Formulas

Question 1

Utility function

Answer 1

E(R)-0.5A sigma^2

Question 2

CML

Answer 2

R= risk free + ((market-risk free)/sigma m) * sigma p

Question 3

Sharpe ratio portfolio

Answer 3

(market- risk free) / sigma m

Question 4

Treynor ratio

Answer 4

(portfolio - risk-free) / beta

Question 5

Sharpe CAPM

Answer 5

(portfolio - risk-free)/sigma p

Question 6

SML

Answer 6

R = risk free + (market- risk free)*beta

Question 7

Estimated return

Answer 7

= (P1+Div1-P0)/P0

Question 8

How to tell if under-priced

Answer 8

estimated - expected > 0

Question 9

IR ratio

Answer 9

(portfolio-benchmark)/sigma er

Question 10

Sortino

Answer 10

(Rp - T)/DR

Question 11

Downside risk

Answer 11

1/n sum (R- mean R)^2 for all R less than mean

Question 12

APT

Answer 12

risk-free + sum of beta*lambda

Question 13

Price of bond

Answer 13

C*(1/r - 1/r(1+r)^t) + FV/(1+r)^t

Question 14

present value for perpetuity

Answer 14

Cash flow/return

Question 15

Current yield

Answer 15

Coupon / Price

Question 16

Fisher relation

Answer 16

(1+R)=(1+r)*(1+h)

Question 17

Zero growth price

Answer 17

Div/r

Question 18

Constant (Pt)

Answer 18

Divt*(1+g)/(r-g)

Question 19

Non-constant P0

Answer 19

D1/1+r + D2/(1+r)^2 + D3/(1+r)^3 + P3/(1+r)^3

Question 20

WACC

Answer 20

cost of equityweight of equity + cost of debtweight of debt*(1-tax rate)

Question 21

Value of a firm

Answer 21

V= c/WACC

Question 22

Expected return on asset with capital structure

Answer 22

Ra= (D/D+E)Rd +(E/E+D)Re

Question 23

return of equity equation

Answer 23

Re=Ra+ D/E(Ra-Rd)

Question 24

Present value of interest rate shield

Answer 24

Value of debt* tax rate

Question 25

Value of levered firm

Answer 25

VL = Vu + tax*debt value

Question 26

Beta of capital structure with no taxes

Answer 26

Ba= (E/E+D)Be + (D/D+E)Bd

Question 27

Beta of capital structure with taxes

Answer 27

Ba= (E/E+D(1-T)Be + (D(1-T)/E+D(1-T))Bd

Question 28

Risk on equity of levered firm

Answer 28

𝛽𝐸 = 𝛽𝐴 + 𝐷(1−𝑇𝑐)/𝐸 (𝛽𝐴 − 𝛽𝐷)