Impact of Variance in Trading: Balancing Risk and Return on Investment

Have you ever wondered why some traders are comfortable taking huge risks while others play it safe? The answer lies in understanding variance. 

Variance is a metric used to calculate the spread of data. It helps to note the return separation values and balance the risk. By this idea, traders can reduce risks and increase profits.

What is variance and its role in trading?

Variance is a statistical metric that measures the spread of data points from their mean value. It indicates how each data point deviates from the central tendency. 

It is calculated by the expected value of the squared differences between each data point and the mean. The value of variance indicates that the data is significant for experiments or other analyses (like trading & investments). 

For Example:

1. High-variance stock’s value means they get a yield in massive gains that lead to significant losses.
2. Low-variance stock value indicates consistency in the market with modest returns that are ideal for investors.

Role of Variance in Trading

Variance plays an essential role in trading to quantify the risk. Some are discussed below: 

• Investors use variance to assess an investment’s risk and get potential profitability. 
• Investors use the variance for returns across assets in their portfolio to decide how to allocate their assets. 
• Traders and market analysts use variance to project the market’s volatility. 
• Variance also helps with budgeting because actual expenses often differ from estimated expenses. It can help establish a financial planning buffer. 
• Companies can analyze variances to identify problems and improve performance.

Relationship Between Variance and Return

The relationship between variance, risk, and return is positively/directly proportional, but with reward, it is inversely proportional. This means that as variance (risk) increases, the potential returns also tend to increase. It is a classic trade-off relation between risk (variance) and return in investing or trading. 

Traders used variance to identify mispriced assets that may offer higher returns without a proportionate increase in risk. They optimize their risk-to-reward ratio and note the value where the potential return exceeds the expected risk, making a remarkable decision.

Variance explains this balance: 

• High Variance = High Risk —> High Reward

• Low Variance = Low Risk —> Moderate Reward

How to Calculate Variance in Trading

To calculate the variance in trading, follow the below simple steps:

• Gather the data. 

• Calculate the average (Mean) return. 

• Subtract the mean from each return.

• Square each deviation to eliminate negative values. 

• Put the values in the variance formula and simplify the results.

Variance Formula:

σ2 = ∑ (xi – μ)2 / N

Breakdown of Term:

• σ2 = Variance
• xi​ = Each data point (e.g., individual returns)
• μ = Mean of the data set
• N = Total number of data points

For a deeper understanding, follow the below examples.

Example: Find the Risk through variance, the monthly returns of stock on different days of the month such as: 5, 8, 3, 7, and 6.

Solution:

Step 1: Gather the Data.

The monthly returns of a stock = {5, 8, 3, 7, 6}

Step 2: Calculate the Mean Return.

μ= 5+8+3+7+6/ 5 = 5.8

Step 3: Now, subtract the mean from each return.

• (5−5.8) =−0.8, 
• (8−5.8) =2.2, 
• (3−5.8) =−2.8, 
• (7−5.8) =1.2, 
• (6−5.8) =0.2

Step 4: Square each difference value of the above step.

• (−0.8)2 = 0.64, 
• (2.2)2 = 4.84, 
• (−2.8)2 = 7.84, 
• (1.2)2 = 1.44, 
• (0.2)2 = 0.04

Step 5: Calculate the variance by putting the values in its formula.

      σ2 = ∑ (xi – μ)2 / N

                                                              σ2= 0.64 + 4.84 + 7.84 + 1.44 + 0.04/5 

                                                              σ2= 2.96

Interpretation:

The variance of the stock returns is 2.96, which indicates the volatility and risk associated with the investment.

Example 2: Trader analyzing two stocks and returns for each stock are as follows:

Stock A: 4%, 6%, 5%, 7%, 8%

Stock B: 10%, 15%, 5%, 12%, 8%

Solution:

Step 1: Calculate the Mean Return for Each Stock

Stock A: μA = 4 + 6 + 5 + 7+ 8/ 5 = 6%

Stock B: μB=10+15+5+12+8/ 5 =10%​

Step 2: Find the difference between the mean or each data value and the squares of them.

For brevity, we directly find the squared deviations:

Stock A: 

(6−6)2 =0,

(5−6)2 = 1,

(7−6)2=1,

(8−6)2 = 4

(4-6)2 = 4, 

Stock B:

(10−10)2=0,

(15−10)2 = 25,

(5−10)2 = 25, 

(12−10)2 = 4,

(8−10)2=4

Step 3: Put values in the variance formula and measure its value. 

Stock A:

σA2 = ∑ (xi – μ)2 / N

σA2 = 4 + 0 + 1 + 1 + 4 / 5 = 2

Stock B:

σB2 = ∑ (xi – μ)2 / N

σB2 = 0 + 25 + 25 + 4 + 4 /5 =11.6

Interpretation

• Stock A has a variance of 2, indicating lower volatility. 
• Stock B, with a variance of 11.6, is much more volatile. 

Depending on the risk tolerance, traders prefer Stock A for low returns, stability, and high profit.

Pro Tips:

To compute variance manually for large or small data sets can be difficult, time-consuming, and chances of error. For easiness, try a variance calculator that helps in the understanding of the calculation process by quick & accurate results. The accurate results help to make an informed decision.

Final Thoughts

Variance is an important measure that helps traders/investors to quantify the risks involved in their trades and investment. Traders make better judgments and maintain their lead by routinely examining market data with variance analysis. Understanding variation can result in more consistent returns, better risk management, and astute trading.