formulas

Question 1

r nom

Answer 1

Nominal interest rate

V1 = V0 ( 1 + rnom )

Question 2

r real

Answer 2

• Real Interest Rate

V1/P1) = (V0/P0)(1 + rreal

Question 3

• M1 (most liquid assets)

Answer 3

= currency + traveler’s checks +

demand deposits + other checkable deposits

Question 4

• M2 (adds to M1 other assets that are not so liquid)

Answer 4

= M1 + small denomination time deposits + savings deposits and money market deposit accounts + money market mutual fund shares

Question 5

• M3

Answer 5

• M2 plus large and long-term deposits

Question 6

Fisher Equation for Money Supply:

Answer 6

MV = PT

• M: Amount of Money
• V: Velocity of Circulation (number of times money changes hands for
buying goods during a given period)
• P: Overall Price Level
• T: Volume of goods and services transacted (Real GDP)

Question 7

future value of a cash flow

Answer 7

FVn = C x ( 1 + r )^n

Question 8

present value of a cash flow

Answer 8

PV = C / ( 1 + r )^n

Question 9

present value of a stream of cash (cash flow stream)

Answer 9

add up the present values of each:

PV = Co + (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + …
+ (Cn / (1 + r)^n)

Question 10

Future Value of Cash Flow Stream

Answer 10

• with a Present Value of PV:

FVn = PV x (1 + r)^n

Question 11

Present Value of a Perpetuity

Answer 11

PV (C in perpetuity) = C/ r

• The value of a perpetuity is simply the cash flow divided by the interest rate.

Question 12

Present Value of an Annuity

Answer 12

PV = (C / (1 + r)) + (C / (1 + r)^2) + (C / (1 + r)^3) + …
+ (C / (1 + r)^n)

Geometric series : where

• 1 / (1 + r) is the first term and the common ratio
• 1 / (1 + r)^n is the last term

              First term− (last term)common ratio PV =  C   ( \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_)
                         1− common ratio
  =  C ( ( 1 - (1 /(1+ r)^n))/r )

Question 13

Future Value of an Annuity

Answer 13

FV (annuity) = PV x ( 1 + r )^n

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

Question 14

present value of Growing Perpetuity

Answer 14

PV (Growing Perpetuity) = C / ( r - g )

Question 15

Present Value of a Growing Annuity

Answer 15

PV = C x (1 / r - g ) x ( 1 - ( 1 + g / 1 + r )^n)

Question 16

Loan or annuity payment

Answer 16

C = P / ( 1 / r x 1 - ( 1 / ( 1 + r )^n ))

Question 17

Growth in Purchasing Power

Answer 17

= 1 + rr
= 1 + r / 1 + i
= growth of money / growth of prices

Question 18

The Real Interest Rate

Answer 18

rr = r - i / 1 + i

~ r - i

Question 19

Coupon Payment

Answer 19

CPN = coupon rate x face value
_________________________________
number of coupon payments per year

Question 20

Price of a Zero-Coupon bond

Answer 20

P = FV / ( 1 + YTMn )^n

Question 21

Yield to Maturity of an n-Year Zero-Coupon Bond

Answer 21

YTMn = ( FV / P )^1/n - 1

Question 22

Risk-Free Interest Rate with Maturity n

Answer 22

Rn = YTMn
(R= r)

Question 23

Yield to Maturity of a Coupon Bond

Answer 23

P = CPN x 1/y ( 1 - ( 1 / (1 + y)^n )) + FV / (1 + y)^n

Question 24

Price of a Coupon Bond

Answer 24

PV = PV (Bond Cash Flows)
= (CPN / 1 + YTM) + CPN / ( 1 + YTM2 )²
+ (CPN + FV / ( 1 + YTMn )^n)

Question 25

expected (mean return) return

Answer 25

E [ R ] = sum of all (probability% * your return) per year

• Calculated as a weighted average of the
possible returns, where the weights correspond
to the probabilities.

Question 26

2 measures of the risk of a probability distribution:

Answer 26

• Variance
The expected squared deviation from the mean:
Var(R) = som of all (Pr * (R - E [ R ] )²

• Standard Deviation
The square root of the variance:
SD (R) = (Var(R) )^(1/2)

Question 27

The Liquidity Preference Framework

- Total wealth in the economy

Answer 27

= the total quantity of bonds + money in the economy
= quantity of bonds supplied + quantity of money supplied
= B^s + M^s

Question 28

The Liquidity Preference Framework

- total amount of wealth

Answer 28

= Quantity of bonds demanded + quantity of money demanded
B^d+M^d

(people cannot buy more assets than their resources allow!)

Question 29

So the expected return of the bond is

Answer 29

= Yield to Maturity – Prob(default) X Expected Loss Rate

rd = (1 - p)y + p(y - L) = y - pL

Question 30

Total Return

Answer 30

= Dividend Yield + Capital Gain Rat

= The expected total return of the stock should equal the expected return of other
investments available in the market with equivalent risk.

Question 31

The Dividend-Discount Model Equation

Answer 31

Po = Div1/ (1 + rE) + Div2/(1 + rE)^2 + … + DivN/(1 + rE)^N + PN/(1 + rE)^N

• holds for any horizon N. Thus all investors (with the same beliefs) will attach the same value to the stock, independent of their investment horizons.