incorporated in an excel sheet. Please note that the excel used here is the continuation of the excel used previously in this chapter.
Take a look at this image -
(image)
I added a new column to the daily returns column, and also included the stock's weight. You will see two new columns at the end: starting value at 100 and totalweight at 100%.
This is the starting value. It's basically the amount of money that we start with. This is Rs.100/-. This means that out of 100 Rupees total corpus Rupees 7 are being invested in Cipla. Rupees 16 and Idea, Rupees 25 in Wonderla, and so on.
If I add the individual weights together, they should all add up at 100%. This indicates that Rs.100 has been invested 100%.
Now we need to look at how each stock performed. Let's start with Cipla to help you better understand the situation. Cipla has a weight of 7%. This means that out of Rs.100 there is Rs.7 invested in Cipla. Our money, i.e. Rs.7/-, changes based on the daily Cipla price movement. Important to remember that if Rs.7 becomes Rs.7.5/- on day 1, then our starting price will be Rs.7.5/- the next day. This is how it looks when I did this calculation on Excel for Cipla.
(image)
Cipla traded at 579.15 on the 1st of September, and this was the day that we decided to put Rs.7 into the stock. Although technically this is impossible, for the sake this example, we will assume it is possible. On day 1, 7 was invested. Cipla closed at 577.95 on the 2nd September, down -0.21% over the previous day. Also, this means that we lose -0.21% of our Rs.7/- investment to make it Rs.6.985. Cipla rose by 0.11% to 578.6 on 6 September, so we gain 0.11% from 6.985 to make 6.993. The rest of these data points are listed below.
Here's how my portfolio looks after I did the math.
(image 3
I have highlighted in blue the daily fluctuations in all stocks' prices.
Think about this: I have divided Rs.100/- among 5 stocks and made different investments. The daily variation in each stock should give me the total daily fluctuation of Rs.100. This gives me a better understanding of how my portfolio is performing. Let's add them up to see how Rs.100 invested in 5 stocks moves each day -
(image 4
Addition of daily portfolio values gives me the time series of daily fluctuations.
(image 5
If you plot the chart, which is the time series data for the daily normalized portfolio valuation, an 'Equity Curve (EQ curve), can be created. Normalized is the fact that I have reduced my investment to Rs.100/.
Here is the EQ curve of the portfolio we have -
Image 6
It's that simple. The Eq curve is a popular method of visualizing portfolio performance. This gives an estimate of the portfolio's returns. This case involved an initial investment of Rs.100/– and the portfolio was valued at 113.84 at the end 6 months later. Take a look at this image.
image 7
Without much thought, I can tell you that the portfolio performed close to 13.8% over the period.
Here's something to consider. We calculated the portfolio variance in the previous chapter. One of the most important things to calculate while doing this was the stock's standard deviation. As you might know, standard deviation is the stock's volatility. It is the stock's risk.
We used the excel function '=STDEV() to calculate the standard deviation. This was applied to the stock's daily return. Think about it: We still have the portfolio's daily value, although this is normalized to Rs.100.
Consider the entire portfolio as one stock. Now calculate its daily returns. Similar to how we calculated daily returns for the stocks in chapter 1. What if I use the '=STDEV() function to calculate the portfolio's daily returns? The portfolio's standard deviation, also known as risk, should result in the value.
Can you see where we are going? Yes, it is possible to calculate portfolio variance using a completely different approach.
Let me copy the portfolio variance value that we calculated in the previous chapter to help you understand this better.
(image 8
The matrix multiplication and correlation matrix techniques were used to calculate the value above.
Now we will examine the portfolio as a whole, and calculate the daily returns for the normalized portfolio value. We should get a value that is equal or close to the portfolio variance calculated before.
I added a column to the daily portfolio normalized valuation and calculated Portfolio's daily returns-
(image 9
Once the returns are in place, I will apply a standard deviation function to the time series data. This should produce a value that is close to the portfolio variance value.
image 10
The STDEV function returns the exact same value.
We will be using the portfolio variance in the next chapter to estimate expected returns and optimization.
Quick Task - Let me leave you with this quick task. Random weights have been assigned to the stocks. You can change the stock weights to see the effect on overall returns. Please comment below with your observations.