CFA L1 Flashcards
Add on yield Formula v Discount yield Formula
Add on Yield: (P1-P0/P0)-1
Discount Yield: (P1-P0/P1)-1
Cyclical v Defensive Stocks
Cyclical: Market goes up, stocks go up - high correlation. Eg: Real Estate
Defensive: Market and stock have comparatively less correlation - stocks not sensitive to market Eg: Pharmaceuticals
Front Running
An Asset manager buying stocks personally prior to making investments through his fund - as bigger investments make the price go up, he will benefit personally. This is illegal.
Joint Probability
= Intersection value / Grand Total
Conditional Probability (Probability of A | B)
= A Intersection B / A Intersection B + A’ Intersection B
= Joint Probability / Total Probability of B
Probability
= Favourable outcomes / Total Outcomes
0 <= P(x) <=1
where P = 0 is an impossible event
P = 1 guaranteed event
Sum of all P(x) = 1
Expected Value of x
E(x) = P(x)
Expected Return of Portfolio
E(Rp) = Sum of wiE(Ri) = w1E(R1) + w2E(R2) + … + wnE(Rn)
Covariance of Expected Returns of two variables
Cov(Ri,Rj) = E[(Ri-E(Ri)*(Rj-E(Rj)]
There is no n as sum of P =1
Covar(Ri,Ri) = Var(Ri)
Sample Covariance of Returns
Sum of [(R1 - R1bar)*(R2 - R2bar) / n-1
Portfolio Variance ie Var(Rp)
Sum of wiwjCov(Ri, Rj)
= W^2Var(Ra) + 2WaWbCov(a,b) + Wb^2*Var(Rb)
- Keeps on adding for every asset added - Number of elements of Cov part = NC2 where N = number of stocks
Roys Safety First Criterion
= | Rp - RL | / SDp
- RL is the threshold level
- Higher the ratio, better as lower shortfall risk
- Shortfall % - z value
Rp - RL | / SDp
Sharpe Ratio
- When RL = Rf
= | Rp - Rf | / SDp - represents return over and above risk free rate per unit of risk
Expected Standard Deviation
= Root of Sum of P(x-E(x))^2
- Denominator = n = 1 (Sum of all P =1)
Expected Variance
Sum of P(x-E(x))^2
Expected Skewness
Sum of P(x-E(x))^3 / SD^3
Expected Kurtosis
Sum of P(x-E(x))^4 / SD^4
Expected Covariance
Sum of P[(x-E(x))*(y-E(y))]
Expected Correlation
Sum of P(Cov(x,y)) / E(SDx)*E(SDy)
= Sum of P(Cov(x,y)) / Root of Sum of P(x-E(x))^2 * Root of Sum of P(y-E(y))^2
Growth v Value Stock
Growth Stock: Exponential Growth, outperforming economy, doesn’t fluctuate too much w market changes ie is less sensitive to market as future earnings are priced in. P/BV is high
Value Stock: Available for cheap, riskier & sensitive to market, P/BV is low
Liquidity
Ability to convert asset into cash at a fair and reasonable price in a short period of time
Illiquidity = Liquidity Risk
Types of Risk
Liquidity Risk
Maturity Risk (risk due to change in rates/volatility in longer term)
Default Risk
MV v BV v IV
Market Value: Price at which asset is sold/bought in the market, based on demand, future CFs
Book Value: As per books of accounts, based on historical pricing
Intrinsic Value: Based on one’s own opinion on what the price SHOULD be, based on models, forecasts, projections
Principal Agent Conflict
Principal - who agent works for
Example of PAC: broker recommending stock to customer based on his commissions instead of for purpose of clients wealth maximization
Compound Interest v Simple Interest
Simple Interest = prt/100
Compound interest = (1+r/100m)^tm
m= periods of compounding
t = number of years
Sum of Infinite GP Series
a/(1-r)
Quadratic Equation
+/-b + [Root of (b^2 - 4ac)] / 2a
HPR
Pn-Po / Po
HPR to EAY
EAY to HPR
HPR to EAY = (1+HPR)^365/n -1
EAY to HPR = (1+EAY)^n/365 -1
BEY
Compounded semi annually
= (1+r/2)^2n
BEY to EAY = (1+BEY/2)^2
BDY
(Pn-Po / Pn) * 360/n
= Discount Rate x 360/n
MMY
(Pn-Po / Po) * 360/n
= HPR x 360/n
Quoted Price
100 - BDY
Purchase Price
Quoted Price x n/360
Nominal Rate
(1+Nominal) = (1+real)x(1+inflation)
Approx Nominal = Real + Inflation
Other risk premiums
Default, Liquidity, Maturity
Annuity Due v Ordinary Annuity
Annuity Due - Investment at start of period
