TIME VALUE OF MONEY
1 Nominal interest rate= real risk-free rate + expected inflation rate
2 Required interest rate on security= nominal risk-free rate + default risk premium+ liquidity
premium + maturity risk premium
3 Effective Annual Return (EAR)= EAR=(1+periodic rate)m -1
Periodic rate= stated annual rate/m
M= number of compounding periods per year
4 FV= PV(1+ I/Y)N
FV
PV=
1+ I
N
Y
FV= future value
PV= Present value
I/Y=Rate of return per compounding period
N=Number of compounding periods
5 PV perpetuity = PMT
(I/Y)
PMT= Fixed periodic cash flow
DISCOUNTED CASH FLOW APPLICATION
6 CF
139
(1+r)t
CF= Expected cash flow
r =Discount rate
7 IRR
CF1 CF2 CF3
0=CF+ + +
(1+IRR) (1+IRR)2 (1+IRR)3
IRR= Internal rate of return.
8 (Ending Value-Beginning Value)
HPR=
(Beginning Value)
HPR= Holding period return
9 RBD= D/F*360/t
RBD= Annualised yield on a bank discount basis
D=Dollar discount= purchase price - face value
F=Face value
t=Number of days until maturity
360=Bank convention of number of days in a year
10 Effective Annual Yield (EAY)= (1+HPY)365/t -1
HPY= Holding period yield
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11 RMM= 360/days*HPY
RMM=Money market yield
12 Bond equivalent yield= {(1+ effective annual yield)1/2-1} * 2
Geometric Mean= [(1+R1)(1+R2)…. (1+Rn)]1/n-1
13
Geometric mean return is also known as compound annual rate of return
N
14 Harmonic Mean=
[
15 Position of observation at a given percentile
y
Ly=(n+1)
100
16 Range= Maximum Value- Minimum Value
;L;
17 Mean Absolute Deviation (MAD)=
n
; $ULWKPHWLFPHDQ
18 Population Variance
(∑(Xi-μ)2)
σ2 =
N
19 Standard Deviation
σ = square root of variance
20 Sample Variance
(∑(Xi-μ)2)
σ2 =
N-1
21 Chebyshev’s Inequality
Percentage of observations that lie within k standard deviations of the mean is at least= 1-1/k2
22 Coefficient of Variation
(standard deviation of x)
CV=
(average value of x)
23 (Rp-RFR)
Sharpe Ratio=
σp
Rp= Portfolio Return
RFR= Risk Free Rate
σp= standard deviation of portfolio return
24 ;L[ 3)
Sample Skewness (Sk) =
S3
s =sample standard deviation
;L[ 4)
25 Sample Skewness (Sk) =
S4
26 Excess Kurtosis= Sample Kurtosis - 3
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PROBABILITY CONCEPTS
27 Multiplication Rule Of Probability,
P(AB)=P(A/B)*P(B)
28 Addition Rule Of Probability,
P(A or B)= P(A)+P(B)-P(AB)
29 Total Probability Rule (Used to determine unconditional probability of an event)
P(A)=P(A/B1)P(B1)+P(A/B2)P(B2)+………+P(A/BN)P(BN)
30 Expected value of random variable= weighted average of possible outcomes,
Weights = probabilities that the outcome will occur
31 Covariance
Cov(Ri, Rj)= E{[Ri-E(Ri)][(Rj-E(Rj)]}
Cov(Ri, Rj)= Corr(Ri, Rj) σ(Ri)σ(Rj)
32 Correlation Cofficient
(Cov(Ri,Rj))
Corr(Ri,Rj)=
(σ(Ri)σ(Rj))
33 Weight of asset in portfolio,
w= market value of investment in asset i/market value of the portfolio
34 Portfolio Expected Value
E(Rp)=w1E(R1) + w2E(R2)+…… wnE(Rn)
35 Variance of 2 Asset Portfolio
36 Variance of 3 asset Portfolio
37 Bayes Formula,
Updated Probability=( Probability of new information for a given event / unconditional
probability of new event )*(prior probability of event)
38 Factorial
n! = n*(n-1)*(n-2)*(n-3)…… *1
0!=1
39 Labelling,
n! / (n1!)*(n2!)*…. ( nn!)
40 Combination,
n Cr=n! /(n-r)!r!
41 Permutation,
n! /(n-r)!
