Portfolio Management  Portfolio Calculations
Individual Investment
The expected return for an individual investment is simply the sum of the probabilities of the possible expected returns for the investment.
Formula 17.3 Expected Return E(R) = p_{1}R_{1} + p_{2}R_{2} + .....+ p_{n}R_{n}Where: p_{n }= the probability the return actually will occur in state n R_{n } = the expected return for state n 
Example:
For Newco's stock, assume the following potential returns.
Figure 3.3: Expected returns for Newco's stock price in the various states
Scenario Probability Expected Return Worst Case 10% 10% Base Case 80% 14% Best Case 10% 18%
Given the above assumptions, determine the expected return for Newco's stock.
Answer:E(R) = (0.10)(10%) + (0.80)(14%) + (0.10)(18%)E(R) = 14.0%
The expected return for Newco's stock is 14%.
Portfolio
To determine the expected return on a portfolio, the weighted average expected return of the assets that comprise the portfolio is taken.
Formula 17.4 E(R) of a portfolio = w_{1}R_{1} + w_{2}R_{q} + ...+ w_{n}R_{n} 
Example:
Assume an investment manager has created a portfolio with the Stock A and Stock B. Stock A has an expected return of 20% and a weight of 30% in the portfolio. Stock B has an expected return of 15% and a weight of 70%. What is the expected return of the portfolio?
Answer:
E(R) = (0.30)(20%) + (0.70)(15%)
= 6% + 10.5% = 16.5%
The expected return of the portfolio is 16.5%
Computing Variance and Standard Deviation for an Individual
To measure the risk of an investment, both the variance and standard deviation for that investment can be calculated.
Formula 17.5 Variance = Where: P_{n }= probability of occurrence R_{n} = return in n occurrence E(R) = expected return 
Formula 17.6 Standard Deviation = 
Example: Variance and Standard Deviation of an Investment
Given the following data for Newco's stock, calculate the stock's variance and standard deviation. The expected return based on the data is 14%.
Figure: Expected return for Newco in various states
Scenario Probability Return Expected Return Worst Case 10% 10% 0.01 Base Case 80% 14% 0.112 Best Case 10% 18% 0.018
Answer:
ฯ^{2 }= (0.10)(0.10  0.14)^{2} + (0.80)(0.14  0.14)^{2 }+ (0.10)(0.18  0.14)^{2}^{ }= 0.0003
The variance for Newco's stock is 0.0003.
Given that the standard deviation of Newco's stock is simply the square root of the variance, the standard deviation is 0.0179 or 1.79%.
Covariance
The covariance is the measure of how two assets relate (move) together. If the covariance of the two assets is positive, the assets move in the same direction. For example, if two assets have a covariance of 0.50, then the assets move in the same direction. If however the two assets have a negative covariance, the assets move in opposite directions. If the covariance of the two assets is zero, they have no relationship.
Formula 17.7 Covariance_{a,b}= 
Example: Calculate the covariance between two assets
Assume the mean return on Asset A is 10% and the mean return on Asset B is 15%. Given the following returns over the past 5 periods, calculate the covariance for Asset A as it relates to Asset B.
Returns
NR_{a} R_{b} 1 10% 18% 2 15% 25% 3 5% 2% 4 13% 8% 5 8% 17%
Answer:
NR_{a} R_{b} R_{a} Avg R_{a} R_{b}Avg R_{b} R_{a} Avg R_{a }R_{b}Avg R_{b} 1 10 18 0 3 0 2 15 25 5 10 50 3 5 2 5 13 65 4 13 8 3 7 21 5 8 17 2 2 4
Sum90.00 The covariance would equal 18 (90/5).
Correlation
The correlation coefficient is the relative measure of the relationship between two assets. It is between +1 and 1, with a +1 indicating that the two assets move completely together and a 1 indicating that the two assets move in opposite directions from each other.
Formula 17.8 
Example: Calculate the correlation of Asset A with Asset B.
Given our covariance of 18 in the example above, what is the correlation coefficient for Asset A relative to Asset B if Asset A has a standard deviation of 4 and Asset B has a standard deviation of 3.
Answer:
Correlation coefficient = 18/(8)(4) = 0.563
Components of the Portfolio Standard Deviation Formula
Remember that when calculating the expected return of a portfolio, it is simply the sum of the weighted returns of each asset in the portfolio. Unfortunately, determining the standard deviation of a portfolio, it is not that simple. Not only are the weights of the assets in the portfolio and the standard deviation for each asset in the portfolio needed, the correlation of the assets in the portfolio is also required to determine the portfolio standard deviation.
The equation for the standard deviation for a two asset portfolio is long, but should be memorized for the exam.
Formula 17.9 

