Financial Economics Formulas

Front 1

Variance terms

Back 1

N

Front 2

Covariance Terms

Back 2

N^2 - N
(but only half are unique)

Front 3

MVP when p = 1

Back 3

=(varB - p*SDa*SDb) / (varA + varB - 2*p*SDa*SDb)

Front 4

MVP when p = 0

Back 4

= varB / (varA + varB)

Front 5

MVP when p = -1

Back 5

= SDb / (SDa + SDb)

Front 6

Expected Return on Portfolio

Back 6

= Xa*Ra + Xb*Rb

Front 7

Variance Portfolio

Back 7

= VARa*Xa^2 + VARb*Xb^2 + 2(Xa*Xb*p*SDa*SDb)

Front 8

Covariance (A,B)

Back 8

= p*SDa*SDb

Front 9

CML Equation

Back 9

E(r) = Rf + (Rm - Rf)*SDstock/SDm

Front 10

Sharpe Ratio

Back 10

(Rm - Rf) / SDmkt

Front 11

SML Equation

Back 11

E(r) = Rf + Beta(Rm-Rf)

Front 12

Beta

Back 12

cov(stock,market) / variance mkt

Front 13

How else can you represent Beta?

Back 13

= p*SDstock / SDmkt

Front 14

Simple idea of Beta in portfolio

Back 14

Xa(Ba) + Xb(Bb) = Beta Port, and if market port = 1

Front 15

Covariance calculation when 2 stocks make up market portfolio and we want the covariance with the market for each

Back 15

Cov(A, M) = cov (A, 0.6A + 0.4B)
= .6(varA) + .4(p*SDa*SDb)

This tells you the covariance of A with the market. Then you rearrange the weights in the equation for B.

Front 16

Covariance of portfolio with the market (stock and risk free comprise portfolio)

Back 16

=cov(Xrf + (1-Xrf), M) = (1-x)*cov(port, market)

Front 17

S.D. portfolio (well-diversified =

Back 17

beta * S.D. market

Front 18

Annual Percentage Rate?

Back 18

1 + APR = (1+Rm)^12
1 + APR = (1+Rs)^2
1 + APR = (1+Rq)^4

Front 19

Real interest rate =

Back 19

(1 + Nominal) / (1 + Inflation)

Front 20

PV of stock with EOY Div

Back 20

= (FVstock + Div) / (1+r)^n

Front 21

PV of Bond with Probability of Corporate Default

Back 21

PV = [(1-prob default) * FV] / (1+r)^n

Front 22

PV stock with div perpetuity

Back 22

= Div / r

Front 23

Growing annuity dividend (e.g.$5 next year and growing for so many years after)

Back 23

PV = C/r*[ ((1+g)^n / (1+r)^n) - 1 ]

Front 24

Growth rate of stocks =

Back 24

g = ROE * plowback

Front 25

Payout ratio =

Back 25

Payout ratio= Div / EPS

Front 26

ROE =

Back 26

NI / Book Equity = EPS / Eq per share = NI/Sales * Sales / Assets * Assets / Equity

Front 27

PVGO =

Back 27

PVGO = -Div + (Div * perpet ROR) / r

Front 28

EPS =

Back 28

EPS = NI / # shares outstanding

Front 29

Price of stock with growth opportunities

Back 29

P = (EPS/r) + PVGO

Front 30

Duration

Back 30

Front 31

Volatility

Back 31

Front 32

Forward Rate (one period)

Back 32

Front 33

What's the forward rate for r1?

Back 33

f1 = r1

Front 34

Multi-Period Forward rate

Back 34

Front 35

Value of a Call =

Back 35

Value Put + Share price - PV (Exercise Price)

Front 36

How would you do option valuation?

Back 36

(1) You would determine a return in both cases (return - exercise price / exercise price)
(2) You would calculate E(r) in each case, needing a probablity of each happening
(3) Then you calculate expected value at the end (prob case 1 * option value) + (prob case 1 * option value)
(4) That gives you value at end, so you use Rf rate to discount back to the present

Front 37

Regular annuity formula

Back 37

PV = C [ (1-(1+r)^-n) / r ]

Front 38

When would you be indifferent between 2 different coupon bonds with the same C but different N?

Back 38

When the coupon rate = discount rate

Front 39

With respect to duration, the higher the interest rate, the _______ the weight of current-versus-future cash flows. Hence, the _____ the duration.

Back 39

higher ; lower

Front 40

What is the duration on a strip?

Back 40

It's maturity, or n, because all cash flows are weighted on the last payment.

Front 41

Why doesn't an annuity have a duration equal to the n?

Back 41

Because the annuity is giving you the same payment every year ; however, the present value of the payments received later will be smaller than the present value of the payments received earlier, so it will be less than the N overall.

Front 42

Why would a 5 year coupon bond have a YTM between the 5-year annuity and the 5- year zero coupon?

Back 42

The yield to maturity of the strip is the 5-year spot rate r5 = 6%, since the unique payment is made at maturity. On the other extreme, the yield to maturity of the annuity, which is y = 5:75%, constitute a weighted average of all spot rates r1 to r5 in which all rates carry an almost equal weight.1 The cash flows of the bond in part (b) is the sum of the cash áows of the annuity in part (e) and the 5-year strip with $100 face value. As such, its yield to maturity would be closer to the strip (which carries higher weight due to the much higher cash áow), but strictly lower, since there are coupon payments at earlier times.

Front 43

Why would the yield to maturity on a 10% coupon bond be smaller than the YTM on a 5% coupon bond when they have the same N, face value, and weight?

Back 43

The yield to maturity is the constant interest rate that would lead to the same present value of a stream of cash áows as that in which each cash áow is discounted at the corre- sponding spot rate. Intuitively, the yield to maturity is a weighted average of spot rates, the weight of a given spot rate t being directly proportional to the cash áow at t .
In this case, the spot rates are increasing in time. The yield to maturity of the stream in (c) is lower than that of the stream in (b) because in the former there are higher cash áows accrued earlier (10 versus 5), hence discounted at lower spot rates