COMMON PROBABILITY DISTRIBUTIONS
42 To standardize a normal variable,
(Observation - Population Mean)
z=
(Standard Deviation)
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43 Roy’s safety first criteria,
([E(Rp)-Rl])
SFR=
(σ p)
**Choose the portfolio with largest SFR
44 Continuously compounded rate of return,
Rcc=ln(1+HPR)
SAMPLING AND ESTIMATION
45 Standard Error of sample Mean,
σx= σ¥Q
σ= Standard deviation of population
n=Size of the sample
46 t-distribution to construct a confidence interval,
When variance is unknown,
x=tα/2 V¥Q
When variance is known,
x=tα/2*σ¥Q
x= Point estimate of population mean
tα/2=The t-reliability factor
V¥Q 6WDQGDUGHUURURIVDPSOHPHDQ
SAMPLING AND ESTIMATION
47 (Sample Mean - Hypothesized Mean)
Test Statistic=
(Standard Error of Sample Mean)
48 t-statistic
When population variance is unknown,
(x-μ)
Tn-1=
(s/√n)
When population variance is known,
(x-μ)
Tn-1=
(σ/√n)
49 (n-1)s2
Chi-square test: X2=
σ2
50 F-distribution test,
F=s12/s22
TECHNICAL ANALYSIS
51 Arms Index or Short Term Trading Index,
(Number of advancing Issues / Number of declining issues)
TRIN=
(Volume of advancing issues / Volume of declining issues)
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DEMAND AND SUPPLY ANALYSIS: INTRODUCTION
52 'HPDQGIXQFWLRQIRUJRRG;
Qdx=f(Px,I,Py,….)
3[ 3ULFHRIJRRG;, 6RPHPHDVXUHRIDYHUDJHLQFRPHSHU\HDU
Py=Prices of related goods
53 3ULFH(ODVWLFLW\RI'HPDQG ¨4XDQWLW\'HPDQGHG¨3ULFH
¨ FKDQJH
54 &URVV3ULFH(ODVWLFLW\ ¨4XDQWLW\'HPDQGHG¨3ULFH2I5HODWHG*RRGV
¨ FKDQJH
55 ,QFRPH(ODVWLFLW\ ¨4XDQWLW\'HPDQGHG¨LQ,QFRPH
¨ FKDQJH
DEMAND AND SUPPLY ANALYSIS: THE FIRM
56 Accounting profit=total revenue-total accounting costs
57 Economic profit=accounting profit-implicit opportunity costs
Or
Economic profit=total revenue-total economic costs
58 Normal profit,
Economic profit=accounting profit-normal profit=0
Normal profit is the accounting profit that makes economic profit equal to zero
59 Marginal Cost,
MC=change in total cost/change in output
AGGREGATE OUTPUT, PRICES AND ECONOMIC GROWTH
60 1RPLQDO*'3 3LW4LW
Pi,t= Price of good i in year t. Qi,t=Quantity of good I produced in year t
61 GDP deflator= (nominal GDP/value of year t output at year t)*100
62 Per Capita Real GDP= GDP/population
63 GDP by expenditure approach,
*'3 &,* ;0
& &RQVXPSWLRQVSHQGLQJ, %XVLQHVVLQYHVWPHQW* *RYHUQPHQWSXUFKDVHV; ([SRUWV
M=Imports
64 GDP by Income Approach,
GDP=national income+ capital consumption allowance+ statistical discrepancy
65 National Income= compensation of employees (wages and benefits)
+ corporate and government enterprise profits before taxes
+Interest Income
+Unincorporated business net income (business owner’s income)
+rent
+indirect business taxes-subsidies
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66 Personal Income= national Income
+transfer payments to households
-indirect business taxes
-corporate income taxes
-undistributed corporate profits
67 Personal disposable income=personal income-personal taxes
68 Quantity Theory Of Money,
MV=PY
M=Money Supply,
V=Velocity of money in transactions,
P=Price level
Y=Real GDP
69 Recessionary Gap or Output Gap=Real GDP-Full Employment GDP
70 Potential GDP=aggregate hours worked*labour productivity
In terms of economic growth,
Growth in potential GDP=growth in labour force+ growth in labour productivity
71 Production Function,
Y=A*f(L,K)
Y=Aggregate economic output,
L=Size of labour force,
K=Amount of capital available,
A=Total factor productivity
UNDERSTANDING BUSINESS CYCLES
72 CPI= (Cost of basket at current prices/cost of basket at base period prices)*100
73 Total amount of money that can be created,
Money created= new deposit/reserve requirement
