Portfolio Standard deviation Risk Premium Return Risk free rate Treasury bills

# Portfolio standard deviation risk premium return risk

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Portfolio Standard deviation Risk Premium = Return – Risk free rate Treasury bills considered risk free. Coefficient of Variation (CV): standardized measure of dispersion about expected value, that shows relative variability/risk per unit of expected return. Covariance How 2 assets move/don’t move tgt. Used to measure how 2 assets’ rate of return vary tgt over same time period. If portfolio SD much lower than either stock SD and avg of both, means negative CV due to negative correlation. Covariance = XY XY X Y Correlation Coefficient, 1 ≥ ρ XY 1 measures the extent to which 2 securities X and Y move together For 2 perfectly -/+ correlated stocks, ρ = -1.0/ 1.0 2 stocks can combine to form riskless portfolio if ρ = -1.0 Risk not reduced at all if 2 stocks have ρ = 1.0 W5: Risk & Return 2 Diversification . ↓variability of returns w/o equivalent ↓ in expected returns, as worse-than-expected returns from 1 asset offset by better-than-expected returns frm another. Well-d portfolios’ total risk (sigma) = systematic risk (which depends on sensitivity to mkt factors) as firm- specific risk close to 0/variance frm mkt risk. BUT for indiv asset, total risk measure =/= systematic risk. Total Risk = Company specific risk(unsystematic/unique /diversifiable) + Market risk (systematic, non-diversifibale) (Note: - B =/= non-systematic risk) Standard deviation  Total Risk Diversifiable Risk: Caused by random events: lawsuit, unsuccessful mkting prog, lose major contract. 1 firm's bad event can be offset by another's good events: Effects elim by portfolio Undiversifiable Risk: Measured by stock beta Factors that affect most firms: war, inflation, recession, high i/r. Most firms affect so mkt risk cant be diversified away by combining stocks: they'll move in same direction (all benefit/suffer but diff degrees). Stock Beta : Beta  Systematic risk (Non-diversifiable risk) measures responsiveness of a security to movements in mkt portfolio Beta is aslope of regression line of asset’s returns on mkt portfolio returns Asset Beta = covariance ( investment return,market r Market portfolioVariance ρ ρ ( ¿¿ ℑ) ( σ i σ M ) ( ¿¿ ℑ)( σ i )( σ M ) σ M 2 = ¿ β i = cov ( r i ,r M ) σ M 2 = ¿ ρ ρ ( ¿¿ MM ) ( σ M σ M ) = 1 ( ¿¿ MM )( σ M )( σ M ) σ M 2 = ¿ M = ¿¿ β ¿ Beta β P = j = 1 m ( W j )( β j ) Returns Portfolio return = (stock % of portfolio)(Ra) + (stock %..) Tells u an asset's risk relative to avg asset. Mkt Beta = 1, most stocks: 0.5 - 1.5 - β i > 1 : Asset’s systematic risk < mkt’s (security’s expected return > risk free rate) - β i < 1 : Asset’s systematic risk > mkt’s (security’s expected return < risk free rate) - Beta = 0: risk free asset (T-bill) Indicates stock's riskiness, if held in a well-diversified portfolio Systematic risk principle: reward for bearing risk depends on investmnt’s systematic risk. Expected return of an asset only depends on that asset's systematic risk. *** can have diff degrees of market risk for diff portfolio.

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