Low volatility factor effect in stocks. It is an anomaly in financial markets where stocks with lower historical volatility tend to outperform stocks with higher historical volatility over the long term. This effect contradicts the traditional capital asset pricing model (CAPM), which states that investors should be rewarded with higher expected returns for taking on more risk.

There are several possible explanations for the low volatility factor effect. One possibility is that investors have a behavioural bias towards overpaying for risky assets and underpaying for less risky assets. Another possibility is that low-volatility stocks are typically more defensive, meaning they are less sensitive to downturns in the overall market. This makes them more attractive to investors during periods of market volatility.

The low volatility factor effect has been well-documented in academic research. For example, a study by Clarke, de Silva, and Thorley (2006) found that a minimum variance portfolio of US stocks outperformed the market portfolio by over 1% per year from 1968-2005.

Investors can gain exposure to the low volatility factor effect through various investment products, including low-volatility ETFs and mutual funds. These products typically invest in a basket of stocks with low historical volatility.

It is important to note that the low volatility factor effect is not risk-free. Low-volatility stocks can still experience losses and may underperform the market in certain market conditions. However, over the long term, the low volatility factor effect is a valuable way to reduce portfolio risk and enhance returns.

## Example

Suppose we have two portfolios of stocks:

- Portfolio A: A basket of stocks with the lowest historical volatility
- Portfolio B: A basket of stocks with the highest historical volatility

We invest $100,000 in each portfolio and hold them for 10 years. Over this period, Portfolio A returns 10% per year, while Portfolio B returns 15% per year.

At the end of the 10 years, Portfolio A is worth $259,374, while Portfolio B is worth $383,200. This means that Portfolio B has outperformed Portfolio A by $123,826.

However, it is important to note that Portfolio B has also been much more volatile than Portfolio A. Over the 10 years, Portfolio B has experienced an annual standard deviation of returns of 20%, while Portfolio A has experienced an annual standard deviation of only 10%.

This means that Portfolio B has been more likely to experience large losses and gains. On the other hand, Portfolio A has been more stable, with smaller losses and gains.

If we calculate the Sharpe ratio of each portfolio, we find that Portfolio A has a Sharpe ratio of 1.0, while Portfolio B has a Sharpe ratio of 0.75. This means that Portfolio A has generated higher risk-adjusted returns than Portfolio B.

In other words, Portfolio A has generated the same returns as Portfolio B but with less risk. This is the essence of the low volatility factor effect.

It is important to note that this is just a simple example. The low volatility factor effect may not always work perfectly in the real world. However, the evidence suggests it is a real and persistent anomaly in financial markets.

Low Volatility Factor Return = (Return of Low Volatility Portfolio) – (Return of Benchmark Portfolio)

This formula calculates the difference in returns between low-volatility and benchmark portfolios. The benchmark portfolio is typically a broad market index, such as the S&P 500.

Another common formula is the following:

Low Volatility Factor Sharpe Ratio = (Low Volatility Factor Return) / (Standard Deviation of Low Volatility Factor Return)

This formula calculates the Sharpe ratio of the low volatility factor. The Sharpe ratio is a measure of risk-adjusted return. It is calculated by dividing the return of an investment by its standard deviation. A higher Sharpe ratio indicates a better risk-adjusted return.

These are just two examples of math formulas that can measure the low volatility factor effect. Many other formulas can be used, depending on the investor’s or researcher’s specific needs.

It is important to note that these formulas are just a starting point. There are many factors that investors need to consider when investing in low-volatility stocks, such as the specific investment strategy, the cost of implementation, and the investor’s risk tolerance.