74 Money Multiplier=1/Reserve Requirement
75 Fisher Effect,
Rnom=Rreal+E(I)+RP
Rnom=Nominal interest rate,
Rreal=Real Interest rate
RP=Risk premium for uncertainty
76 Neutral Interest Rate= Real trend rate of economic growth + inflation target
77 Fiscal Multiplier= 1/[1-MPC(1-t)]
78 Relation between trade deficit, saving and domestic investment,
Exports-imports= private savings+ government savings+ domestic investment
CURRENCY EXCHANGE RATES
79 Real Exchange Rate= Nominal Exchange Rate(d/f)*
(CPI foreign)
(CPI domestic)
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80 Interest Rate Parity,
foward (1+interest rate (domestic)
=
spot (1+interest rate (foreign)
FINANCIAL STATEMENT ANALYSIS: AN INTRODUCTION
81 Accounting Equation, (Balance Sheet)
Assets= liabilities + equity
Assets=liabilities+ contributed capital+ ending retained earnings
Assets=liabilities+ contributed capital+ beginning retained earnings+ revenue-expens-
es-dividends
82 Income statement equation,
Net income=revenues-expenses
83 (cost-residual value)
Straight line depreciation expense=
(useful life)
84 Accelerated depreciation- double declining balance method
DDB depreciation= 2 (cost-accumulated depreciation)
useful life
85 (net income-preferred dividends)
Basic EPS=
(weighted average number of common shares outstanding)
86 (Adjusted income for common shareholders)
Diluted EPS=
(weighted average commom and potential common shares outstanding)
Diluted EPS=
([Net income-preferred dividends]+[convertible preferred dividends]
+[convertible debt interest](1-tax rate))
([Weighted average shares]+[shares from conversion of converted preferred shares]
+[shares from conversion of debt]+[shares issuable from stock options])
UNDERSTANDING CASHFLOW STATEMENTS
87 Free Cash flow to firm,
FCFF= NI+ NCC+ Interest(1-Tax Rate) –FC Inv-WC Inv
FCFF=CFO+ Interest(1-Tax Rate)-FC Inv
NI= Net income
NCC= Non cash charges
FC Inv= Fixed capital investment
WC Inv= Working Capital Investment
88 Free cash flow to equity,
FCFE=CFO-FC Inv + net borrowing
Net borrowing= debt issued- debt repaid
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89 Performance Ratio:
Cash flow to revenue= CFO/Net Revenue
CFO= Cash flow from operations
90 Performance Ratio:
Cash return on asset ratio= CFO/Average total assets
91 Performance Ratio:
Cash return on equity ratio=CFO/Average total equity
92 Performance Ratio:
Cash to income ratio: CFO/Operating Income
93 (CFO-Preferred Dividends)
Cash flow per share=
(Weighted Average Number Of Common Shares)
94 Coverage Ratio:
CFO
Debt coverage=
(Total Debt)
95 Coverage Ratio:
(CFO+interest paid+taxes paid)
Interest coverage ratio:
(interest paid)
If interest paid is classified as a financing activity under ifrs, no interest adjustment is necessary
96 CFO
Reinvestment Ratio=
(Cash paid for long term assets)
97 CFCFO
Debt payment Ratio=
(Cash long term debt repayment)
98 CFO
Dividend Payment Ratio=
(Dividends paid)
99 CFO
Investing and Financing Ratio=
(Cash outflow from investing and financing activities)
FINANCIAL ANALYSIS TECHNIQUES
ACTIVITY RATIOS:
100 Receivables Turnover=net annual sales /average receivables
101 365
Days of sales outstanding=
(Receivables turnover)
102 (Cost of goods sold)
Inventory Turnover=
(Average inventory)
103 365
Days of inventory in hand=
(Inventory turnover)
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104 Purchases
Payables turnover=
(Average trade payables)
105 365
Number of days of payables=
(Payable turnover)
106 (Revenue )
Total asset turnover=
(Average total assets)
107 Revenue
Fixed asset turnover=
(Average net fixed assets)
108 Revenue
Working capital turnover=
