3 Markets & Formulas Flashcards
Holding Period Return
3.10
= Profit ÷ Cost
= (End Val – Start Val + Income)
÷ Start Val
HPR isn’t indexed for time. Don’t worry about time & annualizing.
Assumes dividends aren’t reinvested.
Holding Period Return with Margin
3.10
= (P1 – P0 – margin cost + divs)
÷ Initial Equity
= Profit ÷ Cost
HPR isn’t indexed for time. Don’t worry about time & annualizing.
Assumes dividends aren’t reinvested.
Time-Weighted Return
3.14
- global standard for fund performance
- helpful how generic it is
- time-weighted is misleading bc it refers to time periods
- bottom right on formula sheet (don’t forget to subtract 1 at the end)
- can also use NPV on calc (just do 1 share! n might be 1 more than you think)
don’t forget to subtract 1
How is total investment risk measured?
(which risk statistic)
3.18
Standard Deviation
Total Risk = Systematic Risk + Unsystematic Risk
How is systematic risk measured?
(which risk statistic)
3.18
Beta
Can’t be eliminated through diversification.
When to use which risk metric?
- if R² > 0.70, use Beta (the measure of systematic risk, relative to the system/market)
- if R² < 0.70, use Stand. Dev (the measure of total risk, not relative to anything)
- Remember: “When in doubt, stay Sharpe!”
- balanced/completion - standard dev
- for a slice - use beta
Beta is the measure of systematic risk, which refers to the risk inherent to the entire market or a specific market segment. Beta measures a security’s sensitivity to market movements, with a beta of 1 indicating that the security moves in line with the market, while a beta greater than 1 suggests higher volatility relative to the market.
Standard deviation, on the other hand, is a measure of total risk, which includes both systematic risk and unsystematic risk (company-specific risk). It quantifies the overall volatility of an asset’s returns around its mean return.
In summary:
• Beta → Systematic risk (market risk)
• Standard deviation → Total risk (systematic + unsystematic risk)
R² = Coefficient of Determination
What are R and R²?
3.22ª
R = Correlation Coefficient
- corr. between invmt & benchmark
- ranges -1 to 1
R² = Coefficient of Determination
- how well invmt & benchmark are linked
- ranges 0-1 or 0-100%
- higher -> more correlated)
What is the probability of landing within 1, 2, or 3 standard deviations?
3.26
- … 68%
- … 95%
- … 99%
Standard Deviation
3.26
- Main measure of volatility & risk
- Greater σ means greater variance of expected returns
- rep’d by σ (sigma)
x-bar
- mean (aaverage) of a sample
- i.e., the middle of the bell curve
Inflation-Adjusted Return
= (1+r) / (1+i) - 1
r = nominal rate, i = inflation rate
aka real return
Leptokurtic Distribution
3.30
Slender distribution curve
“more peaked”
Platykurtic Distribution
3.30
Broad distribution curve
“less peaked”
eg, small cap stocks
Mesokurtic Distribution
3.30
Normal distribution curve
What is the skewness of the distribution curve of the stock market?
Positively skewed, aka skewed right
The “long tail” is on the side of the skewness, where there are many outliers.
Skewness refers to asymmetry of the distribution curve.
Strong-Form Set of EMT
Nothing will help you beat the market (long-term)
Semi-Strong Set of EMT
of EMT
Only inside information will help you beat the market (long-term)
Weak-Form Set of EMT
Only fundamental analysis (and insider info) will help you beat the market
NOT technical analysis
Efficient Frontier
- x-axis
- y-axis
- name for the curve?
What is meant/indicated by points…
- above the curve
- on the curve
- below the curve
3.38
- x = Standard Deviation
- y = Expected Return
- Curve = Efficient Frontier or Indifference Curve
- above = impossible (everything else is “the feasible set”)
- on = (equally) efficient
- below = inefficient
Random Walk
The movement of stocks is random and lacks any pattern that can be exploited by an investor.
3.34
Sharpe Ratio
- what does it measure?
- when to use?
- comparative or absolute?
- what does higher mean?
3.42
- measures risk-adjusted return
- use when R^2 < 0.70 (or if unsure)
- is comparative (not absolute)
- higher -> higher risk-adj. rate of return
Treynor Ratio
- what does it measure?
- when to use?
- comparative or absolute?
- what does higher mean?
3.46
- measures risk-adjusted return
- use when R^2 > 0.70
- is comparative (not absolute)
- higher -> higher risk-adj. rate of return
SML
- What does it show?
- Slope?
- Intercept?
3.50
Security Market Line in CAPM (Capital Asset Pricing Model)
- Plots the relationship between a security’s (x) beta and (y) expected return.
- Slope: Market(/Equity) Risk Premium
- Intercept: Risk free rate
Stock Premium
in CAPM
3.50
= Market/Equity Risk Premium times Beta
MRP (Market…)
3.50
A component of CAPM formula.
= Market Return – Risk-Free Rate
aka Equity Risk Premium (ERP)
CAPM
3.50
Capital Asset Pricing Model
Quantifies expected return given a risk-free rate, market return, and Beta.
Plots the Security Market Line.
The foundation for all MPT (Modern Portfolio Theory).
Alpha
and what does it look like on CAPM chart?
3.54
= Actual Return – Expected Return (Per CAPM)
Valid when R² ≥ 0.70
Jensen’s Performance Index
3.54
aka Alpha
= Actual Return – Expected Return (Per CAPM)
Is the indifference curve of a risk-averse investor flat or steep?
Risk averse: steep
Risk tolerant: flat
Dividend Discount Model
3.78
V = value
D1 = dividend at start of next year
r = required rate
g = dividend growth rate
Margin Call Price Formula
3.82
i.e.:
= (initial debt ÷ max debt) * Cost
broker fees can be included as part of the “purchase price”
how does using margin to pay broker fees factor into margin limits / calls?
3.82
Simply include broker fees as part of the purchase cost
What are:
- Min federal stock initial margin reqs
- Min federal maintenance margin reqs
Set by the Fed
3.82
- inital: 50%
- miantenance: 25%
Interest rate is indexed to broker call rate
Holding Period Return on Margin
3.84
HPR
= ((Sale Proceeds – Borrowed) – Int – Cost) ÷ Cost
IRR vs NPV
- NPV is superior
- if NPV and IRR suggest 2 different invmts, choose the one with higher positive NPV
- investing at required rate of return is more reasonable than at the IRR
- can be multiple IRRs but there’s only one NPV
NPV
- Calc’d using uneven cash flow keys (CF0, CFj, and Nj to repeat for multiple years)
- If positive or zero, then the invmt is good. If negative, the invmt isn’t good.
- can be used with changing cash flow signs
Dollar-Weighted Return
3.14
- g, CF0, g CFj, etc, f, IRR
- for specific client situation in specific time pd
- accounts for timing & price/amount of cash flows
- equivalent to IRR but applies to an investor’s personal experience rather than an asset’s performance
aka IRR
YTM and YTC are examples of IRR calcs
IRR
- either use NPV to solve for i OR or g, CF0, g CFj, etc, f, IRR
- assumes reinvmt rate is the IRR (this is a weakness)
- “the discount rate that makes NPV of net cash flow zero”
- can produce multiple or misleading results when cash flows change signs multiple times (i.e., from positive to negative and back)
