FinQuiz Formula Sheet CFA Level I 2016 Reading 5: Time Value of Money 1. Interest Rate (i) • i = Rf + Inf P + Default Risk P + Liquidity P + Maturity P • Nominal Rf i rate = Real Rf i Rate + Inf P • i rate as a growth rate = g = !" # $" % # -1 2. PV and FV of CF = • PV = !" &’( # • PV of Perpetuity = $)* ( • PV (for more than one Compounding per year) = PV= FV N 1+ ( - . /.×1 ℎ 7 = − • FV N = 1+ 1 • FV (for more than one Compounding per year) = FV N = 1+ ( - . .×1 • FV (for Continuous Compounding) = FV N = ( - ×1 • Solving for N = B1 CD ED B1 &’( (where LN = natural log) 4. Stated & Effective Rates • Periodic i Rate = FGHGIJ KLL M NHGI 1O OP QO.ROSLJMLT $I(MOJ7 ML ULI VIH( • Effective (or Equivalent) Ann Rate (EAR = EFF%) = 1+ . −1 • EAR (with Continuous Compounding) = EAR = ( - −1 5. PV & FV of Ordinary Annuity • PV OA = $)* &’( Z L G[& = &/ % %^_ # ( • FV OA = G 1+ 1/G L G[& = &’( # /& ( • Size of Annuity Payment = PMT = $" $" OP KLLSMG‘ !HaGO( • PV of Annuity Factor = &/ % %^ _- b b×# _- b 6. PV & FV of Annuity Due • PV AD = &/ % %^_ # ( + PMT at t = PV OA + PMT • FV AD = &’( # /& ( (1 + ) = FV OA ×(1+r) Reading 6: Discounted Cash Flow Applications 1. NPV = Q! Z &’( Z L G[& − f 2. IRR (when project’s CFs are perpetuity) = NPV = - I O + Q! gNN = 0 3. HPR = $ % /$ h ’i % $ h 4. MMWR = Q! &’gNN Z * M[f =0 (IRR represents the MWR) 5. TWR: • TWR (when no external CF) = r TWR = HPR = r t = )" % /)" h )" h • TWR (for more than one periods) = r TWR = [(1+r t,1 )× (1+r t,2 )×… (1+r t,n )] -1 • Annualized TWR (when investment is for more than one year) = 1+ & 1+ k …+ 1+ L % m _1 • TWR (for the year) = r TWR = [(1+R 1 )× (1+R 2 )×… (1+R 365 )] -1 where R 1 = )" % /)" h )" h 6. Bank Discount Yield = BDY = r BD = opf L $H(/$(MaI $H( therefore Price = Par 1− L×( qr opf 7. Holding Period Yield = HPY = $ % /$ h ’i % $ h 8. Effective Annual Yield = EAY = 1+ opu/G −1 (Rule: EAY > BDY) 9. Money Market Yield (or CD equivalent Yield) r MM : • r MM = HPY × opf G • r MM = (r BD ) × !HaI "HwSI OP GxI *(IH7S(‘ yMww $S(axH7I $(MaI
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FinQuiz Formula Sheet CFA Level I 2016
Reading 5: Time Value of Money 1. Interest Rate (i)
• i = Rf + Inf P + Default Risk P + Liquidity P + Maturity P
• Nominal Rf i rate = Real Rf i Rate + Inf P
• i rate as a growth rate = g = !"#$"
%#-1
2. PV and FV of CF =
• PV = !"&'( #
• PV of Perpetuity = $)*(
• PV (for more than one Compounding
per year) = PV= FVN 1 +(-.
/.×1
𝑤ℎ𝑒𝑟𝑒 𝑟7 = 𝑠𝑡𝑎𝑡𝑒𝑑 𝑎𝑛𝑛 𝑖 − 𝑟𝑎𝑡𝑒 • FVN = 𝑃𝑉 1 + 𝑟 1 • FV (for more than one Compounding
Semiannual Yield × 2 Reading 7: Statistical Concepts & Market Returns 1. Range = Max Value – Min Value 2. Class Interval = i ≥ z/B
{ where
• i = class interval • H = highest value • L = lowest value, k = No. of classes.