(Average working capital)
LIQUIDITY RATIOS
109 (Current Assets)
Current Ratios=
(Current Liabilities)
110 (Cash+Marketable Securities+Receivables)
Quick Ratio=
(Current Liabilities)
111 (Cash+Marketable Securities)
Cash Ratio=
(Current Liabilities)
112 (Cash+Marketable Securities+Receivables)
Defensive Interval=
(Average Daily Expenditures)
113 Cash Conversion Cycle= (Days sales outstanding)+(days on inventory on hand)-(number of
days of payables)
SOLVENCY RATIOS
114 (Total debt)
Debt to equity ratio=
(Total Shareholders Equity)
115 (Total debt)
Debt To Capital=
(Total Debt+Total Shareholders Equity)
116 (Total Debt)
Debt To Assets=
(Total Assets)
117 (Average Total Assets)
Financial Leverage=
(Average Total Equity)
118 (Earnings Before Interest and taxes)
Interest Coverage Ratio=
(Interest payments)
119 (Earnings Before Interest & Taxes+Lease Payments)
Fixed Charge Coverage=
(Interest payments+Lease payments)
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PROFITABILITY RATIOS
120 (Net Income)
Net profit margin=
Revenue
Net income= earnings after taxes but before dividends
121 (Gross profit)
Gross Profit Margin=
Revenue
Gross profit= Net Sales- COGS
122 (Operating Income (EBIT))
Operating profit margin=
Revenue
123 EBT
Pretax margin=
Revenue
124 (Net Income)
Return on assets (ROA)=
(Average Total Assets)
125 (Operating Income)
Operating return on assets=
(Average Total Assets)
126 EBIT
Return on Total Capital=
(Average Total Capital)
127 (Net Income)
Return On Equity=
(Average Total Equity)
Or
(Net Income) Revenue
Return On Equity= *
Revenue Equity
= Net Profit Margin * Equity Turnover
Return On Equity By Du Pont Equation,
(Net Income) (Sales ) (Assets)
Return On Equity= Sales * Assets * Equity
=Net Profit Margin*Asset Turnover*Leverage Ratio
ROE By Extended Dupont Equation,
(Net Income) EBT EBIT Revenue (Total Assets )
ROE= * EBIT * Revenue * (Total Assets) * (Total Equity)
EBT
=Tax Burden *Interest Burden*EBIT Margin*Asset turnover*financial leverage
128 (Net Income-Preferred Dividends)
Return on common equity=
(Average Common Equity)
129 Sustainable growth rate= RR*ROE
RR= Retention rate
=1-dividend payout
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130 (Standard deviation of operating income)
Coefficient of variation sales=
(Mean sales)
131 (Standard deviation of operating income)
CV Operating Income=
(mean operating income)
132 (Standard deviation of net income)
CV Net Income=
(Mean net income)
INVENTORIES
133 COGS= beginning inventory + purchases - ending inventory
LONG LIVED ASSETS
134 Depreciation methods,
i) straight line and ii) ddb covered earlier.
Ii) units of production depreciation=
(Original cost-salvage value)
(life in output units) * Output units in the period
INCOME TAXES
135 (Income tax expense)
Effective tax rate=
(Pretax income)
136 ,QFRPHWD[H[SHQVH WD[HVSD\DEOH¨'7/¨'7$
DTL= Deferred tax liability
DTA= Deferred tax asset
CAPITAL BUDGETING
137 (PV Of future cash flows)
Profitability Index (PI)=
CF0
NPV
=1+
CF0
COST OF CAPITAL
138 WACC= (wd)[kd(1-t)]+(wps)(kps)+(wcc)(Kcc)
Wd= percentage of debt in capital structure.
Wps=percentage of preferred stock in the capital structure.
Wcc=percentage of common stock in the capital structure
139 After tax cost of debt= kd(1-t)
140 Cost of preferred stock (kps)
Kps= Dps/p
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141 Capital asset pricing model (CAPM)
Kce=RFR+β[E(Rm)-RFR]
Kce=Cost of equity capital
RFR= Risk free rate
E(Rm)= Expected return on market.
142 Dividend discount model,
D1
Po= (k-g)
D1= Next year dividend.
K=Required rate of return on common equity.
g = Firm’s expected constant growth rate.
