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:
 All Investors are Efficient Investors  Investors follow Markowitz idea of the efficient frontier and choose to invest in portfolios along the frontier.
 Investors Borrow/Lend Money at the RiskFree Rate  This rate remains static for any amount of money.
 The Time Horizon is equal for All Investors  When choosing investments, investors have equal time horizons for the choseninvestments.
 All Assets are Infinitely Divisible  This indicates that fractional shares can be purchased and the stocks can be infinitely divisible.
 No Taxes and Transaction Costs assume that investors' results are not affected by taxes and transaction costs.
 All Investors Have the Same Probability for Outcomes When determining the expected return, assume that all investors have the same probability for outcomes.
 No Inflation Exists  Returns are not affected by the inflation rate in a capital market as none exists in capital market theory.
 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 riskfree asset is added to a portfolio of risky assets?
To begin, the riskfree asset has a standard deviation/variance equal to zero for its given level of return, hence the "riskfree" label.
 Expected Return  When the RiskFree Asset is Added
Given its lower level of return and its lower level of risk, adding the riskfree asset to a portfolio acts to reduce the overall return of the portfolio.
Example: RiskFree 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 riskfree 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 riskfree asset?
Answer:
The expected return of the new portfolio is: (0.9)(16%) + (0.1)(4%) = 14.4%
With the addition of the riskfree asset, the expected value of the investor's portfolio was decreased to 14.4% from 16%.
 Standard Deviation  When the RiskFree Asset is Added
As we have seen, the addition of the riskfree asset to the portfolio of risky assets reduces an investor's expected return. Given there is no risk with a riskfree asset, the standard deviation of a portfolio is altered when a riskfree asset is added.
Example: Riskfree 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 riskfree 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 riskfree asset?
Answer:
The standard deviation equation for a portfolio of two assets is rather long, however, given the standard deviation of the riskfree asset is zero, the equation is simplified quite nicely. The standard deviation of the twoasset 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 riskfree asset had on the expected return, the riskfree asset also has the affect of reducing standard deviation, risk, in the portfolio.
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