3. Absolute Frequency = Actual No of
Observations (obvs) in a given class interval
4. Relative Frequency = K|7OwSGI !(I}SILa`
*OGHw 1O OP U|~7
5. Cumulative Absolute Frequency = Add up
the Absolute Frequencies 6. Cumulative Relative Frequency = Add up
the Relative Frequencies 7. Arithmetic Mean = FS. OP O|~7 ML JHGH|H7I
1O.OP O|~7 ML GxI JHGH|H7I
8. Median = Middle No (when observations
are arranged in ascending/descending order)
• For Even no of obvs locate median at L
k
• For Odd no. of obvs locate median at L'&
k
9. Mode = obvs that occurs most frequently
in the distribution 10. Weighted Mean = 𝑋� = 𝑤M𝑋ML
M[& = (w1X1+ w2X2+….+ wnXn)
11. Geometric Mean = GM = 𝑋&𝑋k …𝑋Lm
with Xi≥0 for i = 1,2,…n. 12. Harmonic Mean = H.M = 𝑋z =
L%��
m��%
13. Population Mean = µ = ��m�1
with 𝑋M > 0
for i = 1,2,.,.,n.
14. Sample Mean = 𝑋 = ��m�L where n =
number of observation in the sample 15. Measures of Location:
• Quartiles = iM7G(M|SGMOL�
• Quintiles = iM7G(M|SGMOLu
• Deciles = iM7G(M|SGMOL&f
,
• Percentiles = Ly = 𝑛 + 1 `&ff
16. Mean Absolute Deviation = MAD =
�Z/�m��%
L
17. Population Var = σ2 = ��/� �#��%
1
18. Population S.D = 𝜎k= ��/� �#��%
1
19. Sample Var = s2 = ��/� �m��%
L/&
20. Sample S.D = s = ��/� �m��%
L/&
21. Semi-var = ��/� �
L/&!O( Hww ����
22. Semi-deviation (Semi S.D) =
𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = ��/� �
L/&!O( Hww ����
23. Target Semi-var = ��/y �
L/&!O( Hww ���y
where B = Target Value 24. Target Semi-Deviation =
𝑡𝑎𝑟𝑔𝑒𝑡 𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =
��/y �
L/&!O( Hww ���y
25. Coefficient of Variation = CV = F�
where s= sample S.D and 𝑋 = sample mean
26. Sharpe Ratio = )IHL $O(GPOwMO N/)IHL NP N
F.i OP $O(GPOwMO N
27. Excess Kurtosis = Kurtosis – 3
FinQuiz Formula Sheet CFA Level I 2016
28. Geometric Mean R ≈
𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑀𝑒𝑎𝑛 𝑅 − "H(MHLaI OP Nk
Reading 8: Probability Concepts 1. Empirical Prob of an event E = P(E) =
$(O| OP I~ILG �*OGHw $(O|
2. Odds for event E = $(O| OP �
&/$(O| OP �
3. Odds against event E = &/$(O| OP �
$(O| OP �
4. Conditional Prob of A given that B has
occurred = P(A|B) = $ Ky$ y
→ P(B) ≠ 0.
