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Lecture2_StockPricing

# 5 erp 515 507 11 or 11 5 24 variancestandard

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Unformatted text preview: d portfolio returns For example, y = .5 E(rp) = .5(.15) + .5(.07) = .11 or 11% 5-24 Variance/standard deviation on the Portfolios σp2 = (y σs)2 + [(1 - y) σf]2 +2(y σs)[(1 - y) σf] ρ, where ρ is the correlation between riskfree rate and stock return Since ρ = 0 (why?), thus σ p = y σs 5-25 Portfolio expected returns and std. depending on various compositions If y = .5, then E(rp) = 0.11 σ p = .5(.22) = .11 or 11% If y = 1 then E(rp) = 0.15 σ p = 1(.22) = .22 or 22% If y = 0 then E(rp) = 0.07 σ p = 0(.22) = .00 or 0% 5-26 Implementation “1 riskfree 1 risky line” in “Lecture2_StockPricing” 5-27 Figure: Risk-return trade-off of the portfolio of one stock and T-bill Leverage 5-28 Portfolios with leverage • Borrow from banks (at the risk-free rate) and Borrow invest in stock invest • Using 25% leverage (i.e., 125% in stocks) E(rp ) = (-.25) (.07) + (1.25) (.15) = 17% E(r σp = (1.25) (.22) = 27.5% 5-29 Risk-return trade-off Summary: % in stock 0% 50% 100% 125% E(rp ) 7% 11% 15% 17% σp 0.0% 11.0% 22.0% 27.5% • The summary and the upward-sloped capital The allocation line present a clear picture of risk-return trade-off (if you want to earn more, you have to take higher risk) take 5-30 Capital allocation line of 2 risky assets 5-31 Now, what if there is no risk-free asset? We have only two risky assets: one stock and We one bond one rp = w r +w r B B S S rP = Portfolio Return wB = Bond Weight rB = Bond Return wS = Stock Weig ht rS = Stock Return 5-32 Calculations for Two-Risky-Asset Portfolios Return on the portfolio in each period: rP = wB rB + wS rS Expected/average returns on the portfolio: E (rP ) = wB E (rB ) + wS E (rS ) 5-33 Three Rules of Two-Risky-Asset Portfolios Variance of the rate of return on the portfolio: 2 σ P = ( wBσ B ) 2 + ( wSσ S ) 2 + 2( wBσ B )( wSσ S ) ρ BS Portfolio risk depends on the correlation Portfolio between stock returns and bond returns between Covariance and the correlation coefficient ( ρ) provide a measure of the returns on how two assets covary assets 5-34 Covariance and Correlation Coefficient Covariance (time series or cross-section of...
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