  # Expected Returns: Calculating Portfolio Performance and Range Projection

Expected Returns

We must take advantage of the portfolio variance. Let us assess the portfolio variance figure deduced in past chapters –

Portfolio Variance- 1.11%

What can we learn from this figure?

The number tells you the extent of the risk attached to the portfolio. We examined data from a single day, so the Portfolio Variance of 1.11% is concerning on a daily basis.

Risk, variance or volatility is like a coin with two faces. Any price fluctuation below our entry point is deemed a risk and, simultaneously, any shift above it would be termed a return. In the near future ,we will analyse the data we have of the variance to determine what range of movement the portfolio should experience over the course of one year. If you’ve read the Options module, you’ll probably anticipate where this is heading.

We need to calculate the expected return of the portfolio. This is done by adding the average return of each stock multiplied by its weight, and then multiplying that sum by 252 (number of trading days). This allows us to scale the daily returns to their annual figure, taking into account our investments.

Let’s figure out the anticipated yield of the portfolio we have. To start with, here is what I have organized the data like –

The initial three columns are relatively easy to comprehend. The last one is just the product of the daily average yield multiplied by 252, which is a process to convert the stock’s return into an annual rate.

For eg, (Cipla) – 0.06% * 252 = 15.49%.

This implies that if my entire capital were invested in Cipla, the return would be 15.49%. However, with only 7% of my capital allocated to the stock, I should anticipate a lesser yield.

Weight * Expected Return

= 7% * 15.49%

=1.08%

The expected return of the portfolio can be determined by generalising this at a higher level.

Where,

Wt = Weight of each stock

Rt = Expected annual return of the stock

I used the same approach for our five stock portfolio, and these are the results.

We now have two vital portfolio features – the forecasted portfolio yield of 55.14% and the portfolio risk of 1.11%.

To represent the annual variance, we can scale the portfolio variance by multiplying the daily variance by Square root of 252.

Annual variance =

= 1.11% * Sqrt (252)

= 17.64%.

We will set both these essential numbers aside.

You remember our discussion about normal distributions from the options lesson?

If not, you can refer the previous chapters.

Portfolio returns will usually follow a normal distribution, so if you plot the portfolio, it would likely display this behaviour. Knowing that our portfolio follows a normal pattern allows us to estimate its return over the next year with some degree of precision. Omitting plotting it here, feel free to use this as an exercise.

To get an accurate idea of what our portfolio return could be, we simply need to add and subtract its variance from our expected annualised return. This will help us determine the amount it might bring in or lose for the year.

In other words, based on normal distribution, it is possible to observe the range within which the portfolio is likely to fluctuate. The accuracy of this assessment can vary across three levels.

Level 1 – one standard deviation away, 68% confidence

Level 2 – Two standard deviation away, 95% confidence

Level 3 – Three standard deviation away,99% confidence

It is important to take into account that the annualised portfolio variance of 17.64% is also equivalent to 1 standard deviation, which is the measure for variance.

17.64% is one standard deviation, two amounts to 35.28%, and three translates to 52.92%.

– Estimating the portfolio range

Given the annualised variance (17.64%) and expected annual return (55.14%), we can now make a projection of the portfolio’s potential returns for the next year. We are referencing a lower and upper bound to determine this range.

To determine the upper limit of our expected annual return, we simply have to add the annualized portfolio variance to our expectation, making the sum 72.79%. For the lower range, our figure is generated by subtracting the annualised portfolio variance from 55.15%, leaving us with a total of 37.51%.

If you wanted to know what the potential returns could be if you decide to keep your 5 stock portfolio over the coming year, my response would be that they may vary between +37.51% and +72.79%.

Here’s a question-

The range reveals an astonishing result: the portfolio does not suffer any losses. In fact, its worst case scenario stands at a whopping +37.51%, which can only be seen as incredible.

Agreed, it might seem a bit odd. However, the range calculation has been calculated on a statistical basis. Currently in the market (April – May 2017 as written) is in a bull market, with the stocks we have chosen doing very well. This means our numbers are likely to be quite high. To get an accurate idea of the range we should have looked at data from more than one year. But that is not what this exercise is about; the goal here is to learn the art, not to argue over stock selection.

I’m sure I’ve persuaded you of the range calculation, however how can we be certain that the portfolio returns will fall between 37.15% and 72.79%?

Since we are handling level 1 (1 standard deviation), confidence is estimated at 68%.

What if we want a higher degree of confidence?

In this instance, it is necessary to move up the scale to higher deviations.

Let’s do it now.

To determine the range of our 95% confidence interval, we must multiply the 1SD number by 2. This calculation is already familiar to us; 2 standard deviations equate to 35.28%.

We can be 95% confident that the portfolio’s return over the next 12 months will fall within a certain range.

Lower bound = 55.15% – 35.28% = 19.87%

Upper bound = 55.15% + 35.28% = 90.43%

We can boost our level of assurance to 99%, and examine the spread of the yield with 3 standard deviations. At 3 SD, the variation is 52.92%.

Lower bound = 55.15% – 52.92%% = 2.23%

Upper bound = 55.15% + 52.92% = 108.07%