formulas Flashcards
r nom
Nominal interest rate
V1 = V0 ( 1 + rnom )
r real
• Real Interest Rate
V1/P1) = (V0/P0)(1 + rreal
• M1 (most liquid assets)
= currency + traveler’s checks +
demand deposits + other checkable deposits
• M2 (adds to M1 other assets that are not so liquid)
= M1 + small denomination time deposits + savings deposits and money market deposit accounts + money market mutual fund shares
• M3
• M2 plus large and long-term deposits
Fisher Equation for Money Supply:
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)
future value of a cash flow
FVn = C x ( 1 + r )^n
present value of a cash flow
PV = C / ( 1 + r )^n
present value of a stream of cash (cash flow stream)
add up the present values of each:
PV = Co + (C1 / (1 + r)^1) + (C2 / (1 + r)^2) + …
+ (Cn / (1 + r)^n)
Future Value of Cash Flow Stream
• with a Present Value of PV:
FVn = PV x (1 + r)^n
Present Value of a Perpetuity
PV (C in perpetuity) = C/ r
• The value of a perpetuity is simply the cash flow divided by the interest rate.
Present Value of an Annuity
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 )
Future Value of an Annuity
FV (annuity) = PV x ( 1 + r )^n
= C x ( 1 / r ) x (( 1 + r )^n - 1 )
present value of Growing Perpetuity
PV (Growing Perpetuity) = C / ( r - g )
Present Value of a Growing Annuity
PV = C x (1 / r - g ) x ( 1 - ( 1 + g / 1 + r )^n)
Loan or annuity payment
C = P / ( 1 / r x 1 - ( 1 / ( 1 + r )^n ))
Growth in Purchasing Power
= 1 + rr
= 1 + r / 1 + i
= growth of money / growth of prices
The Real Interest Rate
rr = r - i / 1 + i
~ r - i
Coupon Payment
CPN = coupon rate x face value
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number of coupon payments per year
Price of a Zero-Coupon bond
P = FV / ( 1 + YTMn )^n
Yield to Maturity of an n-Year Zero-Coupon Bond
YTMn = ( FV / P )^1/n - 1
Risk-Free Interest Rate with Maturity n
Rn = YTMn (R= r)
Yield to Maturity of a Coupon Bond
P = CPN x 1/y ( 1 - ( 1 / (1 + y)^n )) + FV / (1 + y)^n
Price of a Coupon Bond
PV = PV (Bond Cash Flows)
= (CPN / 1 + YTM) + CPN / ( 1 + YTM2 )²
+ (CPN + FV / ( 1 + YTMn )^n)
expected (mean return) return
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.
2 measures of the risk of a probability distribution:
• 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)
The Liquidity Preference Framework
- Total wealth in the economy
= the total quantity of bonds + money in the economy
= quantity of bonds supplied + quantity of money supplied
= B^s + M^s
The Liquidity Preference Framework
- total amount of wealth
= Quantity of bonds demanded + quantity of money demanded
B^d+M^d
(people cannot buy more assets than their resources allow!)
So the expected return of the bond is
= Yield to Maturity – Prob(default) X Expected Loss Rate
rd = (1 - p)y + p(y - L) = y - pL
Total Return
= 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.
The Dividend-Discount Model Equation
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.
