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
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