Expected Returns: Calculating Portfolio Performance and Range Projection

Expected Returns

The portfolio variance figure calculated in the preceding chapters is not merely a statistical output to be noted and set aside. It is an active instrument for understanding the risk profile of a portfolio and for projecting the range within which returns might reasonably fall over a given period. This chapter puts that figure to practical use.

The portfolio variance established earlier stands at 1.19 per cent on a daily basis. This figure tells an investor how much the portfolio’s daily returns typically deviate from their average. Considered in isolation, a daily variance of 1.19 per cent may appear modest. However, its implications become considerably more meaningful when scaled to an annual timeframe and viewed alongside the portfolio’s expected return.

Before proceeding, it is worth recalling an important characteristic of risk. Variance operates in both directions. Any price movement below the entry point represents downside risk. Any movement above it represents upside return. The same statistical measure captures both possibilities simultaneously. This symmetry is central to how expected return ranges are constructed.

Calculating the Expected Annual Return

The expected return of a portfolio is calculated by multiplying the average daily return of each stock by 252, which is the standard number of trading days in a calendar year. This converts each stock’s daily average return into an annualised figure. Each annualised return is then multiplied by that stock’s weight in the portfolio. Summing these weighted annualised returns across all holdings produces the portfolio’s overall expected annual return.

The formula is expressed as follows.

Expected Portfolio Return = Sum of (Weight of each stock multiplied by Expected annual return of that stock)

To illustrate the logic with a single holding, suppose the specialty chemicals manufacturer in the portfolio has an average daily return of 0.08 per cent. Multiplying this by 252 produces an annualised return of approximately 20.16 per cent. If 22 per cent of the total corpus is allocated to this stock, its contribution to the overall portfolio expected return is 22 per cent multiplied by 20.16 per cent, which equals approximately 4.44 per cent.

Applying this calculation across all five stocks and summing the results produces the portfolio’s total expected annual return. For the five-stock portfolio used throughout this module, the forecasted annual return comes to approximately 58.30 per cent, and the daily portfolio risk stands at 1.19 per cent.

Scaling Variance to an Annual Figure

To make the portfolio variance comparable with the annualised return figure, the daily variance must be scaled to an annual equivalent. This is done by multiplying the daily variance by the square root of 252.

Annual Variance = 1.19 per cent multiplied by the square root of 252 = approximately 18.89 per cent.

This annualised variance figure is equivalent to one standard deviation of the portfolio’s annual returns. It is the core input for projecting the range within which portfolio returns are likely to fall over the course of a year.

Projecting the Return Range

Portfolio returns, like those of individual stocks, tend to follow a normal distribution when observed over a sufficiently long period. This statistical property allows investors to construct confidence intervals around the expected return, expressing the range of outcomes that are likely to occur with varying degrees of certainty.

Three levels of confidence are commonly applied.

Level 1 uses one standard deviation and carries 68 per cent confidence. This means that in roughly 68 out of every 100 years with similar conditions, the portfolio return would be expected to fall within this range.

Level 2 uses two standard deviations and carries 95 per cent confidence. This wider range captures a broader set of probable outcomes.

Level 3 uses three standard deviations and carries 99 per cent confidence. This is the widest range and accounts for all but the most extreme market conditions.

With an annualised variance of 18.89 per cent representing one standard deviation, the figures for each level are as follows.

One standard deviation is 18.89 per cent. Two standard deviations amount to 37.78 per cent. Three standard deviations amount to 56.67 per cent.

Applying the Range to the Expected Return

To determine the upper and lower bounds of likely portfolio performance at each confidence level, the standard deviation figure is added to and subtracted from the expected annual return of 58.30 per cent.

At the 68 per cent confidence level, the portfolio return is expected to fall between 39.41 per cent and 77.19 per cent.

At the 95 per cent confidence level, the range widens to between 20.52 per cent and 96.08 per cent.

At the 99 per cent confidence level, the range extends to between 1.63 per cent and 114.97 per cent.

These ranges do not guarantee outcomes. They express probabilities based on the assumption that the portfolio’s returns follow a normal distribution, which is a reasonable working assumption for a diversified multi-stock portfolio over an annual horizon.

What these projections offer is structured visibility into the spectrum of likely outcomes. Rather than holding a portfolio without any sense of what its risk implies for future performance, an investor who understands variance and expected return can approach the stock market with calibrated expectations and a clearer basis for decision-making.