Portfolio Management - Capital Market Theory

The capital market theory builds upon the Markowitz portfolio model. The main assumptions of the capital market theory are as follows:

  1. All Investors are Efficient Investors - Investors follow Markowitz idea of the efficient frontier and choose to invest in portfolios along the frontier.
  2. Investors Borrow/Lend Money at the Risk-Free Rate - This rate remains static for any amount of money.
  3. The Time Horizon is equal for All Investors - When choosing investments, investors have equal time horizons for the choseninvestments.
  4. All Assets are Infinitely Divisible - This indicates that fractional shares can be purchased and the stocks can be infinitely divisible.
  5. No Taxes and Transaction Costs -assume that investors' results are not affected by taxes and transaction costs.
  6. All Investors Have the Same Probability for Outcomes -When determining the expected return, assume that all investors have the same probability for outcomes.
  7. No Inflation Exists - Returns are not affected by the inflation rate in a capital market as none exists in capital market theory.
  8. There is No Mispricing Within the Capital Markets - Assume the markets are efficient and that no mispricings within the markets exist.



What happens when a risk-free asset is added to a portfolio of risky assets?
To begin, the risk-free asset has a standard deviation/variance equal to zero for its given level of return, hence the "risk-free" label.

  • Expected Return - When the Risk-Free Asset is Added
    Given its lower level of return and its lower level of risk, adding the risk-free asset to a portfolio acts to reduce the overall return of the portfolio.

    Example: Risk-Free Asset and Expected Return
    Assume an investor's portfolio consists entirely of risky assets with an expected return of 16% and a standard deviation of 0.10. The investor would like to reduce the level of risk in the portfolio and decides to transfer 10% of his existing portfolio into the risk-free rate with an expected return of 4%. What is the expected return of the new portfolio and how was the portfolio's expected return affected given the addition of the risk-free asset?

    Answer:
    The expected return of the new portfolio is: (0.9)(16%) + (0.1)(4%) = 14.4%

    With the addition of the risk-free asset, the expected value of the investor's portfolio was decreased to 14.4% from 16%.
  • Standard Deviation - When the Risk-Free Asset is Added
    As we have seen, the addition of the risk-free asset to the portfolio of risky assets reduces an investor's expected return. Given there is no risk with a risk-free asset, the standard deviation of a portfolio is altered when a risk-free asset is added.

    Example: Risk-free Asset and Standard Deviation
    Assume an investor's portfolio consists entirely of risky assets with an expected return of 16% and a standard deviation of 0.10. The investor would like to reduce the level of risk in the portfolio and decides to transfer 10% of his existing portfolio into the risk-free rate with an expected return of 4%. What is the standard deviation of the new portfolio and how was the portfolio's standard deviation affected given the addition of the risk-free asset?

    Answer:
    The standard deviation equation for a portfolio of two assets is rather long, however, given the standard deviation of the risk-free asset is zero, the equation is simplified quite nicely. The standard deviation of the two-asset portfolio with a risky asset is the weight of the risky assets in the portfolio multiplied by the standard deviation of the portfolio.

    Standard deviation of the portfolio is: (0.9)(0.1) = 0.09

    Similar to the affect the risk-free asset had on the expected return, the risk-free asset also has the affect of reducing standard deviation, risk, in the portfolio.
The Capital Market Line


Related Articles
  1. Investing

    Risk-Free Rate of Return

    The risk-free rate of return is the theoretical rate of return of an investment with zero risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free ...
  2. Options & Futures

    How Risk Free Is The Risk-Free Rate Of Return?

    This rate is rarely questioned - unless the economy falls into disarray.
  3. Bonds & Fixed Income

    Understanding The Sharpe Ratio

    This simple ratio will tell you how much that extra return is really worth.
  4. Active Trading

    Modern Portfolio Theory: Why It's Still Hip

    See why investors today still follow this old set of principles that reduce risk and increase returns through diversification.
  5. Bonds & Fixed Income

    Find The Highest Returns With The Sharpe Ratio

    Learn how to follow the efficient frontier to increase your chances of successful investing.
  6. Investing

    Measure Your Portfolio's Performance

    Learn three ratios that will help you evaluate your investment returns.
  7. Investing Basics

    More Ways to Evaluate Portfolio Performance

    The Jensen measure is another tool investors use to include risk when measuring portfolio performance.
  8. Fundamental Analysis

    How Investment Risk Is Quantified

    FInancial advisors and wealth management firms use a variety of tools based in Modern portfolio theory to quantify investment risk.
  9. Personal Finance

    Risk-Free & 20% Return? More Like 100% Scam

    An investment that promises a risk-free return of 20% is 100% likely to be a scam.
  10. Options & Futures

    How & Why Interest Rates Affect Futures

    There are at least four factors that affect change in futures prices, including risk free-interest rates, particularly in a no-arbitrage environment.
RELATED TERMS
  1. Risk-Free Asset

    An asset which has a certain future return. Treasuries (especially ...
  2. Risk-Free Rate Of Return

    The theoretical rate of return of an investment with zero risk. ...
  3. Risk Premium

    The return in excess of the risk-free rate of return that an ...
  4. Sharpe Ratio

    The Sharpe Ratio is a measure for calculating risk-adjusted return, ...
  5. Homogeneous Expectations

    An assumption in Markowitz Portfolio Theory that all investors ...
  6. Post-Modern Portfolio Theory - ...

    A portfolio optimization methodology that uses the downside risk ...
RELATED FAQS
  1. How is it possible for a rate to be entirely risk-free?

    Find out whether there really is such a thing as a risk-free rate of return, and learn why taking the idea of risk-free rates ... Read Answer >>
  2. How is the risk-free rate of interest used to calculate other types of interest rates ...

    Learn how the risk-free rate is used to compare the yields on bonds, and understand how T-bills are used as a proxy for the ... Read Answer >>
  3. How is risk aversion measured in Modern Portfolio Theory (MPT)?

    Find out how risk aversion is measured in modern portfolio theory (MPT), how it is reflected in the market and how MPT treats ... Read Answer >>
  4. How accurate is the equity risk premium in evaluating a stock?

    Learn about the drawbacks of using the equity risk premium to evaluate a stock, and understand how it is calculated using ... Read Answer >>
  5. What two components are used to calculate risk-adjusted return? I ...

    The correct answer is b. Standard deviation and the risk-free rate of return are used to calculate or measure return based ... Read Answer >>
  6. What nations other than the U.S. have risk-free interest rates?

    Find out which countries have risk-free rates of returns. This is typically the yield on a 3-month note, and it can be negative ... Read Answer >>
Hot Definitions
  1. Demand Curve

    The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity ...
  2. Goldilocks Economy

    An economy that is not so hot that it causes inflation, and not so cold that it causes a recession. This term is used to ...
  3. White Squire

    Very similar to a "white knight", but instead of purchasing a majority interest, the squire purchases a lesser interest in ...
  4. MACD Technical Indicator

    Moving Average Convergence Divergence (or MACD) is a trend-following momentum indicator that shows the relationship between ...
  5. Over-The-Counter - OTC

    Over-The-Counter (or OTC) is a security traded in some context other than on a formal exchange such as the NYSE, TSX, AMEX, ...
  6. Quarter - Q1, Q2, Q3, Q4

    A three-month period on a financial calendar that acts as a basis for the reporting of earnings and the paying of dividends.
Trading Center