5. Multiplication Rule (Joint probability that
both events will happen): P(A and B) = P(AB) = P(A|B) × P(B) P(B and A) = P(BA) = P(B|A) × P(A)
6. Addition Rule (Prob that event A or B will occur): P(A or B) = P(A) + P(B) – P(AB) P(A or B) = P(A) + P(B) (when events are mutually exclusive because P(AB) = 0)
7. Independent Events: • Two events are independent if:
P(B|A) = P(B) or if P(A|B) = P(A)
• Multiplication Rule for two independent events = P(A & B) = P(AB) = P(A)× P(B)
• Multiplication Rule for three independent events = P(A and B and C) = P(ABC) = P(A) × P(B) × P(C)
8. Complement Rule (for an event S) = P(S)
+ P(SC) = 1 (where SC is the event not S) 9. Total Probability Rule:
associated with a holding period from 0 to T: R0,T= ln (ST / S0) or 𝑟f,* = 𝑟*/&,* +𝑟*/k,*/& + ⋯+ 𝑟f,& Where, rT-I, T = One-period continuously compounded returns
15. When one-period continuously compounded returns (i.e. r0,1) are IID random variables. 𝐸 𝑟f,* = 𝐸 𝑟*/&,* + 𝐸 𝑟*/k,*/& +⋯+ 𝐸 𝑟f,& = 𝜇𝑇 And 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝜎k 𝑟f,* = 𝜎k𝑇 S.D. = σ (r0,T) = σ 𝑇
16. Annualized volatility = sample S.D. of one period continuously compounded returns × 𝑇
Reading 10: Sampling and Estimation 1. Var of the distribution of the sample mean
= ��
L
2. S.D of the distribution of the sample mean
= ��
L
FinQuiz Formula Sheet CFA Level I 2016
3. Standard Error of the sample mean:
• When the population S.D (σ) is known = 𝜎� =
�L
• When the population S.D (σ) is not known = 𝑠� =
7L where s = sample
S.D estimate of s = 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =
𝑠k 𝑤ℎ𝑒𝑟𝑒 𝑠k = ��/� �m��%
L/&
4. Finite Population Correction Factor = fpc
= 1/L1/&
where N= population
5. New Adjusted Estimate of Standard Error
= (Old estimated standard error × fpc) 6. Construction of Confidence Interval (CI) =
Point estimate ± (Reliability factor × Standard error)
• CI for normally distributed population
with known variance = 𝑥 ± 𝑧H/k�L
• CI for normally distributed population with unknown variance = 𝑥 ± 𝑧H/k
FL
where S = sample S.D. 7. Student’s t distribution
µ = 𝑋 ± 𝑡H/kFL
8. Z-ratio = Z = x −µσ / n
9. t-ratio = t = x −µs / n
Reading 11: Hypothesis Testing 1. Test Statistic =
= Avg. Revenue = Price = Demand 17. Profit can be increased by increasing
output when MR> MC 18. Profit can be increased by decreasing
output when MR< MC
19. Break-even price: P = ATC è Output level where Price = Average Revenue = Marginal Revenue = Average Total Cost è where, Total Revenue = Total Cost.
20. Firms earn Economic Profits when Price >
Average Total Cost 21. Profits occur when Total Revenue (TR) ≥
Total Cost (TC) & when Price = Marginal Costè firm will continue operating.
22. Losses are incurred when there are
Operating profits (Total Revenue ≥ Variable Cost) but Total Revenue < Total Fixed Cost + Total Variable Cost AND when Price = Marginal Cost while losses are < fixed costs è firm will continue operating.
23. Losses are incurred when there are
Operating losses (Total Revenue ≤ Variable Cost) AND when losses ≥ fixed costs è firm will shut down.
