Learn To Invest
Stocks Special Reports LICs Credit Funds ETFs Tools SMSFs
Video Archive Article Archive
News Stocks Special Reports Funds ETFs Features SMSFs Learn
About

News

Standard Deviation and Sharpe Ratio

Morningstar.com.au  |  26 Jul 2022Text size  Decrease  Increase  |  
Email to Friend

Standard Deviation

Standard deviation is the statistical measurement of dispersion about an average, which depicts how widely a stock or portfolio’s returns varied over a certain period of time. Investors use the standard deviation of historical performance to try to predict the range of returns that is most likely for a given investment. When an investment has a high standard deviation, the predicted range of performance is wide, implying greater volatility.

If an investment’s returns follow a normal distribution, then approximately 68 percent of the time they will fall within one standard deviation of the mean return of the investment, and 95 percent of the time within two standard deviations. For example, for a portfolio with a mean annual return of 10 percent and a standard deviation of two percent, you would expect the return to be between eight and 12 percent about 68 percent of the time, and between six and 14 percent about 95 percent of the time.

In this context, the mean annual return is based on an arithmetic average (sum/n) of the monthly returns of the investment (an average, which is then annualized). This is slightly different than the total return of the investment, because the total return is a geometric average of the monthly returns, calculated as [(1+r1)(1+r2)…(1+rn)]-1.

Morningstar calculates standard deviation for stocks, open-end mutual funds, closed-end funds, exchange-traded funds, indexes, separate accounts, variable annuity underlying funds, and variable annuity sub-accounts. Morningstar uses the historical monthly total returns for the appropriate time period (one-, three-, five-, 10-, 15-, and 20-year) to calculate the monthly standard deviation. The monthly standard deviation is then annualized to put it into a more useful one-year context.

Morningstar uses the sample standard deviation method1. The monthly standard deviation is

image

R̄  is also called the arithmetic mean, and it is calculated by adding together all the monthly returns for the portfolio and dividing by the number of months.

Investing Compass
Listen to Morningstar Australia's Investing Compass podcast
Take a deep dive into investing concepts, with practical explanations to help you invest confidently.
Investing Compass

image

Morningstar annualizes the monthly standard deviation to put the number in more useful one-year terms by multiplying it by the square root of 12.2

image

Morningstar tools and websites most commonly display the annualized version of the three-year standard deviation.

 

Sharpe Ratio

The Sharpe Ratio is a risk-adjusted measure developed by Nobel Laureate William Sharpe. It is calculated by using excess return and standard deviation to determine reward per unit of risk. The higher the Sharpe Ratio, the better the portfolio’s historical risk-adjusted performance. Morningstar calculates the Sharpe Ratio for portfolios for one, three, five, and 10 years. Morningstar does not calculate this statistic for individual stocks. The monthly Sharpe Ratio is as follows:

image

The numerator, e , is the average monthly excess return:

image

The denominator, σeM, is a monthly measure of the standard deviation of excess returns. Because this measures the standard deviation of the spread between the portfolio and the risk-free rate, it is slightly different than the standard deviation of total returns displayed in most Morningstar products. The denominator is: 

image

The annualized Sharpe Ratio is the product of the monthly Sharpe Ratio and the square root of twelve. This is equivalent to multiplying the numerator by 12 (to produce an arithmetic annualized excess return) and the denominator by the square root of 12 (annualized standard deviation).4

image

 

1 This corresponds to the Microsoft Excel function “stdev.”

2 Prior to 2/28/2005, Morningstar calculated standard deviation with the population method (divide by n instead of n-1, “stdevp” in Microsoft Excel). Also, prior to this date, Morningstar annualized standard deviation with a method developed by James Tobin. σA=([(σM)2 + (1+avgR)2]12 – [(1+avgR)2]12)1/2

3 Morningstar chooses a risk-free benchmark based on the portfolio’s domicile, e.g. the 3-month Treasury bill for portfolios based in the United States.

Prior to 2/28/2005, Morningstar annualized the Sharpe Ratio with a method developed by James Tobin.

.

© 2022 Morningstar, Inc. All rights reserved. Neither Morningstar, its affiliates, nor the content providers guarantee the data or content contained herein to be accurate, complete or timely nor will they have any liability for its use or distribution. This information is to be used for personal, non-commercial purposes only. No reproduction is permitted without the prior written consent of Morningstar. Any general advice or 'regulated financial advice' under New Zealand law has been prepared by Morningstar Australasia Pty Ltd (ABN: 95 090 665 544, AFSL: 240892), or its Authorised Representatives, and/or Morningstar Research Ltd, subsidiaries of Morningstar, Inc, without reference to your objectives, financial situation or needs. For more information, refer to our Financial Services Guide (AU) and Financial Advice Provider Disclosure Statement (NZ). Our publications, ratings and products should be viewed as an additional investment resource, not as your sole source of information. Morningstar’s full research reports are the source of any Morningstar Ratings and are available from Morningstar or your adviser. Past performance does not necessarily indicate a financial product's future performance. To obtain advice tailored to your situation, contact a licensed financial adviser. Some material is copyright and published under licence from ASX Operations Pty Ltd ACN 004 523 782. The article is current as at date of publication.

Email To Friend