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Wize University Introduction to Finance Textbook > Risk, Return & Portfolio Theory

Portfolio Risk and Return

Covariance and CorrelationPrevious Section
Portfolio Standard Deviation (Special Cases)Next Section
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What is a Portfolio?

A portfolio is a collection of investments that are combined and considered a single asset. Could be made up of different kinds of investments such as bonds and stocks.

The Weights of the Portfolio

  • The weight of an asset is the proportion of the portfolio that is invested in that asset.
  • Can be any value, including negative values and values over 100%.
  • Weights are negative and over 100% when the investor is shorting or borrowing
  • Found by dividing the dollars invested in an asset by the total value of the portfolio.
Example:
An investor constructs the following portfolio: $5,000 into Stock A, $2,000 into Stock B, and $9,000 into Stock C.


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Expected Return

The expected return for an investment portfolio is the weighted average of the expected return of each of its components. Components are weighted by the percentage of the portfolio's total value that each accounts for.

Standard Deviation (Risk)

  • The standard deviation of the rate of return on an investment portfolio.
  • 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.

Standard Deviation of a 2 Asset Portfolio


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Example: Expected Return and Risk of a Portfolio

Suppose you are given the following information for two stocks, A and B, where the return on each varies with the state of the economy. An investor invests $2,000 into Stock A and $3,000 into Stock B.



a) Compute the expected return for each stock

b) Compute the standard deviation for each stock

c) Compute the covariance between the two stocks

d) Compute the expected return of the portfolio

e) Compute the standard deviation of the portfolio

Practice: Expected Return and Risk of a Portfolio

You have $5,000 to invest and are considering investing $3,000 into Stock A and the rest into Stock B.


What is the expected return of the portfolio?
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Example: Shorting

You construct the following portfolio:
  • Long 500 shares of Stock A at $22.50 per share
  • Short 100 shares of Stock B at $10.00 per share
What is the expected return of the portfolio if the expected returns of Stocks A and B are 23% and 12% respectively?

Practice: Shorting

Using this information, answer the following questions:
  • ERX=10%ER_X=10\%
  • ERY=12%ER_Y=12\%
  • σX=20%\sigma_X=20\%
  • σY=15%\sigma_Y=15\%
  • ρXY=0.6\rho_{XY}=0.6

You construct a portfolio by investing $10,000 into stock Y, and shorting $5,000 of stock X.

Round your final answers to 2 decimal places and enter a percentage.
Extra Practice
Which of the following statements about modern portfolio theory is/are TRUE?
You've constructed a portfolio by investing in Stock A, which has an expected return of 5.2% and Stock B which has an expected return of 16%. The standard deviations for Stocks A and B respectively are 8.33% and 7.35%. The covariance between the stocks is 0.00612.
What is the expected return of the portfolio if you short sold $400 worth of Stock A and invested $1400 into Stock B?
You've constructed a portfolio by investing in Stock A, which has an expected return of 5.2% and Stock B which has an expected return of 16%. The standard deviations for Stocks A and B respectively are 8.33% and 7.35%. The covariance between the stocks is 0.00612.
What is the standard deviation of the portfolio if 60% of your funds are invested in Stock A and the rest in Stock B?
You've constructed a portfolio by investing in Stock A, which has an expected return of 5.2% and Stock B which has an expected return of 16%. The standard deviations for Stocks A and B respectively are 8.33% and 7.35%. The covariance between the stocks is 0.00612.
What is the expected return of the portfolio if 60% of your funds are invested in Stock A and the rest in Stock B?
You have a portfolio with two risky assets, Stock A and Stock B. The expected return for Stock A is 12% and the variance is 0.0225. The expected return for Stock B is 16% and the variance is 0.0289. The portfolio is equally invested in both stocks, with 60% in Stock A and 40% in Stock B. What is the standard deviation of the portfolio if the correlation coefficient between the stocks is 0.83?
You have a portfolio with two risky assets, Stock A and Stock B. The expected return for Stock A is 12% and the expected return for Stock B is 16%. The portfolio has 60% in Stock A and 40% in Stock B. What is the expected return for the portfolio?