Call Us: (800)848-2029 Course Info Enroll

Articles for Financial Advisors

The Importance of Standard Deviation in Investment

Back

The Importance of Standard Deviation in Investment

The most frequently used measurement of investment risk is standard deviation. The measurement is used in math and science; it is calculated using a series of numbers. The first step in computing standard deviation is to calculate the mean or average. The second step is to determine the range of returns of the numbers, measured from the mean or average.

 

Standard deviation is a statistical measure of the degree to which an individual value in a probability distribution tends to vary from the mean of the distribution (a bell-shaped curve). The measurement is used widely by mutual fund advisory services and in modern portfolio theory (MPT). In the case of MPT, past performance of an asset class is used to determine the range of possible future performances and a probability is attached to each performance. The standard deviation of performance can then be calculated for each security and for the portfolio as a whole. The greater the degree of dispersion or variance in annual returns, the higher the standard deviation and risk.

Calculating Standard Deviation

With most investments, including mutual funds and ETFs, standard deviation is calculated using monthly returns for the past 36 months. For example, if a fund rose exactly 1% each month for 36 months, its standard deviation would be zero. “Zero” because there is no variation of returns; every monthly return is exactly the same as the average.
 
Standard deviation treats positive numbers the same as negative ones. Thus, if a fund dropped exactly 1% each month, its standard deviation would also be zero. The beauty, or appeal, of standard deviation is it shows an asset’s performance swings over a 36-month period as a single number.
 
As the table below shows, there are six steps involved in computing standard deviation: [1] calculate the average (mean) annual return, [2] then go back and subtract the mean return from the actual return for that period, [3] square that difference (the deviation) for each period, [4] add up all of the squared deviations, [5] divide the sum by the number of periods (this is known as the variance)—typically 36 months of observations, and [6] calculate the square root of the sum of the squared deviations (the resulting number is the standard deviation).
 
Calculating Standard Deviation

Period

Annual Return
Deviation For Each Period
(step #2)
Deviation Squared
(step #3)
 
1
-3.4
-9.6
92.0
 
2
9.9
3.7
13.8
 
3
-2.0
-8.2
67.1
 
4
21.7
15.5
240.6
 
5
-6.2
-12.4
153.5
 
6
11.0
4.8
23.1
 
7
-9.1
-15.3
233.8
 
8
13.1
6.9
47.7
 
9
-1.5
-7.7
59.1
 
10
28.6
22.2
493.3
 
sum 
(1–10)
61.9
 
1,424.0
sum of squared deviations 
(step #4)
average
(step #1)
 
6.2%
 
142.4
divided by number of periods
(step #5)
 
 
 
11.9%
std. dev. (square root of variance) 
(step #6)
The table above consists of just 10 monthly returns in order to make the example easier to follow. The final number in this example, 11.9%, represents one standard deviation. By definition, a portfolio’s or asset’s returns will range within plus or minus one standard deviation of its yearly average ~ 2/3 of the time. Its returns will vary within two standard deviations about 95% of the time. 
 
For example, suppose an asset has an average yearly return of 10% and a standard deviation of 15%. Based on the above definition, we can expect its annual performance will fall within the -5% to +25% range about 2/3 of the time (every two out of three years). And about 95% of the time (19 out of 20 years), returns should lie within the bounds of -20% and +40% (two standard deviations). This shows the magnitude of loss in an unusual year.
 
Standard deviation is a statistical measurement of how far a variable, such as an investment’s return, moves above or below its average (mean) return. An investment with high volatility is considered riskier than an investment with low volatility; the higher the standard deviation, the higher the risk. A traditional bell curve is a good way to visualize the concept of an investment’s returns over an extended period of time.

 

Why Standard Deviation is Widely Used

This yardstick also has its shortcomings because it is based on past data that might not be repeated in the future. Nevertheless, standard deviation is the single best mutual fund and ETF risk measurement because:
 
  1. it is a broader measure than beta; it gauges total risk, not just market-related volatility;
  2. it idoes not depend on any relationship to an arbitrarily chosen market index;
  3. it can measure risk of specialized portfolios as well as broadly diversified ones;
  4. it can be used to gauge the variability of both bond or stock investments, and
  5. it is a tool that helps match the risk level of an asset or portfolio to a client’s risk tolerance.
2011 vs. 2009 vs. 2008 Standard Deviations

Fund Category

Standard Deviation

Fund Category

Standard Deviation

Large Cap Growth

19 / 17 / 18

Foreign Large Growth

23 / 21 / 22

Mid Cap Growth

21 / 20 / 21

Foreign Large Blend

23 / 20 / 20

Small Cap Growth

24 / 21 / 21

Foreign Large Value

24 / 20 / 20

Large Cap Blend

20 / 17 / 16

Foreign Small–Mid Growth

23 / 23 / 25

Mid Cap Blend

22 / 20 / 20

Foreign Small–Mid Value

24 / 22 / 23

Small Cap Blend

25 / 21 / 20

Emerging Markets Stock

26 / 28 / 29

Large Cap Value

20 / 17 / 16

Balanced

16 / 12 / 12

Mid Cap Value

22 / 20 / 18

Convertibles

13 / 15 / 16

Small Cap Value

26 / 21 / 19

Long-Term Government

17 / 14 / 13

Precious Metals

34 / 40 / 42

Med-Term Government

3 / 4 / 4

Natural Resources

27 / 29 / 30

Short-Term Government

2 / 2 / 2

Technology

22 / 22 / 23

Emerging Markets Debt

10 / 12 / 14

Utilities

14 / 16 / 17

High-Yield Bond

10 / 12 / 13

Health Care

17 / 16 / 16

Multi-Sector Bond

7 / 8 / 9

Financial

27 / 23 / 20

World Bond

8 / 7 / 8

Real Estate

30 / 31 / 30

High-Yield Municipal

8 / 9 / 9

Bear Market

28 / 23 / 22

Long-Term Municipal

6 / 6 / 6

World Stock

21 / 19 / 19

Med-Term Municipal

4 / 4 / 4

 

 

Short-Term Municipal

2 / 2 / 2

In summary, look at a fund’s standard deviation compared with its peer group or category (e.g., large cap growth funds had a 19% standard deviation for 2011, 17% for 2009, and 18% for 2008). In the case of large cap blend funds, an appropriate yardstick would be the S&P 500 (a “blend” of large growth and value). For bond funds, the appropriate measurement is likely to be the Barclays Aggregate Bond Index. For some bond funds, such as short-term, high-yield, emerging markets debt or foreign, other indexes would be the appropriate benchmark.

 

Previous Post
The Relationship Between Alpha and Mutual Funds

Next Post
Duration - An Introduction

For Advisors by Advisors. Browse all Programs.

Call Us Now

Telephone : (800) 848-2029

Our Address

PO Box 371243
San Diego, CA, 92137 USA

Send Us A Message

Main Email : info@icfs.com
Student Services: studentservices@icfs.com

Get Updates

Don't miss out! Subscribe to our newsletter by filling out the form below