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FE formulas > CAPM > Flashcards

CAPM Flashcards

1
Q

Return of an asset (probabilities)

A

r_a = p1r1 + p2r2 + p3*r3

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2
Q

Variance of an asset (probabilities)

A

Var_a = p1(r_a1 - r_a)^2 + p2(r_a2 - r_a)^2 + p3*(r_a3 - r_a)^2

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3
Q

Covariance (probabilities)

A

cov = p1(r_a1 - ra)(r_b1 - r_b) + p2(r_a2 - ra)(r_b2 - r_b) + …

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4
Q

Return of a portfolio

A

r_p = xa * ra + xb * rb

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5
Q

Variance of portfolio (basic)

A

Var_p = xa^2 * Var_a^2 + xb^2 * Var_b^2 + 2xaxb*cov_ab

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6
Q

Variance of portfolio (3 assets)

A

Var_p = xa^2 * Var_a^2 + xb^2 * Var_b^2 + xc^2 * Var_c^2 + 2xaxbcov_ab + 2xaxccov_ac + 2xbxc*cov_bc

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7
Q

Variance of portfolio (Cov_ap)

A

Var_p = xacov_ap + xbcov_bp

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8
Q

Variance of portfolio (with beta)

A

Var_p = (beta*sd_m)^2 + Var(e)^2

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9
Q

Covariance ab

A

Cov_ab = Cor_ab * sd_a * sd_b

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10
Q

Covariance ap

A

Cov_ap = xavar_a + xbcov_ab

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11
Q

Covariance ap (3 assets)

A

Cov_ap = xavar_a + xbcov_ab + xc*cov_ac

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12
Q

Correlation ab

A

Cor_ab = Cov_ab/(sd_a * sd_b)

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13
Q

Beta_a (Var_m)

A

Beta_a = Cov_am/Var_m

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14
Q

Beta equality

A

1 = xabeta_a + xbbeta_b

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15
Q

Beta_a (premiums)

A

Beta_a = (ra-rf)/(rm-rf)

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16
Q

Beta_p

A

Beta_p = xa * beta_a + xb * beta_b

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17
Q

R^2

A

Sqrt(R2) = Cor_am = (Beta_a * Sd_M) / Sd_A

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18
Q

Total, systematic, non-systematic variance

A

Var_a = Beta_a^2 * Var_m + Var(e_a)

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19
Q

Proportion of total risk that can be diversified away

A

Sd(e_a)/Sd_a = 1 - (Beta_a*Sd_m)/Sd_a = (Sm - Sa) / Sm

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20
Q

MVP

A

Xa (MVP) = (Var_b - Cov_ab) / (Var_a + Var_b - 2*Cov_ab)

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21
Q

Risk contribution

A

Risk cont = Beta_a * Xa

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22
Q

Holding Period Return

A

HPR = (P1 - P0 + d)/P0 = P1/P0 - 1

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23
Q

Total return

A

R = 1 + r

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24
Q

Real return

A

r_r = (1+r)/(1+i) - 1

25
Q

Risk premium

A

Risk prem. = ra - rf

26
Q

Market risk premium

A

Market risk prem. = rm - rf

27
Q

Arithmetic average

A

ra = average

28
Q

Geometric average x2

A 
(1+r_g) = ((1+r1)*(1+r2)*...*(1+rn))^(1/n)
r_g = (Wn/W0)^(1/n) - 1
29
Q

Effective Annual Rate

A

EAR = (1+APR/k)^k - 1

30
Q

Continuously compounded return

A

R_t = 1 + r = e^(rcc*t)

31
Q

Common stock total return

A

Total return = Capital gains + Dividen yield

32
Q

Price of a share of a company

A

Div. next year / (r-g)

33
Q

Annuity

A

PVann = C*(1-(1+r)^-N)/r

34
Q

Growing annuity

A

PVgann = C/(r-g) * (1-((1+g)/(1+r))^N)

35
Q

Perpetuity

A

PVperp = C/r

36
Q

Growing perpetuity

A

PVgperp = C/(r-g)

37
Q

Discounting

A

PV = C / (1+r)^N

38
Q

Mortgage calculations

A

Annuity factor = (1-(1+r)^-N)/r

Annual payment = Loaned sum / Annuity factor

39
Q

CAPM formula

A

r_a = rf + beta_a * (rm - rf)

40
Q

Treynor black model formula (combining portfolio with an underpriced asset)

A

r_a = alpha_a + rf + beta_a * (rm - rf)

41
Q

3-factor model formula

A

ra-rf = Beta_market * r_market + Beta_sizer_size + Beta_btmr_btm

42
Q

Arbitrage pricing theory

A

ra = E(ra) + Beta_1r_factor1 + beta_2r_factor2 + … + noise_a

43
Q

CML formula

A

ra = rf + Sd_a * (rm-rf)/Sd_m

44
Q

SML formula

A

ra = rf + beta_a * (rm-rf)/Beta_m

45
Q

Skewness

A

Skewness = Mu^3 / Sd^3

46
Q

Kurtosis and excess kurtosis

A

Kurtosis = Mu^4 / Sd^4

Ex. kurtosis = Mu^4 / Sd^4 - 3

47
Q

Sharpe ratio

A

Sp = (rp - rf)/Sd_p

[Slope of the CAL line]

48
Q

Modigliani Modigliani

full

A 
M^2 = ( (ra - rf) / Sd_a ) * Sd_m - (rm-rf)
or
M^2 = rp* - rm
sd_p* = y*sd_p = sd_m
rp* = y*rp + (1-y)*rf
49
Q

Treynor index

A

Tp = (rp-rf)/beta_p

[Slope of the SML line]

50
Q

T^2

A

T^2 = Tp - Tm = Alpha_p/Beta _p

[Difference between the Tp and Tm lines]

51
Q

Jensnes measure (alpha)

A

alpha_p = rp - (rf + beta_p*(rm - rf))

52
Q

Appraisal/information ratio (AR)

A

ARp = alpha_p/Sd(e)

[Gain over non-systematic risk]

53
Q

S^2 of optimal portfolio

A

S^2 = Sm^2 + (Alpha_a/Sd_e)^2

[Highest alpha per tracking error]

54
Q

WACC 1,2

A 
r_assets = r_debt *(D/V) + r_equity (E/V)
r_assets = rf + beta_assets*(rm-rf)
55
Q

r_equity 1,2,3

A 
r_equity = rf + Beta_equity*(rm-rf)
r_equity = r_assets + D/E*(r_assets - r_debt)
r_equity = r_debt + beta_equity*(rm - r_debt)
56
Q

Beta_assets 1,2

A 
Beta_assets = Beta_debt * D/V + Beta_equity * E/V
Beta_assets = (E/V) * Beta_equity
57
Q

Beta_equity

A

Beta_equity = Beta_assets * (1+D/E)

58
Q

Total Beta

A

Total beta = Beta_a/Cor_am = Sd_a/Sd_m

59
Q

Weights in market portfolio

A

Xa = (Sd_b^2(ra-rf) - Cov_ab(rb-rf)) / (Sd_a^2(rb-rf) + Sd_b^2(ra-rf) - 2Cov_ab(ra+rb-2rf))

FE formulas (5 decks)

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