Portfolio Standard Deviation (Formula, Examples)

What is Portfolio Standard Deviation?

Portfolio Standard Deviation is the standard deviation of the rate of return on an investment portfolio and is used to measure the inherent volatility of an investment. It measures the investment’s risk and helps in analyzing the stability of returns of a portfolio.

Portfolio Standard Deviation is calculated based on the standard deviation of returns of each asset in the Portfolio, the proportion of each asset in the overall portfolio i.e. their respective weights in the total portfolio and also the correlation between each pair of assets in the portfolio.

Interpretation of Standard Deviation of Portfolio

This helps in determining the risk of an investment vis a vis the expected return.

A high portfolio standard deviation highlights that the portfolio risk is high and return is more volatile in nature and as such unstable as well.
A Portfolio with low Standard Deviation implies less volatility and more stability in the returns of a portfolio and is a very useful financial metric when comparing different portfolios.

Standard Deviation of Portfolio Example

Raman plans to invest a certain amount of money every month in one of the two Funds which he has shortlisted for investment purpose.

Details of which are reproduced below:

Assuming that stability of returns is most important for Raman while making this investment and keeping other factors as constant we can easily see that both funds are having an average rate of return of 12%,however Fund A has a Standard Deviation of 8 which means its average return can vary between 4% to 20% (by adding and subtracting 8 from average return).
On the other hand Fund, B has a Standard Deviation of 14 which means its return can vary between -2% to 26% (by adding and subtracting 14 from the average return).

Thus based on his risk appetite if Raman wishes to avoid excess volatility he will prefer investment in Fund A compared to Fund B as it offers the same average return with the less amount of volatility and more stability of returns.

Standard Deviation of Portfolio is important as it helps in analyzing the contribution of an individual asset to the Portfolio Standard Deviation and is impacted by the correlation with other assets in the portfolio and its proportion of weight in the portfolio.

How to Calculate Portfolio Standard Deviation?

Portfolio Standard Deviation calculation is a multi-step process and involves the below-mentioned process.

Portfolio Standard Deviation Formula

Assuming a Portfolio comprising of two assets only, the Standard Deviation of a Two Asset Portfolio can be computed using Portfolio Standard Deviation Formula:

Find the Standard Deviation of each asset in the Portfolio
Find the weight of each asset in the overall Portfolio
Find the correlation between the assets in the Portfolio (in the above case between the two assets in the portfolio). Correlation can vary in the range of -1 to 1.
Apply the values in the above-mentioned to derive the Standard Deviation formula of a Two Asset Portfolio.

Let’s understand the portfolio standard deviation calculation of a three asset portfolio with the help of an example:

Calculating Portfolio Standard Deviation of a Three Asset Portfolio

1) – Flame International is considering a Portfolio comprising of three stocks namely Stock A, Stock B & Stock C.

Brief Details provided are as follows:

2) – The correlation between these stock’s returns are as follows:

3) – For a 3 asset portfolio, this is computed as follows:

Where w_A, w_B, wC are weights of Stock A, B, and C respectively in the portfolio
Wheres k_A,s k_B,s k_Care Standard Deviation of Stock A, B, and C respectively in the portfolio
Where R(k_A, k_B), R(k_A, k_C), R( k_B, k_C) are the correlation between Stock A and Stock B, Stock A and Stock C, Stock B, and Stock C respectively.

Standard Deviation of Portfolio: 18%
Thus we can see that the Standard Deviation of Portfolio is 18% despite individual assets in the portfolio with a different Standard Deviation (Stock A: 24%, Stock B: 18% and Stock C: 15%) due to the correlation between assets in the portfolio.

Conclusion

Standard Deviation of Portfolio is an important tool which helps in matching the risk level of a Portfolio with a clients risk appetite and it measures the total risk in the portfolio comprising of both the systematic risk and Unsystematic Risk. A larger standard deviation implies more volatility and more dispersion in the returns and thus more risky in nature. It helps in measuring the consistency in which returns are generated and is a good measure to analyze the performance of Mutual funds and Hedge Funds returns consistency.

However, it is pertinent to note here that Standard Deviation is based out of historic data and Past results may be a predictor of the future results but they may also change over time and therefore can alter the Standard Deviation so one should be more careful before making an investment decision based on the same.

Portfolio Standard Deviation

What is Portfolio Standard Deviation?