143 Bond yield plus risk premium approach,
Kce=bond yield + risk premium
144 Asset Beta,
1
ΒAsset=βEquity 1+ (1-t)D
E
D/E= Comparable company’s debt to equity ratio
145 Project Beta,
ΒProject=βAsset (1+(1-t) D )
E
146 Revised CAPM using country risk premium,
Kce=Rf+β[E(Rm)-RFR+CRP
CRP= Country risk premium
147 (Annualised standard deviation of equity index of developing country)
CRP=
(Annualised standard deviation of sovereign bond
Market in terms of the developed market currency)
Sovereign yield spread= difference between the yields of government bonds in in the
developing country and treasury bonds of similar maturities
148 Break Point (any time the cost of one of the components of the company’s WACC changes.)
(Amount Of Capital at which the components cost of capital changes)
Break Points=
(weight of the he component in the capital structure)
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MEASURES OF LEVERAGE
149 Degree of operating leverage,
(Percentage change in EBIT)
DOL=
(Percentage change in sales)
DOL for a particular level of units,
Q(P-V) (S-TVC)
DOL= =
(Q(P-V)-F) (S-TVC-F)
Q= Quantity of units sold
P=Price per unit
V= Variable cost per unit
F= Fixed costs
S= Sales
TVC=Total variable costs
150 Degree of financial leverage,
(Percentage change in EPS)
DFL=
(Percentage change in EBIT)
DFL for particular level of operating units,
EBIT
DFL=
(EBIT-Interest)
151 Degree Of Total Leverage
DTL=DOL+DFL
(% change in EBIT) (% change in EPS) (% change in EPS)
DTL=
(% change in Sales) * (% change in EBIT) = (% Change in Sales)
Q(P-V) (S-TVC)
DTL=
(Q(P-V)-F-I) = (S-TVC-F-I)
152 Breakeven Quantity Of Sales,
(Fixed perating costs+Fixed financing costs)
QBE=
(Price-Variable cost per unit)
DIVIDENDS AND SHARE REPURCHASE BASICS
153 (Total earnings-After tax cost of funds)
Eps after buyback=
(Shares outstanding after buyback)
WORKING CAPITAL MANAGEMENT
154 (%discount)
Cost of trade credit=(1+ 365/days past discount -1
(1-%discount)
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PORTFOLIO RISK AND RETURN: PART II
155 Expected return when one asset is invested in risky asset and one asset in risk free asset
E(Rp)= WAE(RA)+wBE(RB)
WB=1-WB
156 Capital market line equation,
(E(Rm)-Rf)
E(Rp)= Rf+ σp
(σ m)
157 Total Risk= systematic risk + unsystematic risk
158 General form of multifactor model,
E(Ri)-Rf=βil*E(Factor 1) + βi2*E(factor 2)+………. Βik*E(Factor k)
159 Equation of SML,
(E(Rm)-RFR)
E(Ri)=RFR+ (Cov i,mkt)
(Variance of Market)
160 (Std Dev of m) – (Rm-Rf)
M Square= (Rp-Rf)
(Std Dev of p)
161 (Rp-Rf)
Treynor Measure=
βp
162 Jenson’s Alpha= αp=Rp-[Rf+βp(Rm-Rf)]
MARKET ORGANISATION AND STRUCTURE
163 ((1-initial margin))
Margin call price= Po
((1-maintenance margin))
Po= initial purchase price
SECURITY MARKET INDICES
164 Compounded Returns,
Rp= (1+R1)(1+R2)(1+R3)……. (1+Rk)-1
K= last sub period
165 (Sum of stock prices)
Price weighted Index=
(Number of stocks in index adjusted for splits)
Market weighted Index,
166
(Current total market value of index stocks)
Current index value= *Base year index value
(Base year total market value of index stocks)
167 Equal weighting index,
New index value= Initial index value (1+Change in index)
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EQUITY VALUATION: CONCEPTS AND BASIC TOOLS
168 Dividend discount model,
One year holding period:
Dt (Year End Price)
Vo= +
((1+ke) ) ((1+ke))
Vo= Current stock value
Dt=Dividend at time t
Ke=Required rate of return
Two year holding period DDM,
D1 D2 P2
Value= + +
((1+ke) ) (1+ke)2 ((1+ke)2)
Multi-stage dividend discount model:
D1/ D2 Dn Pn
Value= + + +
(1+ke) ) (1+ke)2 ((1+ke)n ) ((1+ke)n)
(Dn+1)
Pn=
(Ke-gc)
169 Free cash to equity,
FCFE= net income+ depreciation-increase in working capital-fixed capital investment-debt
principal repayments+ new debt issues
FCFE=CFO-FC investment + net borrowing
CFO= Cash flow from operations.
