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L1 - Capital Allocation Line
Name
Equation
Example
Expected Return, E(rCβ)
E(rCβ)=rFβ+y(E(rPβ)βrFβ) or E(rCβ)=yE(rPβ)+(1βy)rFβ
= .04 + .50*(.12-.04) = .08 or 8% or = (.12 * .50) + (.04 * .50) = 8%
Using Helper Formula β£, below, it follows that: Var(rpβ)=w12βΟ12β+w22βΟ22β+2w1βw2βΟ1βΟ2βCorr1,2β Ex: Var = 60%^2*15%^2 + 40%^2*9%^2 + 2*60%*40%*15%*9%*.2 = 0.010692
SD with 2 risky assets
CalcTake square root of variance to get Standard Deviation/Ο (See Helper Formula β‘, below). ΟPβ=Varβ= 0.010692^.5 = 10.34%
Expected Value of Return: CAL: E(rCβ)=rFβ+y(E(rPβ)βrFβ) Two risky assets: E(rpβ)=w1βE(r1)+w2βE(r2β) Classic equation: E(aX+bY)=aE(X)+bE(Y)
Standard Deviation of Return (Risk): CAL: ΟCβ=yΟPβ Two risky assets: ΟPβ=SQRT(Ο1β2w1β2+Ο2β2w2β2+2w1βw2βCov1,2β) ΟPβ=SQRT(Ο1β2w1β2+Ο2β2w2β2+2w1βw2βΟ1βΟ2βCorr1,2β) Classic equation: Var(aX+bY)=a2Var(X)+b2Var(Y)+2abCov(X,Y)
* I wouldn't worry about using the two classic equations - but it's good to know the formulas Bruce used to come up with our equations.
Probability Helper Formulas: Variance and Standard Deviation: Ο=VarβΒ andΒ Var=Ο2 Covariance and Correlation: Ο12β=Ο1βΟ2βCov(r1β,r2β)βΒ andΒ Cov(r1β,r2β)=Ο12βΟ1βΟ2β
L3-L4 - CAPM and EMH
Name
Equation
Capital Asset Pricing Model (CAPM)
ErPβ=rFβ+Ξ²(E(rMβ)βrFβ)
In EMH, Investors value a stock as the PDV of its future cash flows: (for stocks, cash flows = dividends)
Risk free rate OR return on T-Bills OR return on short term government securities OR return on securities perceived to be risk-free
E(rSβ)=12%
Expected (rate of) return offered by a specific security OR Expected rate of return *required by the market* for a specific portfolio (or stock) (E(riβ) and E(rSβ) mean the same thing. 'i' just refers to a numbered security and 's' just refers to a specific stock.)
E(rSβ)βrFβ=7% or E(RSβ)
(Expected) risk premium for a specific security or portfolio Note: I can get 5% by investing in risk-free assets, so I ignore the first 5% of the return from investing in a stock. I'm only interested in the 7% risk premium that I get above the risk-free rate.
Ξ²
Beta (a measure of non-diversifiable risk)
rMβ
The actual return on the market portfolio. Note: We imagine a portfolio consisting of every single stock, bond, and other security in existence. We call this special portfolio "the market portfolio." rMβ is the expected return of the market portfolio.
E(rMβ)
Expected return of the market OR Expected market return OR Expected return of/on the market portfolio
E(rMβ)βrFβ or E(RMβ)
(Expected) Risk Premium of the market OR (Expected) Risk Premium of the market portfolio
RSβ=rSββrFβ RMβ=rMββrFβ
Excess Return of a security Excess Return of the market (The textbook will use this notation.)