Career Education & Resources
How Hard are the CFA Exams?
Learn about the difficulty of the CFA exams with a description of the tests, some statistics on pass rates and suggestions that can help you pass the exams. 
Professionals
What it Takes to be a Financial Analyst
A financial analyst researches companies and economic conditions to make business, sector and industry recommendations. 
Career Education & Resources
Financial Analyst: Career Path & Qualifications
Read about what it takes to become a financial analyst in a corporation or securities firm, and learn how far you can rise in the profession. 
Career Education & Resources
Financial Planner: Career Path & Qualifications
Learn what education and certifications you need to become a financial planner, as well as the future prospects and earnings potential for financial planners. 
Career Education & Resources
Where to Find NonProfit Finance Jobs
The nonprofit sector offers a stable selection of jobs for those who seek other types of fulfillment from their jobs than just purely financial. 
Career Education & Resources
Portfolio Manager: Career Path & Qualifications
Learn about the basic requirements for getting hired as a portfolio manager, and discover how most professionals in the field rise into the position. 
Your Practice
4 Professional Associations Advisors Should Join
These four professional organizations are among the most respected and well known in the industry. 
Professionals
Equity Research: Career Path and Qualifications
Find out what equity research analysts do on a daytoday basis, and learn more about the typical career progression for these securities professionals. 
Professionals
What's on the CFA Level II Exam?
The Chartered Financial Analyst Level II exam is the second of three tests that CFA candidates must pass. 
Professionals
Financial Data Analyst: Career Path & Qualifications
Learn more about the career options available to financial data analysts, and determine whether the profession is a good match for you.

Personal Financial Advisor
Professionals who help individuals manage their finances by providing ... 
CFA Institute
Formerly known as the Association for Investment Management and ... 
Chartered Financial Analyst  CFA
A professional designation given by the CFA Institute (formerly ... 
Security Analyst
A financial professional who studies various industries and companies, ...

What are the differences between a Chartered Financial Analyst (CFA) and a Certified ...
The differences between a Chartered Financial Analyst (CFA) and a Certified Financial Planner (CFP) are many, but comes down ... Read Full Answer >> 
How do I become a Chartered Financial Analyst (CFA)?
According to the CFA Institute, a person who holds a CFA charter is not a chartered financial analyst. The CFA Institute ... Read Full Answer >> 
What types of positions might a Chartered Financial Analyst (CFA) hold?
The types of positions that a Chartered Financial Analyst (CFA) is likely to hold include any position that deals with large ... Read Full Answer >> 
Who benefits the most from prepaid expenses?
Prepaid expenses benefit both businesses and individuals. Prepaid expenses are the types of expenses that are bought or paid ... Read Full Answer >> 
If I am looking to get an Investment Banking job. What education do employers prefer? ...
If you are looking specifically for an investment banking position, an MBA may be marginally preferable over the CFA. The ... Read Full Answer >> 
Can I still pass the CFA Level I if I do poorly in the ethics section?
You may still pass the Chartered Financial Analysis (CFA) Level I even if you fare poorly in the ethics section, but don't ... Read Full Answer >>