170 Dp
Preferred stock value=
kp
Dp= Fixed dividend
Kp=Required rate of return
171 Enterprise Value (EV)
EV= market value of common and preferred stock + market value of debt –cash and short
term investment
172 (Market price per share)
Trailing P/E=
(EPS over previous 12 months)
173 (Market price per share)
Leading P/E=
(Forecast EPS over next 12 months)
174 (Market value of equity) (Market price per share)
P/B Ratio= =
(Book value of equity) (Book value per share)
Book value of equity= common shareholders equity = (total assets- total liabilities)-pre-
ferred stock
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175 (Market value of equity)
P/S Ratio=
(Total sales)
176 (Market value of equity)
P/CF Ratio
(Cash flow)
INTRODUCTION TO FIXED INCOME VALUATION
177 Price of annual coupon bond,
Coupon Coupon (Principal+ Coupon)
Price= + +……… +
((1+YTM)) ((1+YTM)2) ((1+YTM)n)
YTM= Yield to maturity
Price of semi-annual coupon bond,
Coupon Coupon Principal+ Coupon
YTM YTM YTM n*2
Price= 1+ 1+ 2 +……… + 1+
2 2 2
178 Full Price= Flat price + Accrued interest
179 (Annual cash coupon payment)
Current Yield=
(Bond price)
180 Relation between forward rates and spot rates,
(1+s2)=(1+S1)(1+1y1y)
181 Option Value= z spread –OAS
UNDERSTANDING FIXED INCOME RISK AND RETURN
182 Modified duration,
For annual pay bond:
Modified duration= Macualay duration/ (1+YTM)
For semi-annual bond,
ModDursemi=MacDur/(1+ YTM/2 )
V¬_ = price increase
V+=price decrease
V0=current price
(V¬_ -V+)
Approximate modified duration =
92¨\WP
183 $SSUR[LPDWHFKDQJHLQERQGSULFH 0RG'XU ¨<70
184 (V_ -V+)
Effective duration=
9R¨&XUYH
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185 Portfolio duration= W1D1 + W2D2 +……… +WnDn
W= Weight= Full price/total value
D=Duration on bond
186 Money duration= annual modified duration *full price of bond position
Money Duration per 100 units of par value= annual modified duration * full price per 100 of
par value
187 Price value of a basis point (PVBP)= Average of decrease in value of bond when YTM
increases and increase in value of bond when YTM decreases
188 Approximate Convexity= V_-V+ -2Vo / ¨FXUYH 2Vo
189 % change in Bond Price (when duration and convexity are given)
¨%RQG9DOXH GXUDWLRQ ¨VSUHDG ⁄FRQYH[LW\ ¨VSUHDG
190 Duration Gap= Macaulay duration-Investment horizon
191 Return impact (%change in bond price)
For small spread changes,
5HWXUQLPSDFW§0RGLILHGGXUDWLRQ ¨6SUHDG
For larger spread changes,
5HWXUQLPSDFW§0RGLILHGGXUDWLRQ ¨6SUHDG⁄FRQYH[LW\ ¨VSUHDG
192 Yield spread = liquidity premium + credit spread
193 Payment to the long at settlement,
days
(floating-foward)
360
(notional principal)
days
1+[(floating)
360
Days= number of days in the loan term
194 Intrinsic value of call option,
& PD[>6;@
C= Intrinsic Value of Call option
S= Spot price
; 6WULNHSULFH
195 Intrinsic value of a put option,
3 PD[>;6@
P=intrinsic value of put
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196 Option value= intrinsic value+ time value
197 Put-call parity:
&; 5)5 W 63
C= Call
P=Put
S=Stock
; 3UHVHQWYDOXH
198 Put call parity with assets cashflows,
&; 5)5 W 6R²39FI 3
199 Plain vanilla interest rate swap,
((Number of days) notional principal
(Net fixed rate payment)t = (Swap rate- LIBORt-1)
360)*
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