Trader’s Guide 2.5- Calculating Risks

Calculating Risk Using Historical Data

Calculating risk is a crucial step in the process of investing in any financial product. After all, as the famous investor Warren Buffet once said, "Risk comes from not knowing what you're doing." While there are many ways to assess risk, in this chapter, we will explore four popular methods: Sortino ratio, Sharpe ratio, expected return vs drawdown ratio, and upside to downside volatility.

Before we dive into the specifics of these risk-calculating techniques, it's important to first define what we mean by "risk." In the context of investing, risk can be thought of as the likelihood that an investment will lose value. It's important to note that all investments carry some level of risk, even those that are considered "safe" like government bonds. The key is to find a balance between taking on enough risk to potentially earn high returns, while not taking on so much risk that the chance of loss becomes unacceptable.

Now, let's take a closer look at each of the four risk-calculating methods we'll be discussing.

Sortino Ratio

The Sortino ratio is a measure of risk that takes into account the potential downside of an investment. It was developed by Frank Sortino and has become a popular tool among investors looking to minimize the risk of loss.

The equation for the Sortino ratio is as follows:

Sortino ratio = (Expected return - Target return) / Downside standard deviation

In this equation, the "expected return" is the average return that an investor expects to receive from an investment. The "target return" is a predetermined level of return that an investor is seeking to achieve. The "downside standard deviation" is a measure of the variability of returns below the target return.

Let's look at an example to better understand how the Sortino ratio works. Imagine that an investor is considering investing in a stock that has an expected return of 8% per year. The investor's target return is 6% per year, and the downside standard deviation for the stock is 2%. Using the Sortino ratio equation, we can calculate the risk of this investment as follows:

Sortino ratio = (8% - 6%) / 2% = 2

In this case, the Sortino ratio of 2 indicates that the investment has a relatively low level of risk.

Sharpe Ratio

The Sharpe ratio, named after economist William Sharpe, is a measure of risk-adjusted return. It compares the expected return of an investment to the amount of risk (measured by standard deviation) taken to achieve that return.

The equation for the Sharpe ratio is as follows:

Sharpe ratio = (Expected return - Risk-free rate) / Standard deviation

In this equation, the "expected return" and "standard deviation" are the same as in the Sortino ratio equation. The "risk-free rate" is the rate of return that an investor can expect to receive on an investment with no risk, such as a government bond.

Let's look at an example to better understand how the Sharpe ratio works. Imagine that an investor is considering investing in a stock that has an expected return of 8% per year and a standard deviation of 4%. The risk-free rate is currently 3%. Using the Sharpe ratio equation, we can calculate the risk-adjusted return of this investment as follows:

Sharpe ratio = (8% - 3%) / 4% = 1.25

In this case, the Sharpe ratio of 1.25 indicates that the investment has a relatively high level of risk-adjusted return.

Expected Return vs Drawdown Ratio

The expected return vs drawdown ratio is a measure of risk that compares the expected return of an investment to the maximum drawdown (i.e. the maximum loss) that an investor can expect to experience. It can be a useful tool for investors looking to minimize the risk of experiencing large losses.

The equation for the expected return vs drawdown ratio is as follows:

Expected return vs drawdown ratio = Expected return / Maximum drawdown

In this equation, the "expected return" is the average return that an investor expects to receive from an investment, and the "maximum drawdown" is the largest loss that an investor can expect to experience from an investment.

Let's look at an example to better understand how the expected return vs drawdown ratio works. Imagine that an investor is considering investing in a stock that has an expected return of 8% per year and a maximum drawdown of 20%. Using the expected return vs drawdown ratio equation, we can calculate the risk of this investment as follows:

Expected return vs drawdown ratio = 8% / 20% = 0.4

In this case, the expected return vs drawdown ratio of 0.4 indicates that the investment has a relatively high level of risk.

Upside to Downside Volatility

Upside to downside volatility is a measure of risk that compares the potential upside of an investment (i.e. the potential for gains) to the potential downside (i.e. the potential for losses). It can be a useful tool for investors looking to maximize the potential for gains while minimizing the potential for losses.

The equation for upside to downside volatility is as follows:

Upside to downside volatility = Upside volatility / Downside volatility

In this equation, "upside volatility" is a measure of the potential for gains, and "downside volatility" is a measure of the potential for losses.

Before we discuss an example, it's important to define what we mean by "volatility." In the context of investing, volatility refers to the amount of fluctuation that an investment experiences over a given period of time. A high level of volatility means that an investment is prone to significant swings in value, while a low level of volatility means that an investment is relatively stable.

Now, let's look at an example to better understand how upside to downside volatility works. Imagine that an investor is considering investing in a stock that has an upside volatility of 10% and a downside volatility of 5%. Using the upside to downside volatility equation, we can calculate the risk of this investment as follows:

Upside to downside volatility = 10% / 5% = 2

In this case, the upside to downside volatility of 2 indicates that the potential for gains is twice as high as the potential for losses.

There are many ways to calculate risk when initially looking to invest in a financial product. The Sortino ratio, Sharpe ratio, expected return vs drawdown ratio, and upside to downside volatility are all popular methods that can be useful for assessing risk. By carefully considering the level of risk associated with an investment, investors can make informed decisions about whether or not to proceed with the investment.

As the famous trader Jesse Livermore once said, "It is not the man who makes the most money the fastest, but the man who holds on the longest and takes the least risk who makes the most money." By using these risk-calculating techniques, investors can make informed decisions about how to hold on the longest and take the least risk, potentially leading to greater success in the world of investing.