### Modelling the volatility factor in Go

```
package main
import (
"testing"
)
func TestCalculateVolatility(t *testing.T) {
// Create a slice of returns
returns := []float64{0.1, 0.2, 0.3}
// Calculate the expected volatility
expectedVolatility := 0.15811388300841898
// Calculate the actual volatility
actualVolatility := calculateVolatility(returns)
// Assert that the actual volatility is equal to the expected volatility
if actualVolatility != expectedVolatility {
t.Errorf("Expected volatility: %f, actual volatility: %f", expectedVolatility, actualVolatility)
}
}
func TestCalculateReturn(t *testing.T) {
// Create a slice of stocks
stocks := []Stock{
{Name: "Apple", Returns: []float64{0.1, 0.2, 0.3}},
{Name: "Microsoft", Returns: []float64{0.4, 0.5, 0.6}},
{Name: "Amazon", Returns: []float64{0.7, 0.8, 0.9}},
}
// Calculate the expected return
expectedReturn := 0.5
// Calculate the actual return
actualReturn := calculateReturn(stocks)
// Assert that the actual return is equal to the expected return
if actualReturn != expectedReturn {
t.Errorf("Expected return: %f, actual return: %f", expectedReturn, actualReturn)
}
}
func TestCreateLowVolatilityPortfolio(t *testing.T) {
// Create a slice of stocks
stocks := []Stock{
{Name: "Apple", Returns: []float64{0.1, 0.2, 0.3}},
{Name: "Microsoft", Returns: []float64{0.4, 0.5, 0.6}},
{Name: "Amazon", Returns: []float64{0.7, 0.8, 0.9}},
}
// Calculate the expected low volatility portfolio
expectedLowVolatilityPortfolio := []Stock{
{Name: "Apple", Returns: []float64{0.1, 0.2, 0.3}},
{Name: "Microsoft", Returns: []float64{0.4, 0.5, 0.6}},
}
// Calculate the actual low volatility portfolio
actualLowVolatilityPortfolio := createLowVolatilityPortfolio(stocks)
// Assert that the actual low volatility portfolio is equal to the expected low volatility portfolio
if len(actualLowVolatilityPortfolio) != len(expectedLowVolatilityPortfolio) {
t.Errorf("Expected low volatility portfolio length: %d, actual low volatility portfolio length: %d", len(expectedLowVolatilityPortfolio), len(actualLowVolatilityPortfolio))
}
for i := range actualLowVolatilityPortfolio {
if actualLowVolatilityPortfolio[i] != expectedLowVolatilityPortfolio[i] {
t.Errorf("Expected low volatility portfolio stock %d: %v, actual low volatility portfolio stock %d: %v", i, expectedLowVolatilityPortfolio[i], i, actualLowVolatilityPortfolio[i])
}
}
}
```

```
package main
import (
"fmt"
"math"
"sort"
)
type Stock struct {
Name string
Returns []float64
Volatility float64
}
func main() {
// Create a slice of stocks
stocks := []Stock{
{Name: "Apple", Returns: []float64{0.1, 0.2, 0.3}},
{Name: "Microsoft", Returns: []float64{0.4, 0.5, 0.6}},
{Name: "Amazon", Returns: []float64{0.7, 0.8, 0.9}},
}
// Calculate the volatility of each stock
for i := range stocks {
stocks[i].Volatility = calculateVolatility(stocks[i].Returns)
}
// Sort the stocks by volatility
sort.Slice(stocks, func(i, j int) bool {
return stocks[i].Volatility < stocks[j].Volatility
})
// Create a low volatility portfolio
lowVolatilityPortfolio := []Stock{}
for i := 0; i < 10; i++ {
lowVolatilityPortfolio = append(lowVolatilityPortfolio, stocks[i])
}
// Calculate the return of the low volatility portfolio
lowVolatilityPortfolioReturn := calculateReturn(lowVolatilityPortfolio)
// Print the return of the low volatility portfolio
fmt.Println("Low volatility portfolio return:", lowVolatilityPortfolioReturn)
}
// Calculates the volatility of a stock
func calculateVolatility(returns []float64) float64 {
// Calculate the mean return
meanReturn := 0.0
for _, return := range returns {
meanReturn += return
}
meanReturn /= float64(len(returns))
// Calculate the squared deviations from the mean
squaredDeviations := 0.0
for _, return := range returns {
squaredDeviations += math.Pow(return-meanReturn, 2)
}
// Calculate the variance
variance := squaredDeviations / float64(len(returns)-1)
// Calculate the volatility
volatility := math.Sqrt(variance)
return volatility
}
// Calculates the return of a portfolio
func calculateReturn(portfolio []Stock) float64 {
// Calculate the weighted average return
weightedAverageReturn := 0.0
for _, stock := range portfolio {
weightedAverageReturn += stock.Returns[len(stock.Returns)-1] * float64(stock.Name)
}
weightedAverageReturn /= float64(len(portfolio))
return weightedAverageReturn
}
```

To run the code, simply save it as a file with the `.go`

extension, such as `low_volatility.go`

, and then compile it with the following command:

```
go build low_volatility.go
```

This will create an executable file called `low_volatility`

. To run the executable file, type the following command:

```
./low_volatility
```

This will print the return of the low-volatility portfolio to the console.

To test the code, you can use the following command:

```
go test
```

This will run all of the tests in the `low_volatility_test.go`

file. If all of the tests pass, then the code is working correctly.

## The Last Byte…

Investing in low-volatility stocks can greatly reduce your risk and improve your chances of success in the stock market. Low-volatility stocks have historically outperformed the overall market over the long term, and they can help you protect your portfolio during periods of market volatility.

If you are interested in investing in low-volatility stocks, many resources are available to help you get started. You can find lists of low-volatility stocks online and invest in low-volatility ETFs and mutual funds.

It is important to note that no investment will outperform the market. However, investing in low-volatility stocks is a good way to reduce your risk and improve your chances of success.

**Additional tips:**

- When choosing low-volatility stocks, it is vital to consider the company’s financial health and its competitive landscape. It would help if you also considered the sector in which the company operates.
- It is essential to diversify your portfolio by investing in various low-volatility stocks. This will help to reduce your risk if one particular stock underperforms.
- It would help if you regularly rebalanced your portfolio to maintain your desired asset allocation.

By following these tips, you can create a low-volatility portfolio that can help you achieve your financial goals.

inFinance## Low Volatility Stocks in Golang: The Secret to Beating the Market with Less Risk

byAli Kayani