If you invest 50% of your money in Asset A and 50% in Asset B, what is the expected return and standard deviation for assets, A and B, as well as for the portfolio? State Probability A B Boom .4 30% -5% Bust .6 -10% 25% Asset A E(A) = 0.4(0.3) + 0.6(-0.10) = 0.06 Var(A) = 0.4(0.3 – 0.06) 2 + 0.6(-0.10 – 0.06) 2 = 0.0384 SD(A) = 0.1960 Asset B E(B) = 0.4(-0.05) + 0.6(0.25) = 0.13 Var(B) = 0.4(-0.05 – 0.13) 2 + 0.5(0.25 – 0.13) 2 = 0.0216 SD(B) = 0.1470 Portfolio E(P boom ) = 0.5(0.3)+0.5(-0.05) = 0.125 E(P bust ) = 0.5(-0.1) + 0.5(0.25) = 0.075 E(P) = 0.4(0.125) + 0.6(0.075) = 0.095 Var(P) = 0.4(0.125 – 0.095) 2 + 0.6(0.075 – 0.095) 2 = 0.0006 SD(P) = 0.0245 Expected and Unexpected Returns Total Return = Expected Return + Unexpected Return R = E(R) + U
36 Diversification Principle of Diversification Portfolio diversification The investment in several different asset classes or sectors. Not just holding a lot of assets o E.g. if you own 50 internet stocks, you are not diversified. However, if you own 50 stocks that span 20 different industries, then you are diversified. Argument for Diversification Substantially reduce the variability of returns without an equivalent reduction in expected returns. This is because worse than expected returns from one asset are offset by better than expected returns from another. However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion Systematic and Unsystematic Risks Systematic Risks Unsystematic Risks Risk that influences a large number of assets. Also known as Market Risk or Non-diversifiable risks . Examples of Systematic Risk General economic conditions (E.g. GDP, Interest Rates, Inflation, etc.) Risks that affect nearly all companies to some degree. Risk that affects at most a small number of assets. Also known as Unique or Asset-specific Risk . Examples of Unsystematic Risks Oil strike by a company, part shortages, etc. Risks that only affect the company and perhaps a few others (Primary competitors and suppliers) Recall from earlier: R = E(R) + U = E(R) + Systematic Portion + Unsystematic Portion Total Risk Total Risk = Systematic Risks + Unsystematic Risks The standard deviation of returns is a measure of total risk. For well diversified portfolios, unsystematic risk is very small. Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk.