Sunday, December 11, 2011

Capital Market Theory

CFA Level 1 - Portfolio Management

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?

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?

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.

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