Equity Curve what is, how to Construct and Risk Assessment

Equity Curve

Numbers alone tell only part of the story of a portfolio’s performance. The equity curve transforms those numbers into a visual narrative, plotting the daily value of a portfolio on a normalised scale and revealing, at a glance, how an investment has grown, contracted, or fluctuated over a given period. For any investor tracking a multi-stock equity portfolio in the stock market, the equity curve is one of the most informative tools available.

The equity curve for the five-stock portfolio constructed throughout this module is built on a starting value of 100 rupees. This normalisation to a base of 100 makes it straightforward to measure performance in percentage terms and to compare the portfolio’s results against a benchmark index such as the Nifty 50 or the BSE Sensex.

The five stocks and their assigned weights are as follows.

Pharmaceutical company at 10 per cent. Telecommunications firm at 18 per cent. Entertainment and leisure operator at 22 per cent. Multiplex cinema chain at 28 per cent. Specialty chemicals manufacturer at 22 per cent.

Building the Equity Curve

The investment weight assigned to each stock determines how the starting corpus of 100 rupees is distributed. A 10 per cent allocation to the pharmaceutical company means 10 rupees of the total corpus is invested there. An 18 per cent allocation to the telecommunications firm means 18 rupees is placed in that holding, and so on across all five stocks. The individual weights must sum to exactly 100 per cent, confirming that the entire corpus is deployed.

Once this distribution is established in Excel, the daily value of each holding is tracked by applying each day’s percentage return to the previous day’s closing value for that holding. This is a compounding calculation: if the pharmaceutical company holding opens at 10 rupees and rises by 0.35 per cent on day one, the new value becomes 10.035 rupees. The following day’s calculation begins from 10.035 rupees, not from the original 10 rupees.

To illustrate with a specific example, suppose the telecommunications holding opens at 18 rupees. On the first trading day it falls by 0.18 per cent, leaving a balance of 17.968 rupees. On the second trading day it rises by 0.22 per cent, bringing the balance to 18.007 rupees. Each subsequent day follows the same logic, with the previous day’s closing value serving as the new base.

This process is repeated for all five stocks across the full six-month observation period. Once the daily values for all five holdings are calculated, summing them across each row produces the total daily portfolio value. This time series of daily total values is what is plotted to produce the equity curve.

Reading the Equity Curve

The equity curve produced for this five-stock portfolio begins at 100 rupees and ends at approximately 116.40 rupees over the six-month period, representing a return of roughly 16.4 per cent across the observation window.

This single visual line communicates a great deal. It shows not only the final return but also the path taken to get there. A curve that rises steadily with shallow drawdowns suggests a portfolio with controlled volatility and consistent performance. A curve that swings sharply upward and downward before reaching the same final value tells a very different story about the risk experienced along the way, even if the end result appears similar.

The equity curve also makes benchmark comparison straightforward. Plotting the Nifty 50 or Sensex on the same chart, normalised to the same starting value of 100 rupees, immediately reveals whether the portfolio outperformed or underperformed the broader market over the same period and by how much.

Portfolio as a Whole

The equity curve serves a further analytical purpose beyond performance visualisation. It allows the entire portfolio to be treated as a single instrument and its risk to be measured directly.

In the preceding chapter, portfolio variance was calculated using matrix multiplication applied to the weighted standard deviations and the Correlation Matrix. That method produced a portfolio variance figure of approximately 1.19 per cent. There is an alternative and more direct route to the same figure.

By calculating the daily percentage returns of the normalised portfolio value, in exactly the same way that daily returns were calculated for individual stocks earlier in this module, and then applying the STDEV function in Excel to that returns series, the result is the standard deviation of the portfolio as a whole.

This figure should align closely with the portfolio variance calculated through the matrix method. The fact that both approaches converge on the same result is not a coincidence. It confirms that treating the portfolio as a single composite instrument and measuring its return volatility directly is mathematically equivalent to the more involved matrix calculation.

This equivalence is useful in practice. Once an equity curve has been constructed, the portfolio’s risk can be monitored on an ongoing basis simply by updating the daily return series and recalculating the standard deviation. There is no need to repeat the full matrix process each time, provided the portfolio weights remain unchanged.

Understanding both methods, and the fact that they produce the same result, gives investors a more complete and flexible toolkit for risk assessment.