  # Equity Curve what is, how to Construct and Risk Assessment

Equity Curve

We will use this chance to create an equity curve for the five-stock portfolio. This curve visually reveals the performance of said portfolio on a normalised scale of 100. It also gives us insight into how a Rs. 100 invested in this portfolio would fare throughout the allotted period. Moreover, we can use it to compare the portfolio’s results with its benchmark, such as Nifty 50 or BSE Sensex.

We can uncover useful information about our portfolio by examining its equity curve. We will explore this further shortly.

We shall now construct an equity curve for the 5 stock portfolio. We assigned random weights to these stock to form our portfolio – here are their names and weightings:

What is ‘investment weight’? This term describes the proportion of your corpus invested in any given stock. Say that out of Rs. 100,000/-, you have put Rs. 7,000/- in Cipla and Rs. 22,000/- in Alkem Lab- it gives you a better idea of how these investments measure up against one another.

Developing an equity curve often involves normalising a portfolio to Rs.100. This enables us to observe the behaviour of an investment of Rs.100/- across the duration. This process is included in the same excel sheet used in the preceding chapter.

Take a look at the image below –

Gaze upon the image presented here –

I have added a column beside the daily return column, which contains the weight of each stock. Lastly, two more columns are included – with the starting value set to 100 and the total weight at 100%.

The starting value is Rs.100/-. This total corpus will be distributed with Rs.7 in Cipla, Rs.16 in Idea, Rs.25 in Wonderla and so forth.

Adding the individual weights together should amount to 100%, representing that all of Rs.100 is being invested.

Let’s use Cipla as an example to shed light on how our investments have performed. We have assigned 7% of a Rs.100 sum to it, which equates to Rs.7 investment. Depending on the daily price movement, this amount either increases or reduces. It is crucial to note that if Cipla’s value rose from Rs.7 to Rs.7.5, then the next day we start at Rs.7.5 and not Rs.7 – I’ve used Excel for this calculation and these are the results it yield

On September 1st, Cipla closed at 579.15 when we decided to invest Rs.7 in the stock. We understand that this is not a realistic figure, but let us just assume it is possible and move on. On day one, we invested our Rs.7 and the following day, Cipla dropped by -0.21%, so we lost 0.21% of our total investment of Rs.7, which meant 6.985 was left in our account value by 2nd Sept. By 6th Sept, Cipla had gone up by 0.11%, so we gained 0.11% on 6.985 bringing our account balance back up to 6.993 from there onwards through the rest of the data points.

After assessing all the stocks in my portfolio, here’s the table-

The daily variation in stocked prices and underlined it in blue have been calculated.

Let me investigate how my Rs.100, invested across five stocks, varies day-to-day. By summing up the daily changes in each stock, I can track the total fluctuations of this portfolio. Doing this will give me a better outlook on how my investments are maturing. Let’s add them up and see what happens!

An ‘Equity Curve’ (EQ Curve) can be created by plotting the time series data of daily normalised portfolio value, as it has been scaled down to Rs.100/-.

This is the EQ curve that we have for our portfolio.

It is effortless to use the Eq curve to observe the portfolio performance; it provides a fast assessment of the gains generated. In this case, we had invested Rs.100/- and ended up with Rs.113.84 six months later, which we can see in the accompanying image.

I’m aware that the portfolio’s performance over the timeframe has been around 13.8%.

– Portfolio as a whole

Now, consider the fact that in the last chapter we worked out the portfolio variance. This involved calculating the standard deviation of each equity position. You probably know that this indicates volatility, which is basically the risk associated with every stock.

We calculated the standard deviation by using the ‘=STDEV()’ Excel function on the daily return rate of the stock. Take note: We had already obtained the daily value of the portfolio (which was normalised to Rs.100).

Let us imagine the portfolio as a single stock and compute its daily returns, similar to how we did with the stocks in the prior chapter. We can then apply the ‘=STDEV()’ function on these results for a value that stands for risk (otherwise known as Variance of the portfolio).

For further understanding, here is the portfolio variance value we calculated in the preceding chapter

We computed the aforesaid value with matrix multiplication and correlation matrix method.

We shall now analyse the entire portfolio, computing the daily returns of its normalised value. Doing so should give us a standard deviation figure close to that of the portfolio variance we found earlier

I have added a column to the daily regularised portfolio value and calculated the Portfolio’s daily yields.

Once I have the returns in place, I can use the standard deviation function on the time series data to estimate a value near our previous portfolio variance determination.

That’s right, the STDEV function yields the same result!