Measuring Risk with Standard Deviation Investment Returns

Standard deviation is a crucial metric for measuring risk in investment returns. It indicates how much the actual returns deviate from the expected returns.

A higher standard deviation means higher risk and lower returns, while a lower standard deviation means lower risk and higher returns. This is evident in the example of two investment portfolios, where one has a standard deviation of 5% and the other has a standard deviation of 10%.

The 68-95-99.7 rule, also known as the empirical rule, states that about 68% of data points fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. This rule applies to investment returns as well, indicating that most returns will fall within a certain range of the expected returns.

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Standard deviation measures how far an asset's returns have been from its average return, either over its full history or for a specific period.

It's like knowing when a friend will arrive, and expecting them to be within a certain time frame, plus or minus a certain amount of time. For investments, this time frame is called the standard deviation.

Standard deviation is a basic mathematical concept that measures volatility in the market or the average amount by which individual data points differ from the mean.

A higher standard deviation means an investment is more volatile, with larger price swings, while a lower standard deviation means it's less volatile, with smaller price swings.

The standard deviation is expressed as a percentage and can be used to show how much the returns of a mutual fund scheme are likely to deviate from its average annual returns.

A standard deviation of 3 can be considered better or worse than another with a standard deviation of 4 or 2, depending on your risk appetite and investment time frame.

Standard deviation is a measure of absolute risk, and it can be used to determine the probability that a value will fall within a certain range.

For normal distributions, 68% of all values will fall within 1 standard deviation of the mean, 95% of all values will fall within 2 standard deviations, and 99.7% of all values will fall within 3 standard deviations.

The greater the standard deviation, the greater the volatility, and, therefore, the greater the risk. More volatile assets have a wider bell-shaped curve, reflecting a greater dispersion in their returns.

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Standard deviation is a crucial measurement in statistics, especially when it comes to investment returns. It helps us understand the range of expected results and how likely it is for results to fall outside that range.

A city might receive an average of 50 rainy days per year, with a standard deviation of 10, so most years there's between 40-60 rainy days. But if next year there happens to be 70 rainy days, that would be two standard deviations above the mean.

In investment returns, a greater standard deviation indicates greater volatility, meaning returns may fluctuate on either side of the average. This can be seen in the example of Fund C, where 68% of the time future returns may range between 7% and 13% (10% average plus or minus its standard deviation of 3).

The 68-95 rule is also applicable to any statistical data set, stating that 68% of the time returns will fall within one standard deviation of the average return, while 95% of the time they will fall within two standard deviations.

Here's a breakdown of the 68-95 rule for Fund C's future returns:

This means that 68% of the time Fund C's future returns will be between 7% and 13%, and 95% of the time they will be between 4% and 16%.

Calculating standard deviation is a crucial step in understanding investment returns. It's a measure of how much the returns on an investment vary from the average return.

To calculate standard deviation, you need to follow these steps. First, you need to find the average return, which is the sum of all the returns divided by the number of periods. For example, in Example 1, the average return is 6.2%.

Next, you need to find the deviation for each period, which is the difference between the return for that period and the average return. In Example 1, the deviation for period 1 is -9.6.

Then, you need to square each deviation, which means multiplying it by itself. This is shown in Example 1, where the deviation squared for period 1 is 92.0.

After that, you need to sum up all the squared deviations, which is 1,424.0 in Example 1.

The next step is to divide the sum of the squared deviations by the number of periods minus one. This is shown in Example 1, where the result is 142.4.

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Finally, you take the square root of the result, which is 11.9% in Example 1. This is the standard deviation.

Here's a summary of the steps:

The formula for standard deviation is shown in Example 4:

σ = √[(∑(Ri - Ravg)^2) / (N - 1)]

Where:

The standard deviation formula can also be used to calculate the standard deviation for a sample, as shown in Example 3.

Calculating standard deviation is a straightforward process that involves several steps. You start by finding the average return, or mean, of the data points within the period, which is 6.2% in this case.

To calculate the standard deviation, you need to find the deviation for each period. This is done by subtracting the average return from each individual return. For example, the deviation for period 1 is -9.6.

Once you have the deviations for each period, you need to square them. This is done by multiplying each deviation by itself. For example, the squared deviation for period 1 is 92.0.

Next, you need to sum up the squared deviations. This is done by adding up all the squared deviations, which in this case is 1,424.0.

After that, you divide the sum of the squared deviations by the number of periods. In this case, the number of periods is 10, so you divide 1,424.0 by 10, resulting in 142.4.

Finally, you take the square root of the result to find the standard deviation. In this case, the square root of 142.4 is 11.9%.

Here's a summary of the steps:

The standard deviation is a measure of the spread or dispersion of the data points from the average return. In this case, the standard deviation is 11.9%, which means that most of the data points are within 11.9% of the average return.

Interpreting standard deviation is a crucial step in understanding investment returns. The standard deviation can be a helpful guideline, but it isn't always accurately predictive.

It tells you how volatile the asset has been in the past, which can be used to analyze price performance trends. You can get a sense of how much an investment might fluctuate from its expected return over a given period of time if past trends continue.

However, you can't assume that past trends will always be the case, so it's essential to consider your investment goals and risk tolerance. Assets with certain standard deviation results that fit your goals and risk tolerance might be preferable.

For more insights, see: Managing Investment Risk

Standard deviation is a powerful tool in finance that helps investors understand the risk and potential return of an investment. It's a measure of how much an investment's price can fluctuate from its average price.

The 68-95-99.7 rule states that within a normal distribution, an asset's returns may fall within one standard deviation of the average 68% of the time, within two standard deviations 95% of the time, and within three standard deviations 99.7% of the time. This means that if an investment has a high standard deviation, you can expect large price swings.

Investors use standard deviation to gauge an asset's potential volatility and rate of return. For example, the S&P 500's average annual return was 11.21%, but it had an annual standard deviation of about 15.25%. This means that there's around a two-in-three chance the next year's returns will fall within the -4.04% to 26.4% range.

Finding standard deviation involves calculating the square of the difference between the actual rate of return and the average rate of return for each month. For instance, in January, the square of the difference between the actual rate of return (1.59) and the average rate of return (2.33) would be 0.55.

An asset's standard deviation isn't a guarantee of success or failure, but it can be informative. For example, emerging market and U.S. small-cap stocks have a higher standard deviation than U.S. investment-grade bonds, indicating wilder price swings.

Here's a key takeaway: the higher an investment's standard deviation, the wilder the price swings you'll experience. Conversely, a low standard deviation means prices are calm, and investments come with low risk.

Here's an interesting read: Historical Rates of Return by Asset Class