- CFA Exams
- 2023 Level I
- Topic 9. Portfolio Management
- Learning Module 62. Portfolio Risk and Return: Part I
- Subject 3. Variance and Covariance of Returns

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##### Subject 3. Variance and Covariance of Returns PDF Download

Investment is all about reward versus variability (risk). The return measures the reward of an investment and dispersion is a measure of investment risk.

σ

Standard Deviation of Portfolio [0.5

The

**variance**is a measure of how spread out a distribution is. It is computed as the average squared deviation of each number from its mean. The formula for the variance in a population is:where μ is the mean and N is the number of scores.

To compute variance in a sample:

where m is the sample mean.

The formula for the

**standard deviation**is very simple: it is the square root of the variance. It is the most commonly used measure of spread.The

**standard deviation of a portfolio**is a function of:

- The weighted average of the individual variances, plus
- The weighted covariances between all the assets in the portfolio.

In a two-asset portfolio:

The maximum amount of risk reduction is predetermined by the correlation coefficient.

__Thus, the correlation coefficient is the engine that drives the whole theory of portfolio diversification.__

*Example with perfect positive correlation (assume equal weights):*What is the standard deviation of a portfolio (E), assuming the following data?

σ

_{1}= 0.1, w_{1}= 0.5, σ_{2}= 0.1, w_{2}= 0.5, ρ_{12}= 1Solution:

Cov

_{12}= σ_{1}x σ_{2}x ρ_{12}= 0.1 x 0.1 x 1 = 0.01Standard Deviation of Portfolio [0.5

^{2}x 0.1^{2}+ 0.5^{2}x 0.1^{2}+ 2 x 0.5 x 0.5 x 0.01]^{1/2}= 0.10 (perfect correlation)If there are three securities in the portfolio, its standard deviation is:

**Learning Outcome Statements**

CFA® 2023 Level I Curriculum, Volume 5, Module 62

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**User Contributed Comments**
4

User |
Comment |
---|---|

lucymiami |
is there any way to calculate covariances or correlations on return using BA II Plus calculator, thnx |

jejasin |
unfortunately, no. Just have to remember these. |

maryprz14 |
I forgot what was p! :/ |

CFANathan |
p = correlation coefficient |

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