22. Average propensity to consume (APC) = 8''ìî'ñòî #ûê$ðõøòéûê
)îñù úêíûõî
23. Quantity theory of money equation:
Nominal Money Supply × Velocity of Money = Price Level × Real Income or Expenditure
24. % ∆ in unit labor cost = % ∆ in nominal
wages - % ∆ in productivity 25. Economic growth = Annual % ∆ in real
GDP 26. Total Factor Productivity growth = Growth
in potential GDP – [Relative share of labor in National Income × (Growth in labor) + [Relative share of capital in National Income × (Growth in capital)]
27. Growth in potential GDP = Growth in
technology + (Relative share of labor in National Income × Growth in Labor) +
FinQuiz Formula Sheet CFA Level I 2016
(Relative share of capital in National Income × Growth in capital]
28. Capital share =Corporate profits + net
interest income + net rental income + (depreciation/ GDP)
29. Labor share = 7õøùûóîî #ûõøîê$ñòéûê
ýôë
Reading 18: Understanding Business Cycles 1. Price index at time t2 =
"HwSI OP GxI QO.7S.RGMOL yH7{IG HG G �"HwSI OP GxI QOL7S.RGMOL yH7{IG HG G %
×100
Inflation Rate = ëìéíî úêöî9 ñò òéõî òk &ff
− 1
2. Fisher Index = 𝐼𝑝 ×𝐼𝐿 (where, IL =
Laspeyres index and Ip = Paasche Index) 3. 𝑈𝑛𝑖𝑡 𝑙𝑎𝑏𝑜𝑟 𝑐𝑜𝑠𝑡 (𝑈𝐿𝐶) 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 =
= Fair value at the date of revaluation – Any subsequent Accumulated Dep or Amortization
5. Impairment Loss (IFRS) = Recoverable
Amount – Net Carrying Amount Where, Recoverable amount = Max [(Fair value – Costs to sell); Value in Use)] and Value in use = PV of Expected Future CFs
of asset > Tax base of asset 5. Deferred tax asset = Carrying amount of
asset < Tax base of asset 6. Deferred tax asset = Carrying amount of
liability > Tax base of asset 7. Deferred tax liability = Carrying amount of
liability < Tax base of asset 8. Company’s tax expense (or credit)
reported on its income statement = Income tax liability currently payable + ∆ in deferred tax asset / liability Where,
• Income Tax liability currently payable = Taxable income × Tax rate
• ∆in deferred tax asset / liability = Diff b/w the balance of the deferred tax asset / liability for the current period and the balance of the previous period.
9. The company’s tax expense (or credit) reported on its income statement = Taxes payable + (∆ Deferred tax liability - ∆ Deferred tax asset) Where,
• Income Tax liability currently payable = Taxable income × Tax rate
Reading 39: Working Capital Management 1. Operating cycle = No of days of inventory
+ No of days of receivables 2. Net operating cycle = No of days of
inventory + No of days of receivables – No of days payables
3. Money Market Yield =
Vñíî *ñùðî/ëðìí2ñ$î øìéíîëðìí2ñ$î øìéíî
× opf
/û ûü öñó$ òû õñòðìéòó
4. Bond Equivalent Yield =
Vñíî *ñùðî/ëðìí2ñ$î øìéíîëðìí2ñ$î øìéíî
×opu
/û ûü öñó$ òû õñòðìéòó
5. Discount-basis Yield =
Vñíî *ñùðî/ëðìí2ñ$î øìéíîVñíî +ñùðî
×opf
/û ûü öñó$ òû õñòðìéòó
6. Wght Avg collection period = wghts × Avg no of days to collect accounts within each aging category Where, Weights = % of total receivables in each category
period or investment horizon = 79øîíòîö ôé* éê óì ò&'ìîC ) ûê $òûí1 w +
LG[&
79øîíòîö øìéíî éê ê øîìéûö$&'ìîC ) ûê $òûí1 �
4. CFO = NI + Non-cash exp – Invst in WC
5. FCFE = CFO – FCInv + Net Borrowing 6. Value of a share for a non-div-paying
stock = V#V7 éê óîñì ò&'ìîC ) ûê $òûí1 w
ò[&
7. Req RoR on sharei = Current expected Rf
rate + Beta i [MRP]
8. Value of a pref stock (non-callable, non-convertible) =
( ) ( )rD
rD
