Introducing the statistics of risk

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4.2

Remember how we looked at the expected returns for a stock and for a portfolio in the previous chapter? Just like that, risk also exists at two levels - at the level of each individual asset, and at the level of the portfolio as a whole. Before we get into the details of how to quantify risk, let’s first understand the case of risk at these two levels.

Say you’ve purchased 10 shares of a company. Equity, as we generally consider, is a high-risk investment. So, if you only have equity in your portfolio, the overall risk of your portfolio will also be high. Even among equity shares, some are riskier than others, just like how some deliver higher returns than others.

To balance out risk even further, you could consider investing in bonds. Bonds, particularly the government-backed ones, come with guaranteed income and so, they have practically zero risk. This will bring the portfolio risk down even further. Think of it like a nice recipe where you balance out the overall taste by adding different levels of spices, salt, and other condiments.

So, what is portfolio risk? Let’s break it down.

Decoding portfolio risk

Portfolio risk is the probability that the mix of assets in a portfolio will fail to deliver the expected portfolio returns. Each asset in the portfolio carries its own level and nature of risk, and these elements of risk together make up the risk of the portfolio, as a whole. The risk posed by the overall portfolio can theoretically be altered by modifying the constituents of the portfolio.

Let’s take a very rudimentary example to understand this.

Case 1: Consider this portfolio.

• Equity: 80%
• Bonds: 20%

At first glance, you would call this a high risk portfolio, right?

Case 2: Now, let’s move things around a bit.

• High-risk equity: 40%
• Low-risk equity: 40%
• Bonds: 20%

In this portfolio, the overall risk appears to be lower.

Case 3:  Check out this portfolio now.

• High-risk equity: 10%
• Low-risk equity: 10%
• Bonds: 80%

Clearly, this portfolio’s risk has reduced tremendously. Now, this brings us to another important topic. What influences the risk of an investment portfolio? Let’s see.

Factors that affect portfolio risk

The risk of an investment portfolio is a complex concept. Many factors play major roles in influencing this risk. This is why it’s important for you, as the investor, to understand the driving forces behind your portfolio’s risk level. Take a look at what they are.

1. The component assets in the portfolio

The assets in your portfolio greatly influence the risk in the portfolio as a whole. The logic behind this is simple. It’s common knowledge that fixed income or debt instruments tend to be less risky than equity, right? So, a debt-oriented portfolio will naturally be less risky, overall, than an equity-oriented portfolio. That is because most of the assets in the former kind bear low risk.

This is the principle behind the different types of mutual funds available for investors. Surely you’ve heard of them - equity funds, debt funds, large cap funds and so on. With every change in the assets that make up the portfolio, the portfolio risk also changes.

2. The amount of money invested in each asset class

This is basically, the proportion of your capital that you infuse into different asset classes. If you have Rs. 1 lakh, and if you invest 70% of that in debt, and the remaining 30% in equity, the risk of that portfolio will be different from the case in which you invest, say 40% in debt and 60% in equity.

Basically, we’re talking about the weightage here. If you place more of your capital on the less risky side of the spectrum, your overall portfolio will be low-risk. Conversely, if you place more of your capital in riskier assets, the risk of the overall portfolio will be high.

3. The level of diversification in the portfolio

Placing all your eggs in one basket is never a good idea. You may have no doubt heard this repeated time and time again. That is because a portfolio that is undiversified or very narrowly diversified has greater risk of loss. Think of it like this. If you have Rs. 10,000 to invest, and if you put all of that in the stocks of one company, you may feel good about that fact that you have invested. But if that company’s stock price plummets, you could end up losing a huge chunk of your capital.

On the other hand, let’s say you invest a portion of that Rs. 10,000 in the stocks of one company, and the remaining capital in the stocks of another company. And let’s say the companies belong to different industries or sectors of the economy. In this case, the chances of both the companies performing badly are lower. This, in turn, reduces the risk in your portfolio. That’s what diversification is all about. You can even diversify across asset classes like bonds, gold, ETFs and more.

4. The factors affecting the risk of the individual assets

Each individual asset in any portfolio is subject to its own driving forces. These forces influence the risk of that individual asset. For example, bond prices are influenced by the interest rates in the economy. Stock prices depend on the company’s performance. Demand and supply influence the prices of all assets.

Naturally, these factors are also relevant when we look at the overall portfolio risk. The increase in the risk associated with any individual asset pulls the portfolio risk higher. And vice versa. So, the factors that affect the risk of the constituent assets also play a key role in determining the portfolio risk.

Quantifying risk

All this talk about risk is good enough to help you understand the concept of risk. But as an investor, what you would really like to know is this - How much risk are you taking by investing in an asset?

