FM210 FORMULAS

Question 1

APR to EAR

Answer 1

EAR = (1+ APR/k)^k

Question 2

EAR to APR

Answer 2

r(k)

Question 3

PV

Answer 3

= C/(1+r)^T

Question 4

NPV = -costs + FCF

Question 5

Growth in purchasing power

Answer 5

= Growth of money/growth of prices = (1+r)/(1+pi) = (1+i)

Question 6

Annuity with growth

Answer 6

C(1- (1+g/1+r)^n) / (r-g))

Question 7

Annuity PV

Answer 7

C(1- 1/(1+r)^n / r)

Question 8

Perpetuity with growth

Answer 8

PV = C/r-g

Question 9

Perpetuity

Answer 9

C/r

Question 10

What if CFS occur at the beginning of the period?

Answer 10

1. Annuity due
   PV = C + C(1 - 1/(1+r)^n-1 / r)
2. Future Values
   FV = C((1+r)^n - 1 / r))

Question 11

Expected dividend yield

Answer 11

E0(Dt) / (1+E(r)^t)

Question 12

If all future dividends are at a constant level D,

Answer 12

P0 = D/E(r)

Question 13

If all future dividends grow at a constant rate in the future (GORDON GROWTH FORMULA)

Answer 13

P0 = D/E(r) - g

Question 14

ROE

Answer 14

EPSt / BV of Equity per sharet-1

Question 15

g (growth on earnings/dividends)

Answer 15

ROE x Plowback Ratio

Question 16

Change in earnings

Answer 16

New investment x ROE

Question 17

new investment

Answer 17

earnings x plowback ratio

Question 18

earnings growth rate

Answer 18

plowback ratio x ROE

Question 19

Dt

Answer 19

EPS x payout ratio

Question 20

Book Equity per sharet

Answer 20

Book Equity per sharet-1 + EPS(1-payout ratio)

Question 21

P0

Answer 21

EPS1/ E(r) + PVGO

Question 22

EPS1/P0

Answer 22

E(r) x (1 - PVGO/P0)

Question 23

YTM of coupons

Answer 23

CF/ (1+y)^t

Question 24

Dmac

Answer 24

1. work out the coupon PV or whatever
2. put the weights against each of the years PV
3. put it over the number you got in (1)

Question 25

Dmod

Answer 25

Dmac/(1+y)

Question 26

Change in price

Answer 26

-Dmod(P0)(change in y)

Question 27

spot rate formula

Answer 27

(1+rt)^t(1+tfT)^T = (1+rt+T)^t+T

Question 28

E(R)

Answer 28

piRi

Question 29

o^2R

Answer 29

pi(Ri - E(R)^2)

Question 30

oX,Y

Answer 30

E((X - E(X)(Y - E(Y))

Question 31

pX,Y

Answer 31

oX,Y / oXoY

Question 32

mean of R

Answer 32

Ri/N

Question 33

S(R)^2

Answer 33

1/N-1 x (Ri - mean of R)^2

Question 34

Cov(X,Y)

Answer 34

1/N-1 x (Xi - mean of X)(Yi - mean of Y)

Question 35

Corr(X,Y)

Answer 35

Cov(X,Y)/ S(X)S(Y)

Question 36

E(Rp)

Answer 36

= wiE(Ri)

Question 37

oRp

Answer 37

1/N . o^2 + (1- 1/N)Cov

Question 38

Bi (against a portfolio)

Answer 38

Cov(Ri, Rp) / o^2Rp

Question 39

Bi (against the market

Answer 39

Cov(Ri, Rm)/ o^2R,=m

Question 40

Bp

Answer 40

wiBi

Question 41

E(Rp) equation line

Answer 41

rrf + (E(RA) - rrf/ oRA) oRp

Question 42

Sharpe Ratio

Answer 42

the gradient of the capital allocation line (CAL). If the risky asset is in the market then its the gradient of the capital market line (CML) E(RA) - rrf / oRA

Question 43

E(Ri) using CML equation

Answer 43

rrf + Bi(E(RM) - rrf)

Question 44

Bm

Answer 44

Cov(Rm, Rm) / Var(Rm)

Question 45

Brf

Answer 45

Cov(rf, Rm)/ Var(Rm)

Question 46

Gradient of the SML

Answer 46

E(Rm) - rrf

Question 47

The price of a forward contract on an investment asset that pays no income is

Answer 47

F0,T = S0(1+rrf)^T

Question 48

The price of a forward contract that pays a fixed known income is

Answer 48

F0,T = (S0 - I)(1+ rrf)^T

Question 49

If the underlying asset pays a fixed known yield e.g. dividend yield, then the forward pricing equation is

Answer 49

F0,T = S0(1+ rrf - y)^T

Question 50

the price of a forward contract on an invest commodity that has fixed known storage costs is

Answer 50

F0,T = (S0 + u)(1+ rrf)^T

Question 51

The price of a forward on consumption commodities with net convenience yield

Answer 51

F0,T = S0(1+ rrf - NCY)^T

Question 52

The straddle

Answer 52

The straddle involves going long in a put option with strike price K and going long in a call option on the same underlying with the same exercise date and strike price K. An investor might use the straddle strategy if they believe a stocks price will move significantly but is unsure as to which direction it will move.

Question 53

reverse straddle

Answer 53

involves going short in a put option with strike price K and going short in a call option on the same underlying with the same exercise date and strike price K. might be used if the investor believes that the stock will have little volatility and the stock price at time T will be close to the exercise price.

Question 54

bull spread

Answer 54

bull spread involves going long a call option with strike price K1 and going short a call option on the same underlying and exercise date with a higher strike price K2. might do this if they have a mildly bullish view but want a portfolio that is protected against extreme price movements

Question 55

bear spread

Answer 55

involves going short a put option with strike price K1 and going long a put option on the same underlying and exercise date with a higher strike price K2. might do this if they have a mildly bearish view about the price of the underlying but want a position thats not too sensitive to extreme mkt movements

Question 56

Co + K/(1+rrf)^T = So + Po

Answer 56

if Po> C+ K/(1+ rrf)^T - So then short the put and long the call

Question 57

Up node in delta

Answer 57

Cuu - Cud/ Suu - Sud

Question 58

Down node in delta

Answer 58

Cdu - Cdd/ Sdu - Sdd

Question 59

B of option

Answer 59

Cd(u) - Cu(d) / u-d

Question 60

C

Answer 60

So(delta) + B/1+ rrf

Question 61

risk neutral method

Answer 61

1 + rrf - d/ u-d

Question 62

F0,T(HC/FC)

Answer 62

S0(HC/FC)(1+ rhome/ 1+ rforeign)^T