Investing in multiple assets can diversify your portfolio, but it also brings a mixture of risks and rewards. How do you measure the overall risk? That’s where the Portfolio Standard Deviation (SD) Calculator comes into play. It’s a tool designed to help investors understand the total risk associated with their mix of investments.

## Purpose and Functionality

The Portfolio SD Calculator measures the risk (volatility) of your combined investments. By inputting details about your assets, their weights in your portfolio, and how they move together (correlation), you can see the big picture of your investment risk. This calculation is crucial for making informed investment decisions and for balancing your investment strategy.

## Step-by-Step: How Does It Work?

Let’s break down the process with an easy-to-follow example, using a portfolio with just two assets for simplicity.

### Formula Inputs:

**Weight of Each Asset**: How much of your money is in each investment? For example, 50% in stocks (Asset 1) and 50% in bonds (Asset 2).**Standard Deviation of Each Asset**: How much does the return from each investment typically go up or down? Imagine stocks vary by 10% (SD1) and bonds by 15% (SD2).**Correlation Between the Assets**: Do the investments move in the same direction at the same time, or do they move independently? Suppose they have a correlation of 0.5 (ρ12), meaning they are somewhat related but not perfectly in sync.

## Calculation:

In simple words, the formula for portfolio SD looks at how much each investment can go up or down, how much of your money is in each, and how these investments move relative to each other. Then it combines all this information to give you a single number that represents the overall risk.

For our two-asset portfolio, the calculation follows these steps:

- Multiply each asset’s weight by its standard deviation (how much it can go up or down).
- Square these numbers (make them positive and bigger).
- Multiply the weights of the two assets by their standard deviations and by their correlation (how they move together).
- Add all these numbers up.
- Find the square root of this total to get back to a number that makes sense (since we squared them before).

**Using our example values:**

- The overall risk (Portfolio SD) combines the risk from stocks, the risk from bonds, and how they affect each other.
- After doing the math, you might find that your portfolio’s overall risk is 12.5%.

### For More Complex Portfolios:

When you have more than two investments, the idea is the same, but there’s more math involved because you have to consider how each investment pairs with every other investment in your portfolio.

## Example Calculation in a Table:

Asset | Weight | Standard Deviation | Contribution to Portfolio SD |
---|---|---|---|

Stock | 50% | 10% | Part of the total calculation |

Bond | 50% | 15% | Part of the total calculation |

Total Portfolio SD | 12.5% |

## Conclusion: The Benefits and Applications

The Portfolio SD Calculator is more than just a math exercise. It’s a lens through which you can view the risk of your investment strategy. Whether you’re a seasoned investor or just starting, understanding the combined risk of your investments helps you make decisions that align with your risk tolerance and financial goals. By quantifying risk, you can adjust your portfolio to achieve the right balance for your needs.