Is it not? That is why it becomes necessary to quantify risk for your portfolio. But remember how a portfolio consists of many assets? So, to quantify portfolio risk, it is necessary to first learn how to quantify the risk of a single asset. Let’s begin there.

Measuring the risk of a single asset

Remember your high school statistics? It is time to revisit those tools now. Mean, median and mode - these are things you will no doubt recall, to a good degree. But what we need to look at here is the standard deviation and the variance.

The standard deviation measures how far each value in a data set deviates from the average (or the mean).

• So, let’s say you’re taking the price of the asset as the variable. Then, the standard deviation shows you how far the prices of the asset deviate from its average price.
• Similarly, if you take the returns from the asset as the variable, the standard deviation shows you how far the actual returns of the asset deviate from its average returns.

Both these variables can be used to quantify risk. Now, what’s the relationship between variance and standard deviation? Let’s just look at that before we move on.

 Variance = (Standard deviation)2 or Standard deviation = Square root of the variance

Here’s an example to help you understand this better. Let’s assume that over a 5-day period, the prices of a stock are as follows.

 Rs. 102 Rs. 100 Rs. 97 Rs. 99 Rs. 107

The average price over the 5-day period comes in at Rs. 101 (Sum of the stock prices divided by 5). And here’s how the variance and standard deviation calculation for this data set would look.

 Day Price Deviation (Price - Mean) Deviation2 1 Rs. 102 +1 1 2 Rs. 100 -1 1 3 Rs. 97 -4 16 4 Rs. 99 -2 4 5 Rs. 107 +6 36 Sum of deviations squared 58
• Variance

= (Sum of deviations squared) ÷ (Number of variables)

= 58 ÷ 5

= 11.6

• Standard deviation

= Square root of the variance

= Square root of 11.6

= 3.40

So, the standard deviation here is Rs. 3.40. What does this mean? To understand this, we need to revisit the empirical rule. Remember we discussed it in the module on pair trading? We’ll reiterate it here.

According to the empirical rule:

• 68% of values are within one standard deviation (1 SD) away from the mean.
• 95% of values are within two standard deviations (2 SD) away from the mean.
• 99.7% of values are within three standard deviations (3 SD) away from the mean.

Graphically, this is how the empirical rule is depicted.

So, this means that the price of the asset will deviate from the mean by 1 SD (i.e. Rs. 3.40) 68% of the time. And it will lie between 2 SD on either side of the mean 95% of the time.

To sum it up:

• You can say, with a 68% certainty, that the price of the stock will lie between Rs. 97.60 and Rs. 104.40 (i.e. 1 SD from the mean of Rs. 101 on either side).
• You can say, with a 95% certainty, that the price of the stock will lie between Rs. 94.20 and Rs. 107.80 (i.e. 2 SD from the mean of Rs. 101 on either side).
• You can say, with a 99.7% certainty, that the price of the stock will lie between Rs. 90.80 and Rs. 111.20 (i.e. 3 SD from the mean of Rs. 101 on either side).

This will give you a fair idea of the possible price fluctuations. Similarly, you can also use the returns from the stock as the variable. That will give you a fair idea of the possible changes in the expected returns. Both these approaches will eventually help you create an investment plan, because you will have a price range or a return range to rely on.

The smaller the standard deviation, the less risk in the stock or the asset. This is because the fluctuations will be smaller, so you can operate with a greater degree of certainty.

Measuring portfolio risk

Measuring the risk of a single asset is fairly simple. You just need to calculate the standard deviation of that asset. But what do you do if you have a portfolio of different assets? The short answer to that has to do with variance, covariance and matrices. But that requires getting into the details. And that’s just what we’re going to be looking at in the coming chapters.

Wrapping up

Portfolio risk is an important aspect in every investor’s journey. The minute you put your capital into more than one asset, portfolio risk comes into play. It is not just relevant to a group of stocks. A portfolio consisting of any kind of assets has its own risks. Real estate, gold, bonds, money market instruments, deposits and more - all of them contribute to the portfolio risk. Keep going with Smart Money to learn how you can measure the risk of a portfolio.

A quick recap

• Portfolio risk is the probability that the mix of assets in a portfolio will fail to deliver the returns expected from them.
• Each asset in the portfolio carries its own level and nature of risk, and these elements of risk together make up the risk of the portfolio, as a whole.
• The risk of an investment portfolio is a complex concept. Many factors play major roles in influencing this risk.
• The kind of assets in your portfolio, the amount of money you put into each of those assets, and the level of diversification in the portfolio all impact its risk.
• The factors affecting the risk of the individual assets also affect portfolio risk.
• You can quantify the risk of a single asset by calculating its standard deviation. This gives you an idea of how much the price or the returns from a stock will fluctuate.