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Unformatted text preview: d portfolio returns
For example, y = .5
E(rp) = .5(.15) + .5(.07)
= .11 or 11%
524 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
525 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%
526 Implementation
“1 riskfree 1 risky line” in “Lecture2_StockPricing” 527 Figure: Riskreturn tradeoff of the portfolio
of one stock and Tbill Leverage 528 Portfolios with leverage
• Borrow from banks (at the riskfree 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% 529 Riskreturn tradeoff
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 upwardsloped capital
The allocation line present a clear picture of riskreturn
tradeoff (if you want to earn more, you have to
take higher risk)
take
530 Capital allocation line of 2 risky assets 531 Now, what if there is no riskfree 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
532 Calculations for TwoRiskyAsset 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 )
533 Three Rules of TwoRiskyAsset 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
534 Covariance and Correlation Coefficient
Covariance (time series or crosssection of...
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This document was uploaded on 03/03/2014.
 Spring '09

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