grgD
V 0000 0
011=
−
+=
−
+=
9. Value of a pref stock (non-callable, non-convertible) with maturity at time n =
𝑉f =𝐷f
(1 + 𝑟)G+
L
G/&
𝐹1 + 𝑟 L
Gordon Growth Model:
10. Value of a share of stock = ( )
rggr
DgrgD
V <−
=−
+= ,
1 100
11. Sustainable dividend growth rate = g = ROE × b
where b = earnings retention rate = (1 - Dividend payout ratio)
Two-stage valuation model: 12. Value of share today = V0 =
𝑉f =𝐷f 1 + 𝑔7 G
(1 + 𝑟)G+
𝑉L(1 + 𝑟)L
L
M[&
𝑉L =𝐷L'&𝑟 − 𝑔B
𝐷L'& = 𝐷f(1 + 𝑔7)L 1 + 𝑔B 13. Justified P/E = ëf
7& = ô%/7%
ì/'= ø
ì/'
14. EV = MV of stock + MV of debt – Cash
and cash Equivalents
15. Asset-based value = Value of Equipment and inventory – Value of Liabilities
Reading 52: Fixed Income Securities: Defining Elements 1. Inf adj Principal amount of a zero-coupon-
indexed bond = [Par value × (1 + CPI)]
2. Inf adj coupon payment for an interest-indexed bond = [(coupon rate × Par value) × (1+CPI)]
FinQuiz Formula Sheet CFA Level I 2016
3. Inf adj Principal amount of a capital-
indexed bond = [Par value × (1 + CPI)]
4. Inflation adjusted coupon payment for a capital-indexed bond = [Par value × (1 + CPI)] × coupon rate
Reading 53: Fixed Income Markets: Issuance, Trading & Funding Reading 54: Introduction to Fixed Income Valuation 1. Amount of discount below par value =
Present value of deficiency 2. Present value of deficiency =
#ûðøûê ìñòî/&ñì1îò öé$íûðêò ìñòî ×ëñì *ñùðî&'&ñì1îò öé$íûðêò ìñòî w
êò[&
3. Bond price =
PV =PMT(1+ r)1
+PMT(1+ r)2
+...+ PMT +FV(1+ r)N
4. % Price change = /î< øìéíî/.ùö øìéíî
.ùö øìéíî
5. Bond price (given sequence of spot rates)
= PV = PMT(1+ Z1)
1 +PMT(1+ Z2 )
2 +...+PMT +FV(1+ ZN )
N
6. Full price of bond = Flat price of bond + Accrued interest
7. Accrued interest = AI = G* ×𝑃𝑀𝑇
8. Full price of a fixed-rate bond between
coupon payments = PVFull
=PMT
(1+ r)1−t/T+
PMT(1+ r)2−t/T
+...+ PMT +FV(1+ r)N−t/T
9. Full price of a fixed-rate bond between
coupon payments
PV × (1+ r)t/T
10. Interpolated yield (say for 3-year, given market discount rates for 2 and 5 yrs) =
(Average yield for 2 year bonds) + o/ku/k
×
(average yield for 5 year bonds – average yield for 2 year bonds)
Relation b/w two spot rates and Implied Forward Rate: 18. (1 + zA)A × (1 + IFRA,B-A)B-A = (1 + zB)B Z-spread over the benchmark spot curve: Price of a bond =
PV =PMT
(1+ z1 + Z )1 +
PMT(1+ z2 + Z )
2 +...+PMT +FV(1+ zN + Z )
N
FinQuiz Formula Sheet CFA Level I 2016
19. OAS = Z-spread – Option value (bps per
year)
20. G-spread = Yield-to-maturity on Corporate bond – Yield-to-maturity on a government bond
21. Interpolated Spread = I-spread = YTM of the bond - Linearly interpolated yield to the same maturity on an appropriate reference curve
Reading 55: Introduction to Asset Backed Securities 1. Loan-to-value ratio (LTV) =
8õûðêò ûü &ûìò'ñ'îëìûøîìòó +ñùðî
2. Monthly CF for a MPS = Monthly CF of
underlying pool of mortgages - Servicing fee - Other fees
3. Pass-through rate = Mortgage rate on the
underlying pool of mortgages – Servicing Fee - Other fees
4. SMM = Pre-pmt for month ÷ (Beg
mortgage balance for month – Scheduled principal re-pmt for month)
5. CPR = 1 − (1 − SMM)12 6. CF Construction (Monthly CF for MPS):
• Profit from Call option = – Max (0, ST - X) + C0
• Profit from Put option = – Max (0, X- ST) + P0
8. To eliminate arbitrage opportunity:
Forward Price should be = Spot Price × 1 + 𝑖 𝑟𝑎𝑡𝑒 % G
Reading 59: Basics of Derivative Pricing & Valuation 1. Pricing of risky assets = S0 = 7 (÷!)