Ordinary Annuity - Investment at the end
PV(Annuity Due) = PV(Ordinary) x (1+r), same for FV
Perpetuity
PMT/r
Continously Compounded Rate
P*e^r
RCC to EAY/Discrete = e^r -1
EAY to Rcc = ln(1+r)
Outstanding Principal at any time
PV of remaining EMIs
Principal Repaid
Outstanding at yn-1 - Oustanding at yn
Interest Repaid
EMI - Principal repaid
Growth rate
(FV/PV)^1/n -1
Time Weighted Return
= (1+r1)(1+r2)….*(1+rn)
Like an average, quantum and timing does not matter
Money Weighted Return
=IRR
Quantum & Timing matters, tips towards higher return
NPV
- assumes reinvestment at Re
= PV(inflows) - PV(outflows)
IRR
- assumes reinvestment at IRR
= Rate at which PV(outflows) = PV(inflows)
NPV & IRR
- NPV is positive when PV(I) > PV(O), ie IRR > Re
- NPV is negative when PV(I) <(O) ie IRR < Re
- NPV is 0 when PV(I) = PV(O), ie IRR = Re (indifferent to acceptance of project, depends on management decision taking other factors into consideration)
- NPV & IRR will always give same decision but might give different ranks - we generally accept NPV ranks in case of conflict (independent projects)
Types of Capital Investment
- Going Concern: necessary for survival of business or to reduce costs
- Regulatory/Compliance: necessary by law, enforced by Gov or authorities - usually due to safety or environmental concerns
- Expansion: Vertical/Horizontal integration, involves complex and detailed analysis
- New Business: Entering into a completely new market, also involves complex and detailed analysis
Principals of Capital Allocation
- Based on Cashflows not Accounting Income
- Based on After Tax Cashflows
- Opportunity Costs to be taken into account
- Timing of Cashflows to be taken into account
- Financing cost to be taken into account
Sunk Costs
- Costs that will be incurred irrespective of whether a project is accepted or not
- Sunk costs not to be taken into account while calculating (may be taken after if relevant)
Hard Rationing of Capital
- Calculate Profitability Index
- Rank by PI
- Calculate best combination based on capital budget
Profitability Index
Pv(Inflows)/PV(outflows)
Capital Allocation Pitfalls - Cognitive Biases
- Poor forecasting
- Not considering opportunity Costs/Internal Costs
- Incorrectly accounting for inflation
Capital Allocation Pitfalls - Behavioural Biases
- Pet Project of Management
- Inertia of setting Capital Budget (not being updated)
- Basing investment decisions on EPS/ROE (as incentives may be tied to it/short term outlook)
- Failure to generate alternate investment ideas
Real Options
are future actions that a f irm can take, given that they invest in a project today
Timing Options
allows a co to take delayed a delayed decision as it expects to have more/better information in the future
Abandonment Option
If NPV today exceeds NPV of in future - abandonment is better
Expansion Options or Growth Options
Will allow company to make further investments based on future performance of project
Flexibility Options
Price-setting Flexibility: change prices in future
Production Flexibility: change operational factors
Return on Invested Capital
= NI + Interest*(1-t) / Avg BV of Capital (E+P+D)
= NOPAT / Avg BV of Capital
= NOPAT/Sales * Sales/Avg BV of Capital
= Operating Margin After Tax * Asset/Capital Turnover
Is the Co creating value for Shareholders? (ROIC)
ROIC > Kc, +ve , Yes
ROIC < Kc, -ve, No
ROIC = Kc, 0, No
Process of Capital Allocation
- Idea generation
- Analysing Project Proposals (Expected Profitability)
- Creating firm wide capital budget (prioritise profitability and consider timing of cashflows, available resources and overall strategy)
- Monitor decisions and conduct post-audit (identify systematic errors, improve performance)
Hurdle Rate
Minimum IRR at which a project will be accepted
NPV Advantage
Direct measure of profitability