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## 2. Capital Asset Pricing Model Capm Notes This is an extract of our 2. Capital Asset Pricing Model Capm document, which we sell as part of our Corporate Finance Notes collection written by the top tier of University Of London (examined By LSE) students.

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Capital Asset Pricing Model (CAPM)
Mean-variance Analysis and CAPM
Expected Rate of Return
Probability
P(X) = Probability that X happens
P(Y) = Probability that Y happens
Note: P(X) + P(Y) = 1
Change in Price (P) = (P1 - P0) / P0
P0 = Purchase Price (Period 0)
P1 = Stock Price at Period 1
Rate of Return (R) = Change in Price (%)
Stock A

Stock B

R under P(X)

RAX = (PAX1 - PA0) / PA0

RB = (PBX1 - PB0) / PB0

R under P(Y)

RAY = (PAY1 - PA0) / PA0

RB = (PBY1 - PB0) / PB0

Expected Rate of Return on Stock A
E(RA) = P(X) x RAX + P(Y) x RAY
Expected Rate of Return on Stock B
E(RB) = P(X) x RBX + P(Y) x RBY
Expected Rate of Return on the Portfolio
E(RP) = aE(RA) + bE(RB)
Weighting: a + b = 1 or b = 1 - a a = (No. of Stock A x PA0) / (No. of Stock A x PA0 + No. of Stock B x PB0)
b = (No. of Stock B x PB0) / (No. of Stock A x PA0 + No. of Stock B x PB0)
Standard Deviation () = Risk
A = {[P(X) x RAX - E(RA)]2 + [P(Y) x RAY - E(RA)]2}0.5
B = {[P(X) x RBX - E(RB)]2 + [P(Y) x RBY - E(RB)]2}0.5
Variances (2)

1 Variance of return (risk) on the portfolio: P2 = a2A2 + b2B2 + 2abAB
Covariances (AB)
Relationship between the rate of return on Stock A and Stock B
AB = E(RAB) - E(RA) x E(RB)
E(RAB) = [E(RA) + E(RB)] / 2
Correlation Coefficient (AB)
Relationship between the rate of return on Stock A and Stock B
Value between -1 and +1
AB = AB / AB

2 2

2 A

or 2

AB =ABAB

2 B

 P = a  + b  + 2abABAB
Perfectly positively correlated: AB = 1
Positively correlated: 0 < AB < 1
Uncorrelated: AB = 0
Negatively correlated: -1 < AB < 0
Perfectly negatively correlated: AB = -1
Portfolio with 3 Stocks (N = 3)
Expected Rate of Return on Stock A
E(RA) = P(X) x RAX + P(Y) x PAY
Expected Rate of Return on Stock B
E(RB) = P(X) x RBX + P(Y) x RBY
Expected Rate of Return on Stock C
E(RC) = P(X) x RCX + P(Y) x RCY
Expected Rate of Return on the Portfolio
E(RP) = aE(RA) + bE(RB) + cE(RC)
Weighting: a + b + c = 1

a=

b=

No. of Stock A x PA0
No. of Stock A x PA0 + No. of Stock B x PB0 + No. of Stock C x PC0
No. of Stock B x PB0
No. of Stock A x PA0 + No. of Stock B x PB0 + No. of Stock C x PC0 2 c=

No. of Stock B x PC0
No. of Stock A x PA0 + No. of Stock B x PB0 + No. of Stock C x PC0

Standard Deviation () = Risk
A = {[P(X) x RAX - E(RA)]2 + [P(Y) x RAY - E(RA)]2}0.5
B = {[P(X) x RBX - E(RB)]2 + [P(Y) x RBY - E(RB)]2}0.5
C = {[P(X) x RCX - E(RC)]2 + [P(Y) x RCY - E(RC)]2}0.5
Variances (2)
Variance of return (risk) on the portfolio:
P2 = a2A2 + b2B2 + c2C2 + abAB + baBA + acAC + caCA + bcBC + cbCB
P2 = a2A2 + b2B2 + c2C2 + 2abAB + 2acAC + 2bcBC
N(N - 1) = 6
N = Number of Stocks in the Portfolio
Diversification
 To eliminate risk derived from individual stocks by reducing the portfolio variance
 The portfolio variance (P ) falls as the number of the assets held increases (N  )
P2 = (N / N2) VarP + [N (N - 1) / N2] CovP
P = (1 / N) VarP + (1 - 1 / N) CovP
VarP = Average Variance
CovP = Average Covariance
Two Stocks

Three Stocks

VarP = (A + B) / 2

VarP = (A + B + C) / 3

CovP = (AB + BA) / 2

CovP = (AB + BA + AC + CA + BC + CB) / 3

CovP = 2AB / 2

CovP = (2AB + 2AC + 2BC) / 3

CovP = AB

CovP = 2 (AB + AC + BC) / 3

Note: 1 / N + (1 - 1 / N) = 1

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