&'ì'² �
2. Commodity = F 0, T = S0 e (r – δ)T
where, δ = Convenience yield − Cost of carry
3. S0 = 7 (÷!)&'ì'² � – θ + γ
where, θ (theta) = PV of the costs and γ (gamma) = PV of benefits
4. Arbitrage and Derivatives = Underlying
asset + Opposite position in derivative = Underlying payoff – Derivative payoff = Rf return
5. Pricing and Valuation of Forward
Contracts: • At Expiration F (0, T) = S0 (1 + r) T or
S0 = F (0, T) / (1 + r) T • Value of forward (long) during
contract life (where t < T) = Vt (0, T) = St – F (0, T) / (1 + r) (T – t)
• Value of forward (short) during contract life (where t < T ) = Vt (0, T) = F (0, T) / (1 + r) (T – t) - St
• Value of forward (long) at expiration (where t = T) = VT (0, T) = ST - F (0, T)
• Value of forward (long) at initiation (where t = 0) = Vt (0, T) = S0 – F (0, T) / (1 + r) T = 0
• Forward price of an asset with benefits and/or costs = (S0 – γ + θ) (1 + r) T = S0 (1 + r) T – (γ - θ) (1+ r) T
• Value of Forward contract with benefits and/or costs during the life of the contract = St – (γ - θ) (1 + r) T - F (T) / (1 + r) (T – t)
FinQuiz Formula Sheet CFA Level I 2016
6. FRAs: An example of 3 × 9 FRA (read as
three by nine): • Contract expires in 90 days • Underlying loan settled in 270 days • Underlying rate is 180-day LIBOR • For Synthetic FRA (take long position
in a 300-day Euro$ T.D and short position in a 30-day Euro$ T.D
• For synthetic forward position in a 90-day zero-coupon that begins in 30 day (buy 120 day & sell 30 day (zero coupon bonds)
7. Pricing and Valuation of Swap Contract (a
fixed for floating swap contract): • Fixed Periodic rate =
RN =1 - ZN
Z1 +Z2 +....+ZN
• Where Zn are n period zero coupon bonds (i.e. $1 discount factors)
)360/(1 1Zn daysLn ×+
=
• Value of a fixed rate side (per $1 NP) = V fixed rate = [Fixed payment × (Z1 +Z2 +....+ZN )] + ($1 × ZN)
• Value of a floating rate side (per $ 1 NP) = V floating rate = ($1 + 1st floating pmt) × Z1
Pricing and valuation of Options:
8. Payoff of Call options:
• At expiration call option = c T = Max (0, ST –X)
• Profit (call buyer) = Max (0, ST – X) – c0
• Profit (call seller) = -Max (0, ST – X) + c0
9. Payoff of Put options: • p T = Max (0, X- ST) • Profit (put buyer) = Max (0, X-ST) – p0 • Profit (put seller) = - Max (0, X – ST) +
p0
10. Max Profit/Loss for Option writer/holder: • Max profit of option seller/writer è
Option premium. • Max loss of option seller/writer è
unlimited. • Max loss of option holder èOption
premium Put-Call Parity 11. Protective Put
• Value PP = p0 + S0 • Payoff at expiration (put out-of-the-
money) = ST. • Payoff at expiration (put in-the-
money) = (X-ST) + ST = X. 12. Fiduciary Call
• Value FC = c0 + X / (1+r) T • Payoff at expiration (when call out-of-
the-money) = X. • Payoff at expiration (call in-the-
