Understanding 'Risk Management & Trading Psychology'

Lesson -> The Expected Returns

7.1 - Expected Returns

These chapters will provide valuable insight, particularly for those who are not familiar with portfolio techniques. We will explore the areas of portfolio optimization and expected return framework. The concept of portfolio optimization, which we will cover in the next chapter, is like a magic wand. It helps you decide how much you should invest in a stock (within your portfolio) to achieve the best return and risk. These topics are not something that the financial elite prefer to discuss, but we will be discussing them today and working towards making financial knowledge accessible to all.

Please note that you will need to be familiar with the topics we have covered in the preceding chapters to fully understand this discussion. Please read them if you haven't already. These are high quality materials and you will be a better market participant if they are read only a few times. This excel sheet is a continuation from the one in the previous chapters.

Let's get started, assuming that you are ready.

It's time to put the portfolio variance to use. Let's start by taking a look at the portfolio variance number that was calculated in the previous chapters.

(image 1

What does this number tell us?

This number will give you an indication of the level of risk associated with your portfolio. We used daily data to calculate the Portfolio Variance, which represents daily risk.

Risk, variance, or volatility are like two faces to a coin. Risk is any price movement below our entry prices. Return is the opposite. The variance data will be used soon to determine the expected range in which the portfolio will move throughout the year. You will know where we are going if you have read the Options module.

Before we can do that, however, it is necessary to calculate the expected return on the portfolio. The portfolio's expected return is simply the sum of the stock's average return multiplied with its weight, and then multiplied again by 252 (number trading days). We are simply scaling the daily returns to their annual return and scaling it according the amount of investment we made.

Let's calculate the expected return on the portfolio we have. I'm certain you will be able to understand it better. Let me start by putting together the following data:

(image 2

The first three columns are quite simple, I think. Simply multiply the daily average return with 252 to get the last column -- this is a simple step to annualize stock returns.

Example: Cipla - 0.06% *252 = 15.49%.

What does this all mean? Let's say that I invested all my money in Cipla, and not any other stocks. If this is the case, the Cipla weight would be 100%, and I can expect a 15.49% return. The expected return on Cipla is - however, I have only invested 7% of my capital.

Weight * Expected Return

= 7% * 15.49%

1.08 %

This can be generalized at portfolio level to obtain the expected return on the portfolio - . (image 3)


Wt = Weight for each stock

Rt = Expected annual stock return

Here's what I have:

(image 4

We have reached two very important parameters for our portfolio at this point. These are the expected portfolio returns 55.14% and the portfolio variance of 1.11%.

We can actually scale the portfolio variance to reflect the annual variance. To do this, multiply the daily variance by the Square root of 252.

Annual variance =

= 1.11% * Sqrt (252


These important numbers will be kept aside.

Now it is time to go back to our discussion about normal distribution using the options panel.

I suggest that you read the "Dalton board experiment" and quickly understand normal distribution. This will allow you to form an opinion about future outcomes. It is crucial to understand normal distribution and its characteristics at this stage. Before you proceed, I encourage you to go through it.

Portfolio returns are usually distributed. I won't plot the distribution of a portfolio here so you might be able to do it as an exercise. However, it is possible to obtain a normal distribution portfolio if you plot the distribution. If the portfolio is not normally distributed, we can predict the expected return over the next year.

Simply add the portfolio variance to the expected annualized returns to estimate the return. This will give you a certain level of confidence. This will give us an estimate of how much the portfolio will earn or lose in a given year.

Also, we can predict the range in which the portfolio will fluctuate based on normal distribution. This predication is accurate at three levels.

  • Level 1 - 68% confidence, one standard deviation away
  • Level 2 - Two standard deviation away, 95% confidence
  • Level 3 - Three standard deviations away from 99 percent confidence

Variance is measured in terms standard deviation.

So, 17.64% represents 1 standard deviation. Two standard deviations are 17.64% * 2. = 35.28%, and three standard deviations would be 17.64%* 3. = 52.92%.

This may not make sense if you're reading it for the first time. It is therefore important to know the characteristics of normal distribution. The same is explained in the options section (link provided earlier).

7.2 - Estimating portfolio range

We can now estimate the range in which portfolio returns will vary over the next 12 months based on the annualized variance (17.64%), and the expected annual return (55.14%). When we talk about a range, it is not about a lower or higher bound number.

The annualized portfolio variance must be added to the expected annual returns to calculate the upper bound. This is 17.64% + 5.15 = 72.79%. The lower bound range can be calculated by subtracting the annualized portfolio variance (i.e. 55.15% - 17.64% = 37.51%).

If you asked me how the returns would be if I decided to keep the five stock portfolio for the next year, my answer would be +37.51% to +72.79%.

At this stage, three quick questions may arise.

  1. This range indicates that the portfolio doesn't lose any money. How is this possible? The worst-case scenario still has a staggering +37.51% which is actually quite amazing.
    1. It sounds strange, it is true. The range calculation is based on statistics. We are currently in a bullish market (April 2017 - May 2017 as I write this), and the stocks we selected have shown good trending. The numbers that we have here are clearly biased. We should have taken data from at least the last year to get a full picture of the range. This is not important. Our goal is to learn and not debate stock selection.
  2. Okay, you may be convinced about the range calculation. But what guarantee is there that portfolio returns will vary between 37.15% to 72.79%?
    1. As I said, we are dealing at level 1 (standard deviation). The confidence is only about 68%.
  3. What if I need more confidence?
    1. In this instance, you'll need to shift gears towards higher standard deviations.

Let's do it now.

We must shift gears to calculate the range with 95% confidence. This means that we need to multiply the 1 standard deviation number with 2. This is because we have already done this math before and know that the 2 ndSD is 35.28%.

This would mean that the portfolio's potential return over the next year with 95% confidence, would be -

Lower bound = 55.15% - 35.28% = 19.87%

Lower bound = 55.15% + 35.28 = 90.43%

Further, we can increase our confidence to 99%.You can also examine the return range for 3 standard deviations. This is because at 3 SD, the variance is 52.92%.

Lower bound = 55.15% - 52.92%% = 2.23%

Lower bound = 55.15% + 52.92 = 108.07%

You may have noticed that the greater the confidence level, so the wider the range. This chapter will be concluded with a list of tasks.

  1. You can plot the frequency distribution of this five stock portfolio. Watch the distribution and see if there is a bell curve.
  2. The range is for one year. What if we were to calculate the range for three months or three weeks? What would you do?

These tasks will be amazing if you attempt them. 

To Summarize

  1. The portfolio's returns are dependent on the stocks included in it.
  2. To calculate the impact of a stock on the overall portfolio's returns, one must multiply the average return by the stock's weight.
  3. The portfolio's expected return is the sum of all the returns from each stock (which is based on its weight).
  4. You can convert the daily variance to an annualized variance by multiplying by square root 252
  5. We calculate the portfolio variance using the default 1 standard deviation value
  6. We simply need to multiply the 2 nd and the 3 rdSD by 2, and then add 3
  7. You can calculate the expected return on your portfolio as a range
  8. We simply need to subtract the expected return from the portfolio's variance in order to get the range.
  9. Each standard deviation has a confidence level. Higher standard deviations will give you a higher level of confidence.