## Expected Return vs. Standard Deviation: An Overview

As an investor, you may want some assurance that your money will grow and net you a profit. While it may be difficult to predict exactly how much you may earn, there are a few ways that you can try to determine your return. An expected return and a standard deviation are two statistical measures that investors can use to analyze their portfolios. The expected return is the anticipated amount of returns that a portfolio may generate, whereas the standard deviation of a portfolio measures the amount that the returns deviate from its mean.

### Key Takeaways

- Investors and portfolio managers can calculate the anticipated values of their portfolios by using the expected return and standard deviation.
- Expected return uses historical returns and calculates the mean of an anticipated return based on the weighting of assets in a portfolio.
- Standard deviation takes into account the expected mean return and calculates the deviation from it.
- Investors should be cautious about relying solely on expected returns and standard deviation to evaluate their portfolios.
- Other factors to consider include economic conditions, market sentiment, and interest rates.

## Expected Return

An investor's expected return is the total amount of money they expect to gain or lose on a particular investment or portfolio. Investors commonly use the expected return to help them make key decisions on whether to invest in new vehicles or continue to hold on to their existing investments.

The expected return is generally based on historical returns. As such, it doesn't indicate the potential for future performance and shouldn't be used as the only decision-making tool. This metric can, however, give investors a reasonable expectation of what they may expect in the short- and long-run.

An investment's expected return is able to measure the mean, or expected value, of the probability distribution of investment returns. It is commonly seen with hedge fund and mutual fund managers, whose performance on a particular stock isn't as important as their overall return for their portfolio.

### Calculating Expected Return

The expected return is calculated by multiplying the weight of each asset by its expected return. Then add the values for each investment to get the total expected return for your portfolio. Hence, the formula:

Expected Portfolio Return = (Asset 1 Weight x Expected Return) + (Asset 2 Weight x Expected Return)...

Now let's use a hypothetical example to show how to apply the formula. The table below shows a portfolio with three different investments, each with different weightings and expected returns.

Asset |
Weight |
Expected Return |

A | 35% | 6% |

B | 25% | 7% |

C | 40% | 10% |

The expected return of the overall portfolio would be 7.85%. We arrive at this result by using the formula above:

(35% x 6%) + (25% x 7%) + (40% x 10%) = 7.85%

An investor uses an expected return to forecast, and standard deviation to discover what is performing well and what is not.

## Standard Deviation

The standard deviation of a portfolio measures how much the investment returns deviate from the mean of the probability distribution of investments. Put simply, it tells investors how much the investment will deviate from its expected return. As such, investors can use this metric to help determine an investment or portfolio's annual return by considering its historical volatility.

It is a common calculation used to judge the realized performance of a portfolio manager. This means that a fund company may calculate the risk of employing a portfolio manager who deviates too far from the mean in a negative direction, especially for large funds that have multiple managers with different investing styles. This can go the other way as well, and a portfolio manager who outperforms their colleagues and the market can often expect a hefty bonus for their performance.

Using the standard deviation helps measure both market and security volatility. This allows the investor or manager predict trends in the investment's performance. A higher standard deviation means there's a higher variable between prices and the mean. Put simply, an investment with higher volatility means a higher standard deviation, so there are more risks and rewards.

### Calculating Standard Deviation

The standard deviation of a two-asset portfolio is calculated as follows:

σP =√(wA2 * σA2 + wB2 * σB2 + 2 * wA * wB * σA * σB * ρAB)

Where:

- σP = portfolio standard deviation
- wA = weight of asset A in the portfolio
- wB = weight of asset B in the portfolio
- σA = standard deviation of asset A
- σB = standard deviation of asset B; and
- ρAB = correlation of asset A and asset B

For example, consider a two-asset portfolio with equal weights, standard deviations of 20% and 30%, respectively, and a correlation of 0.40. Therefore, the portfolio standard deviation is:

[√(0.5² x 0.22 + 0.5² x 0.32 + 2 x 0.5 x 0.5 x 0.2 x 0.3 x 0.4)] = 21.1%

## Special Considerations

The expected return and standard deviation of an investment are just two methods that investors can use to help evaluate the future performance of investments and portfolios. These calculations are generally easy and straightforward. But they shouldn't be the only thing investors use to make their investment decisions.

One reason is that many mathematical formulas use historical returns as the basis of calculation. As such, they may not be a reliable way to indicate future performance. Put simply, just because an investment did well last year doesn't mean that it will continue to do so next year.

With this in mind, other considerations can also come into play that may cause investments to deviate from the outcomes that result from using these formulas. These include:

- Changes in the economy
- Financial market conditions
- Market sentiment and expectations
- Interest rates and currency risks
- Availability and productivity of capital
- Other factors, such as labor costs, policies, regulations, and taxation

## Is Expected Return the Same as Standard Deviation?

The expected return is one method investors can use to help measure the potential for investment returns. This figure is based on historical returns. Standard deviation, on the other hand, measures the extent to which an investment's return deviates from the expected return. Investments that are more volatile (those that have bigger risks) have a higher standard deviation (and higher rewards).

## How Do You Calculate Expected Return?

Expected returns are based on historical returns. Take the individual investments in your portfolio and multiply their weighting by their expected return. Add the result for each investment together to get the expected result of your portfolio.

## How Do You Calculate Standard Deviation?

In order to calculate standard deviation, figure out the mean or the average in the data set. For each of those numbers and square the result. Once that's done, determine the mean of each of those squared differences, then take the square root of that figure. The result is the standard deviation.

## Does a Higher Standard Deviation Mean a Higher Expected Return?

Investments that are more volatile tend to have higher returns. An investment with a higher standard deviation means it will be more risky and volatile. Therefore, the expected return should also be higher.