money) = X + (ST – X) = ST. 13. Put-Call Parity (to avoid arbitrage) = c0 +
X / (1+r) T = p0 + S0
• Synthetic long position in a call =
C = p 0+S 0−X
(1+ r)T
• Synthetic long position in a put =
p 0= c 0−S 0+X
(1+ r)T
• Synthetic long position in an
underlying = S0 = c 0+X
(1+ r)T− p0
• Synthetic long position in a riskless
bond = X
(1+ r)T= p 0+S0 − c0
14. Put-Call-Forward Parity = F0(T) / (1 + r) T
+ p0 = c0 + X/(1 + r) T 15. Valuing a callable bond using Binomial
Model:
• Ru = Rd × e2σ 𝑡 • Value at time 0 = V0 = hS0 − c0 • Value at time 1 will either V1
+ = hS1+ -
c1+ or V1
- = hS1- - c1
-
FinQuiz Formula Sheet CFA Level I 2016
• If the portfolio was hedged, then V+
would equal V-.
• Value of the call =
• Value of the put = Reading 60: Risk Management Applications of Option Strategies 1. For Call Option Buyer
• cT = max (0, ST –X) • When ST ≤ X àcT = 0 • When ST > X àcT = ST – X • Value at expiration = cT • Profit = cT – c0 • Maximum profit = ∞è no upper limit • Maximum loss = c0 • Breakeven = ST* = X + c0
2. For Call Option Seller
• cT = max (0, ST –X) • When ST ≤ X àcT = 0 • When ST > X àcT = ST –X • Value at expiration = -cT • Profit = –cT+ c0 • Maximum profit = c0 • Maximum loss = ∞è no upper limit • Breakeven = ST* = X +c0
3. For Put Option Buyer
• pT = max (0, X - ST) • When ST < X àpT = X - ST • When ST ≥ X àpT = 0 • Value at expiration = pT • Profit = pT – p0 • Maximum profit = X – p0 • Maximum loss = p0 • Breakeven = ST* = X –p0
4. For Put Option Seller
• pT = max (0, X –ST) • When ST < X àpT = X – ST • When ST ≥ X àpT = 0 • Value at expiration = –pT • Profit = –pT + p0 • Maximum profit = p0 • Maximum loss = X - p0 • Breakeven = ST* = X - p0
5. Covered Call = Long stock position + Short call position
• Value at expiration = VT = ST – max
(0, ST – X) • When ST ≤ X àVT = ST • When ST > X àVT = ST - ST +X = X • Profit = VT – S0 + c0 • Maximum Profit = X – S0 + c0 • Maximum Loss = S0 – c0 • Breakeven =ST* = S0 – c0
6. Protective Put = Long stock position +
Long Put position
• Value at expiration: VT = ST + max (0, X - ST)
• When ST ≤ X àVT = ST + X - ST = X • When ST > X àVT = ST • Profit = VT – S0 - p0 • Maximum Profit = ∞ • Maximum Loss = S0 + p0 – X • Breakeven =ST* = S0 + p0
Reading 61: Introduction to Alternative Investments 1. Total Return = Alpha R + Beta R 2. Asset Based Valuation = Co value = Co’s
assets value – Co’s liabilities value Real Estate Valuation
8. Roll yield = Spot price of a commodity – Futures contract price or Roll yield = Futures contract price with expiration date ‘X’– Futures contract price with expiration date ‘Y.
9. Returns on a passive investment in
commodity futures = Return on the collateral + RP or convenience yield net of storage costs.
10. Sharpe ratio = (Investment return – Rf return) / S.D. of return