CV Standard Deviation Expected Rate of Return Mean \u03c3 r Risk aversion assumes

Cv standard deviation expected rate of return mean σ

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CV = Standard Deviation Expected Rate of Return / Mean = σ r Risk aversion : assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium = mean return – risk free rate PORTFOLIO Expected Portfolio Return: ! ! = ! ! ! ! ! ! ! ! Portfolio Risk / SD Applying the standard deviation & CV formulas: SD of 2 Stock Portfolio: SD of a portfolio can be lower than any of its investments: negative correlation between stocks → negative covariance COVARIANCE : measures how two assets’ rates of return vary together over the same mean time period. CORRELATION COEFFICIENT ρ XY : extent to which X & Y move together → affects variance of portfolio (-1 to 1) Standardises the unit of covariance measure ! ! , ! = !"# ! ! , ! ! σ ! σ ! 2 stocks can be combined to form riskless portfolio if p= -1.0 Risk is not reduced at all if the 2 stocks have p = +1.0 As p à -1, risk gets eliminated. As p à +1, no risk gets eliminated. Total Risk = Company-Specific Risk + Market Risk Company-specific risk (unsystematic risk): can be diversified away in a portfolio while market risk (systematic risk) cannot. For a well-diversified portfolio, total risk σ is essentially systematic risk. MEASURING ASSET’S MARKET RISK – BETA: (mostly 0.5 – 1.5) β i <1 : asset has less systematic risk than market β i >1 : asset has more systematic risk than market β market = 1 β risk free asset = 0 Portfolio Volatility : total risk of portfolio (portfolio SD) Combined stocks positively correlated → risk level drops a bit Combined stocks negatively correlated → risk level drops a lot Beta (β): measures risk of security held in a large portfolio Measures the responsiveness of security to movements in the market portfolios Slope of the regression line of the asset’s returns on the market portfolio’s returns. Depending on the time period, beta will change. Therefore, we have to compare 2 stocks/markets in the same time period. SECURITY MARKET LINE (SML): risk return relationship between β of a security and its required rate of return. Reward-to-risk ratio = slope of the line β for market ALWAYS 1 hence Slope = R M – R f = market risk premium In equilibrium, all assets and portfolios must have the same reward-to-risk ratio. Equilibrium means expected return = required return CAPITAL ASSET PRICING MODEL (CAPM): Defines relationship between risk and required return R f : risk-free rate (R M – R f ): market risk premium Required risk premium= Beta * market risk premium Portfolio Beta : sum of each asset’s beta x portfolio weight Fairly priced asset: expected return is on the SML Under-priced asset: above the SML (expected>required) Over-priced asset: below the SML Impact of Inflation Change On SML Impact of a Risk Aversion Change: More risk averse à SML steeper More risk loving à SML less steep MARKOWITZ PORTFOLIO THEORY: combining stocks into portfolios can reduce SD below that from a simple weighted average calculation Efficient portfolio : provides the greatest expected return for given level of SD/ lowest risk for a given expected return Efficient frontier:
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